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e||o.documentElement})}}),b.each({scrollLeft:"pageXOffset",scrollTop:"pageYOffset"},function(e,n){var r=/Y/.test(n);b.fn[e]=function(i){return b.access(this,function(e,i,o){var a=or(e);return o===t?a?n in a?a[n]:a.document.documentElement[i]:e[i]:(a?a.scrollTo(r?b(a).scrollLeft():o,r?o:b(a).scrollTop()):e[i]=o,t)},e,i,arguments.length,null)}});function or(e){return b.isWindow(e)?e:9===e.nodeType?e.defaultView||e.parentWindow:!1}b.each({Height:"height",Width:"width"},function(e,n){b.each({padding:"inner"+e,content:n,"":"outer"+e},function(r,i){b.fn[i]=function(i,o){var a=arguments.length&&(r||"boolean"!=typeof i),s=r||(i===!0||o===!0?"margin":"border");return b.access(this,function(n,r,i){var o;return b.isWindow(n)?n.document.documentElement["client"+e]:9===n.nodeType?(o=n.documentElement,Math.max(n.body["scroll"+e],o["scroll"+e],n.body["offset"+e],o["offset"+e],o["client"+e])):i===t?b.css(n,r,s):b.style(n,r,i,s)},n,a?i:t,a,null)}})}),e.jQuery=e.$=b,"function"==typeof define&&define.amd&&define.amd.jQuery&&define("jquery",[],function(){return b})})(window);
diff --git a/source/javascripts/libs/swfobject-dynamic.js b/source/javascripts/libs/swfobject-dynamic.js
new file mode 100644
index 0000000..b021614
--- /dev/null
+++ b/source/javascripts/libs/swfobject-dynamic.js
@@ -0,0 +1,298 @@
+/*! SWFObject v2.2
+ is released under the MIT License
+*/
+
+var swfobject = function() {
+
+ var UNDEF = "undefined",
+ OBJECT = "object",
+ SHOCKWAVE_FLASH = "Shockwave Flash",
+ SHOCKWAVE_FLASH_AX = "ShockwaveFlash.ShockwaveFlash",
+ FLASH_MIME_TYPE = "application/x-shockwave-flash",
+ EXPRESS_INSTALL_ID = "SWFObjectExprInst",
+
+ win = window,
+ doc = document,
+ nav = navigator,
+
+ plugin = false,
+ regObjArr = [],
+ objIdArr = [],
+ storedAltContent,
+ storedAltContentId,
+ storedCallbackFn,
+ storedCallbackObj,
+ autoHideShow = true,
+
+ /* Centralized function for browser feature detection
+ - User agent string detection is only used when no good alternative is possible
+ - Is executed directly for optimal performance
+ */
+ ua = function() {
+ var w3cdom = typeof doc.getElementById != UNDEF && typeof doc.getElementsByTagName != UNDEF && typeof doc.createElement != UNDEF,
+ u = nav.userAgent.toLowerCase(),
+ p = nav.platform.toLowerCase(),
+ windows = p ? /win/.test(p) : /win/.test(u),
+ mac = p ? /mac/.test(p) : /mac/.test(u),
+ webkit = /webkit/.test(u) ? parseFloat(u.replace(/^.*webkit\/(\d+(\.\d+)?).*$/, "$1")) : false, // returns either the webkit version or false if not webkit
+ ie = !+"\v1", // feature detection based on Andrea Giammarchi's solution: http://webreflection.blogspot.com/2009/01/32-bytes-to-know-if-your-browser-is-ie.html
+ playerVersion = [0,0,0],
+ d = null;
+ if (typeof nav.plugins != UNDEF && typeof nav.plugins[SHOCKWAVE_FLASH] == OBJECT) {
+ d = nav.plugins[SHOCKWAVE_FLASH].description;
+ if (d && !(typeof nav.mimeTypes != UNDEF && nav.mimeTypes[FLASH_MIME_TYPE] && !nav.mimeTypes[FLASH_MIME_TYPE].enabledPlugin)) { // navigator.mimeTypes["application/x-shockwave-flash"].enabledPlugin indicates whether plug-ins are enabled or disabled in Safari 3+
+ plugin = true;
+ ie = false; // cascaded feature detection for Internet Explorer
+ d = d.replace(/^.*\s+(\S+\s+\S+$)/, "$1");
+ playerVersion[0] = parseInt(d.replace(/^(.*)\..*$/, "$1"), 10);
+ playerVersion[1] = parseInt(d.replace(/^.*\.(.*)\s.*$/, "$1"), 10);
+ playerVersion[2] = /[a-zA-Z]/.test(d) ? parseInt(d.replace(/^.*[a-zA-Z]+(.*)$/, "$1"), 10) : 0;
+ }
+ }
+ else if (typeof win.ActiveXObject != UNDEF) {
+ try {
+ var a = new ActiveXObject(SHOCKWAVE_FLASH_AX);
+ if (a) { // a will return null when ActiveX is disabled
+ d = a.GetVariable("$version");
+ if (d) {
+ ie = true; // cascaded feature detection for Internet Explorer
+ d = d.split(" ")[1].split(",");
+ playerVersion = [parseInt(d[0], 10), parseInt(d[1], 10), parseInt(d[2], 10)];
+ }
+ }
+ }
+ catch(e) {}
+ }
+ return { w3:w3cdom, pv:playerVersion, wk:webkit, ie:ie, win:windows, mac:mac };
+ }()
+
+
+ /* Main function
+ - Will preferably execute onDomLoad, otherwise onload (as a fallback)
+ */
+ function main() {
+ if (plugin) { testPlayerVersion(); }
+ else { matchVersions(); }
+ }
+
+ /* Detect the Flash Player version for non-Internet Explorer browsers
+ - Detecting the plug-in version via the object element is more precise than using the plugins collection item's description:
+ a. Both release and build numbers can be detected
+ b. Avoid wrong descriptions by corrupt installers provided by Adobe
+ c. Avoid wrong descriptions by multiple Flash Player entries in the plugin Array, caused by incorrect browser imports
+ - Disadvantage of this method is that it depends on the availability of the DOM, while the plugins collection is immediately available
+ */
+ function testPlayerVersion() {
+ var b = doc.getElementsByTagName("body")[0];
+ var o = createElement(OBJECT);
+ o.setAttribute("type", FLASH_MIME_TYPE);
+ var t = b.appendChild(o);
+ if (t) {
+ var counter = 0;
+ (function(){
+ if (typeof t.GetVariable != UNDEF) {
+ var d = t.GetVariable("$version");
+ if (d) {
+ d = d.split(" ")[1].split(",");
+ ua.pv = [parseInt(d[0], 10), parseInt(d[1], 10), parseInt(d[2], 10)];
+ }
+ }
+ else if (counter < 10) {
+ counter++;
+ setTimeout(arguments.callee, 10);
+ return;
+ }
+ b.removeChild(o);
+ t = null;
+ matchVersions();
+ })();
+ }
+ else {
+ matchVersions();
+ }
+ }
+
+
+ /* Cross-browser dynamic SWF creation
+ */
+ function createSWF(attObj, parObj, id) {
+ var r, el = getElementById(id);
+ if (ua.wk && ua.wk < 312) { return r; }
+ if (el) {
+ if (typeof attObj.id == UNDEF) { // if no 'id' is defined for the object element, it will inherit the 'id' from the alternative content
+ attObj.id = id;
+ }
+ if (ua.ie && ua.win) { // Internet Explorer + the HTML object element + W3C DOM methods do not combine: fall back to outerHTML
+ var att = "";
+ for (var i in attObj) {
+ if (attObj[i] != Object.prototype[i]) { // filter out prototype additions from other potential libraries
+ if (i.toLowerCase() == "data") {
+ parObj.movie = attObj[i];
+ }
+ else if (i.toLowerCase() == "styleclass") { // 'class' is an ECMA4 reserved keyword
+ att += ' class="' + attObj[i] + '"';
+ }
+ else if (i.toLowerCase() != "classid") {
+ att += ' ' + i + '="' + attObj[i] + '"';
+ }
+ }
+ }
+ var par = "";
+ for (var j in parObj) {
+ if (parObj[j] != Object.prototype[j]) { // filter out prototype additions from other potential libraries
+ par += '' + par + ' ';
+ objIdArr[objIdArr.length] = attObj.id; // stored to fix object 'leaks' on unload (dynamic publishing only)
+ r = getElementById(attObj.id);
+ }
+ else { // well-behaving browsers
+ var o = createElement(OBJECT);
+ o.setAttribute("type", FLASH_MIME_TYPE);
+ for (var m in attObj) {
+ if (attObj[m] != Object.prototype[m]) { // filter out prototype additions from other potential libraries
+ if (m.toLowerCase() == "styleclass") { // 'class' is an ECMA4 reserved keyword
+ o.setAttribute("class", attObj[m]);
+ }
+ else if (m.toLowerCase() != "classid") { // filter out IE specific attribute
+ o.setAttribute(m, attObj[m]);
+ }
+ }
+ }
+ for (var n in parObj) {
+ if (parObj[n] != Object.prototype[n] && n.toLowerCase() != "movie") { // filter out prototype additions from other potential libraries and IE specific param element
+ createObjParam(o, n, parObj[n]);
+ }
+ }
+ el.parentNode.replaceChild(o, el);
+ r = o;
+ }
+ }
+ return r;
+ }
+
+ function createObjParam(el, pName, pValue) {
+ var p = createElement("param");
+ p.setAttribute("name", pName);
+ p.setAttribute("value", pValue);
+ el.appendChild(p);
+ }
+
+ /* Cross-browser SWF removal
+ - Especially needed to safely and completely remove a SWF in Internet Explorer
+ */
+ /* Functions to optimize JavaScript compression
+ */
+ function getElementById(id) {
+ var el = null;
+ try {
+ el = doc.getElementById(id);
+ }
+ catch (e) {}
+ return el;
+ }
+
+ function createElement(el) {
+ return doc.createElement(el);
+ }
+
+ /* Flash Player and SWF content version matching
+ */
+ function hasPlayerVersion(rv) {
+ var pv = ua.pv, v = rv.split(".");
+ v[0] = parseInt(v[0], 10);
+ v[1] = parseInt(v[1], 10) || 0; // supports short notation, e.g. "9" instead of "9.0.0"
+ v[2] = parseInt(v[2], 10) || 0;
+ return (pv[0] > v[0] || (pv[0] == v[0] && pv[1] > v[1]) || (pv[0] == v[0] && pv[1] == v[1] && pv[2] >= v[2])) ? true : false;
+ }
+
+
+ /* Filter to avoid XSS attacks
+ */
+ function urlEncodeIfNecessary(s) {
+ var regex = /[\\\"<>\.;]/;
+ var hasBadChars = regex.exec(s) != null;
+ return hasBadChars && typeof encodeURIComponent != UNDEF ? encodeURIComponent(s) : s;
+ }
+
+ return {
+ /* Public API
+ - Reference: http://code.google.com/p/swfobject/wiki/documentation
+ */
+
+ embedSWF: function(swfUrlStr, replaceElemIdStr, widthStr, heightStr, swfVersionStr, flashvarsObj, parObj, attObj, callbackFn) {
+ var callbackObj = {success:false, id:replaceElemIdStr};
+ if (ua.w3 && !(ua.wk && ua.wk < 312) && swfUrlStr && replaceElemIdStr && widthStr && heightStr && swfVersionStr) {
+ widthStr += ""; // auto-convert to string
+ heightStr += "";
+ var att = {};
+ if (attObj && typeof attObj === OBJECT) {
+ for (var i in attObj) { // copy object to avoid the use of references, because web authors often reuse attObj for multiple SWFs
+ att[i] = attObj[i];
+ }
+ }
+ att.data = swfUrlStr;
+ att.width = widthStr;
+ att.height = heightStr;
+ var par = {};
+ if (parObj && typeof parObj === OBJECT) {
+ for (var j in parObj) { // copy object to avoid the use of references, because web authors often reuse parObj for multiple SWFs
+ par[j] = parObj[j];
+ }
+ }
+ if (flashvarsObj && typeof flashvarsObj === OBJECT) {
+ for (var k in flashvarsObj) { // copy object to avoid the use of references, because web authors often reuse flashvarsObj for multiple SWFs
+ if (typeof par.flashvars != UNDEF) {
+ par.flashvars += "&" + k + "=" + flashvarsObj[k];
+ }
+ else {
+ par.flashvars = k + "=" + flashvarsObj[k];
+ }
+ }
+ }
+ if (hasPlayerVersion(swfVersionStr)) { // create SWF
+ var obj = createSWF(att, par, replaceElemIdStr);
+ callbackObj.success = true;
+ callbackObj.ref = obj;
+ }
+ if (callbackFn) { callbackFn(callbackObj); }
+ }
+ else if (callbackFn) { callbackFn(callbackObj); }
+ },
+
+ ua: ua,
+
+ getFlashPlayerVersion: function() {
+ return { major:ua.pv[0], minor:ua.pv[1], release:ua.pv[2] };
+ },
+
+ hasFlashPlayerVersion: hasPlayerVersion,
+
+ createSWF: function(attObj, parObj, replaceElemIdStr) {
+ if (ua.w3) {
+ return createSWF(attObj, parObj, replaceElemIdStr);
+ }
+ else {
+ return undefined;
+ }
+ },
+
+ getQueryParamValue: function(param) {
+ var q = doc.location.search || doc.location.hash;
+ if (q) {
+ if (/\?/.test(q)) { q = q.split("?")[1]; } // strip question mark
+ if (param == null) {
+ return urlEncodeIfNecessary(q);
+ }
+ var pairs = q.split("&");
+ for (var i = 0; i < pairs.length; i++) {
+ if (pairs[i].substring(0, pairs[i].indexOf("=")) == param) {
+ return urlEncodeIfNecessary(pairs[i].substring((pairs[i].indexOf("=") + 1)));
+ }
+ }
+ }
+ return "";
+ }
+ };
+}();
diff --git a/source/javascripts/modernizr-2.0.js b/source/javascripts/modernizr-2.0.js
new file mode 100644
index 0000000..9dca7b0
--- /dev/null
+++ b/source/javascripts/modernizr-2.0.js
@@ -0,0 +1,5 @@
+/* Modernizr 2.6.2 (Custom Build) | MIT & BSD
+ * Build: http://modernizr.com/download/#-video-mq-cssclasses-teststyles-testprop-testallprops-prefixes-domprefixes-load
+ */
+;window.Modernizr=function(a,b,c){function A(a){j.cssText=a}function B(a,b){return A(m.join(a+";")+(b||""))}function C(a,b){return typeof a===b}function D(a,b){return!!~(""+a).indexOf(b)}function E(a,b){for(var d in a){var e=a[d];if(!D(e,"-")&&j[e]!==c)return b=="pfx"?e:!0}return!1}function F(a,b,d){for(var e in a){var f=b[a[e]];if(f!==c)return d===!1?a[e]:C(f,"function")?f.bind(d||b):f}return!1}function G(a,b,c){var d=a.charAt(0).toUpperCase()+a.slice(1),e=(a+" "+o.join(d+" ")+d).split(" ");return C(b,"string")||C(b,"undefined")?E(e,b):(e=(a+" "+p.join(d+" ")+d).split(" "),F(e,b,c))}var d="2.6.2",e={},f=!0,g=b.documentElement,h="modernizr",i=b.createElement(h),j=i.style,k,l={}.toString,m=" -webkit- -moz- -o- -ms- ".split(" "),n="Webkit Moz O ms",o=n.split(" "),p=n.toLowerCase().split(" "),q={},r={},s={},t=[],u=t.slice,v,w=function(a,c,d,e){var f,i,j,k,l=b.createElement("div"),m=b.body,n=m||b.createElement("body");if(parseInt(d,10))while(d--)j=b.createElement("div"),j.id=e?e[d]:h+(d+1),l.appendChild(j);return f=["",'"].join(""),l.id=h,(m?l:n).innerHTML+=f,n.appendChild(l),m||(n.style.background="",n.style.overflow="hidden",k=g.style.overflow,g.style.overflow="hidden",g.appendChild(n)),i=c(l,a),m?l.parentNode.removeChild(l):(n.parentNode.removeChild(n),g.style.overflow=k),!!i},x=function(b){var c=a.matchMedia||a.msMatchMedia;if(c)return c(b).matches;var d;return w("@media "+b+" { #"+h+" { position: absolute; } }",function(b){d=(a.getComputedStyle?getComputedStyle(b,null):b.currentStyle)["position"]=="absolute"}),d},y={}.hasOwnProperty,z;!C(y,"undefined")&&!C(y.call,"undefined")?z=function(a,b){return y.call(a,b)}:z=function(a,b){return b in a&&C(a.constructor.prototype[b],"undefined")},Function.prototype.bind||(Function.prototype.bind=function(b){var c=this;if(typeof c!="function")throw new TypeError;var d=u.call(arguments,1),e=function(){if(this instanceof e){var a=function(){};a.prototype=c.prototype;var f=new a,g=c.apply(f,d.concat(u.call(arguments)));return Object(g)===g?g:f}return c.apply(b,d.concat(u.call(arguments)))};return e}),q.video=function(){var a=b.createElement("video"),c=!1;try{if(c=!!a.canPlayType)c=new Boolean(c),c.ogg=a.canPlayType('video/ogg; codecs="theora"').replace(/^no$/,""),c.h264=a.canPlayType('video/mp4; codecs="avc1.42E01E"').replace(/^no$/,""),c.webm=a.canPlayType('video/webm; codecs="vp8, vorbis"').replace(/^no$/,"")}catch(d){}return c};for(var H in q)z(q,H)&&(v=H.toLowerCase(),e[v]=q[H](),t.push((e[v]?"":"no-")+v));return e.addTest=function(a,b){if(typeof a=="object")for(var d in a)z(a,d)&&e.addTest(d,a[d]);else{a=a.toLowerCase();if(e[a]!==c)return e;b=typeof b=="function"?b():b,typeof f!="undefined"&&f&&(g.className+=" "+(b?"":"no-")+a),e[a]=b}return e},A(""),i=k=null,e._version=d,e._prefixes=m,e._domPrefixes=p,e._cssomPrefixes=o,e.mq=x,e.testProp=function(a){return E([a])},e.testAllProps=G,e.testStyles=w,g.className=g.className.replace(/(^|\s)no-js(\s|$)/,"$1$2")+(f?" js "+t.join(" "):""),e}(this,this.document),function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f')
+ var mobileNav = $('fieldset.mobile-nav').append('');
+ mobileNav.find('select').append('Navigate… ');
+ var addOption = function(i, option) {
+ mobileNav.find('select').append('» ' + $(this).text() + ' ');
+ }
+ mainNav.find('a').each(addOption);
+ $('ul.subscription a').each(addOption);
+ mobileNav.find('select').bind('change', function(event) {
+ if (event.target.value) { window.location.href = event.target.value; }
+ });
+}
+
+function addSidebarToggler() {
+ if(!$('body').hasClass('sidebar-footer')) {
+ $('#content').append('');
+ $('.toggle-sidebar').bind('click', function(e) {
+ e.preventDefault();
+ $('body').toggleClass('collapse-sidebar');
+ });
+ }
+ var sections = $('aside.sidebar > section');
+ if (sections.length > 1) {
+ sections.each(function(index, section){
+ if ((sections.length >= 3) && index % 3 === 0) {
+ $(section).addClass("first");
+ }
+ var count = ((index +1) % 2) ? "odd" : "even";
+ $(section).addClass(count);
+ });
+ }
+ if (sections.length >= 3){ $('aside.sidebar').addClass('thirds'); }
+}
+
+function testFeatures() {
+ var features = ['maskImage'];
+ $(features).map(function(i, feature) {
+ if (Modernizr.testAllProps(feature)) {
+ $('html').addClass(feature);
+ } else {
+ $('html').addClass('no-'+feature);
+ }
+ });
+ if ("placeholder" in document.createElement("input")) {
+ $('html').addClass('placeholder');
+ } else {
+ $('html').addClass('no-placeholder');
+ }
+}
+
+function addCodeLineNumbers() {
+ if (navigator.appName === 'Microsoft Internet Explorer') { return; }
+ $('div.gist-highlight').each(function(code) {
+ var tableStart = '',
+ lineNumbers = '',
+ tableMiddle = ' ',
+ tableEnd = '
',
+ count = $('.line', code).length;
+ for (var i=1;i<=count; i++) {
+ lineNumbers += ''+i+' \n';
+ }
+ var table = tableStart + lineNumbers + tableMiddle + ''+$('pre', code).html()+' ' + tableEnd;
+ $(code).html(table);
+ });
+}
+
+function flashVideoFallback(){
+ var flashplayerlocation = "/assets/jwplayer/player.swf",
+ flashplayerskin = "/assets/jwplayer/glow/glow.xml";
+ $('video').each(function(i, video){
+ video = $(video);
+ if (!Modernizr.video.h264 && swfobject.getFlashPlayerVersion() || window.location.hash.indexOf("flash-test") !== -1){
+ video.children('source[src$=mp4]').first().map(i, function(source){
+ var src = $(source).attr('src'),
+ id = 'video_'+Math.round(1 + Math.random()*(100000)),
+ width = video.attr('width'),
+ height = parseInt(video.attr('height'), 10) + 30;
+ video.after('');
+ swfobject.embedSWF(flashplayerlocation, id, width, height + 30, "9.0.0",
+ { file : src, image : video.attr('poster'), skin : flashplayerskin } ,
+ { movie : src, wmode : "opaque", allowfullscreen : "true" }
+ );
+ });
+ video.remove();
+ }
+ });
+}
+
+function wrapFlashVideos() {
+ $('object').each(function(i, object) {
+ if( $(object).find('param[name=movie]').length ){
+ $(object).wrap('
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+ }
+ });
+ $('iframe[src*=vimeo],iframe[src*=youtube]').wrap('
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+}
+
+$('document').ready(function() {
+ testFeatures();
+ wrapFlashVideos();
+ flashVideoFallback();
+ addCodeLineNumbers();
+ getNav();
+ addSidebarToggler();
+});
+
+// iOS scaling bug fix
+// Rewritten version
+// By @mathias, @cheeaun and @jdalton
+// Source url: https://gist.github.com/901295
+(function(doc) {
+ var addEvent = 'addEventListener',
+ type = 'gesturestart',
+ qsa = 'querySelectorAll',
+ scales = [1, 1],
+ meta = qsa in doc ? doc[qsa]('meta[name=viewport]') : [];
+ function fix() {
+ meta.content = 'width=device-width,minimum-scale=' + scales[0] + ',maximum-scale=' + scales[1];
+ doc.removeEventListener(type, fix, true);
+ }
+ if ((meta = meta[meta.length - 1]) && addEvent in doc) {
+ fix();
+ scales = [0.25, 1.6];
+ doc[addEvent](type, fix, true);
+ }
+}(document));
+
+/*! SWFObject v2.2 modified by Brandon Mathis to contain only what is necessary to dynamically embed flash objects
+ * Uncompressed source in javascripts/libs/swfobject-dynamic.js
+ *
+ released under the MIT License
+*/
+var swfobject=function(){function s(a,b,d){var q,k=n(d);if(g.wk&&g.wk<312)return q;if(k){if(typeof a.id==l)a.id=d;if(g.ie&&g.win){var e="",c;for(c in a)if(a[c]!=Object.prototype[c])c.toLowerCase()=="data"?b.movie=a[c]:c.toLowerCase()=="styleclass"?e+=' class="'+a[c]+'"':c.toLowerCase()!="classid"&&(e+=" "+c+'="'+a[c]+'"');c="";for(var f in b)b[f]!=Object.prototype[f]&&(c+='"+c+
+" ";q=n(a.id)}else{f=i.createElement(o);f.setAttribute("type",m);for(var h in a)a[h]!=Object.prototype[h]&&(h.toLowerCase()=="styleclass"?f.setAttribute("class",a[h]):h.toLowerCase()!="classid"&&f.setAttribute(h,a[h]));for(e in b)b[e]!=Object.prototype[e]&&e.toLowerCase()!="movie"&&(a=f,c=e,h=b[e],d=i.createElement("param"),d.setAttribute("name",c),d.setAttribute("value",h),a.appendChild(d));k.parentNode.replaceChild(f,k);q=f}}return q}function n(a){var b=null;try{b=i.getElementById(a)}catch(d){}return b}
+function t(a){var b=g.pv,a=a.split(".");a[0]=parseInt(a[0],10);a[1]=parseInt(a[1],10)||0;a[2]=parseInt(a[2],10)||0;return b[0]>a[0]||b[0]==a[0]&&b[1]>a[1]||b[0]==a[0]&&b[1]==a[1]&&b[2]>=a[2]?!0:!1}function u(a){return/[\\\"<>\.;]/.exec(a)!=null&&typeof encodeURIComponent!=l?encodeURIComponent(a):a}var l="undefined",o="object",m="application/x-shockwave-flash",v=window,i=document,j=navigator,g=function(){var a=typeof i.getElementById!=l&&typeof i.getElementsByTagName!=l&&typeof i.createElement!=l,
+b=j.userAgent.toLowerCase(),d=j.platform.toLowerCase(),g=d?/win/.test(d):/win/.test(b),d=d?/mac/.test(d):/mac/.test(b),b=/webkit/.test(b)?parseFloat(b.replace(/^.*webkit\/(\d+(\.\d+)?).*$/,"$1")):!1,k=!+"\u000b1",e=[0,0,0],c=null;if(typeof j.plugins!=l&&typeof j.plugins["Shockwave Flash"]==o){if((c=j.plugins["Shockwave Flash"].description)&&!(typeof j.mimeTypes!=l&&j.mimeTypes[m]&&!j.mimeTypes[m].enabledPlugin))k=!1,c=c.replace(/^.*\s+(\S+\s+\S+$)/,"$1"),e[0]=parseInt(c.replace(/^(.*)\..*$/,"$1"),
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+a&&b&&d&&i&&k){d+="";i+="";var p={};if(f&&typeof f===o)for(var m in f)p[m]=f[m];p.data=a;p.width=d;p.height=i;a={};if(c&&typeof c===o)for(var n in c)a[n]=c[n];if(e&&typeof e===o)for(var r in e)typeof a.flashvars!=l?a.flashvars+="&"+r+"="+e[r]:a.flashvars=r+"="+e[r];if(t(k))b=s(p,a,b),j.success=!0,j.ref=b}h&&h(j)},ua:g,getFlashPlayerVersion:function(){return{major:g.pv[0],minor:g.pv[1],release:g.pv[2]}},hasFlashPlayerVersion:t,createSWF:function(a,b,d){if(g.w3)return s(a,b,d)},getQueryParamValue:function(a){var b=
+i.location.search||i.location.hash;if(b){/\?/.test(b)&&(b=b.split("?")[1]);if(a==null)return u(b);for(var b=b.split("&"),d=0;d');
+ (function(){
+ var pinboardLinkroll = document.createElement('script');
+ pinboardLinkroll.type = 'text/javascript';
+ pinboardLinkroll.async = true;
+ pinboardLinkroll.src = url;
+ document.getElementsByTagName('head')[0].appendChild(pinboardLinkroll);
+ })();
+}
+
+function pinboardNS_show_bmarks(r) {
+ var lr = new Pinboard_Linkroll();
+ lr.set_items(r);
+ lr.show_bmarks();
+}
+
+function Pinboard_Linkroll() {
+ var items;
+
+ this.set_items = function(i) {
+ this.items = i;
+ }
+ this.show_bmarks = function() {
+ var lines = [];
+ for (var i = 0; i < this.items.length; i++) {
+ var item = this.items[i];
+ var str = this.format_item(item);
+ lines.push(str);
+ }
+ document.getElementById(linkroll).innerHTML = lines.join("\n");
+ }
+ this.cook = function(v) {
+ return v.replace('<', '<').replace('>', '>>');
+ }
+
+ this.format_item = function(it) {
+ var str = "";
+ if (!it.d) { return; }
+ str += "" + this.cook(it.d) + " ";
+ if (it.n) {
+ str += "" + this.cook(it.n) + " \n";
+ }
+ if (it.t.length > 0) {
+ for (var i = 0; i < it.t.length; i++) {
+ var tag = it.t[i];
+ str += " " + this.cook(tag).replace(/^\s+|\s+$/g, '') + " ";
+ }
+ }
+ str += "
\n";
+ return str;
+ }
+}
+Pinboard_Linkroll.prototype = new Pinboard_Linkroll();
+pinboardNS_fetch_script("https://feeds.pinboard.in/json/v1/u:"+pinboard_user+"/?cb=pinboardNS_show_bmarks\&count="+pinboard_count);
+
diff --git a/source/javascripts/slash.js b/source/javascripts/slash.js
new file mode 100644
index 0000000..5288572
--- /dev/null
+++ b/source/javascripts/slash.js
@@ -0,0 +1,62 @@
+(function($){
+ // Open external links in new window
+ var externalLinks = function(){
+ var host = location.host;
+
+ $('body').on('click', 'a', function(e){
+ var href = this.href,
+ link = href.replace(/https?:\/\/([^\/]+)(.*)/, '$1');
+
+ if (link != '' && link != host && !$(this).hasClass('fancybox')){
+ window.open(href);
+ e.preventDefault();
+ }
+ });
+ };
+
+ // Append caption after pictures
+ var appendCaption = function(){
+ $('.entry-content').each(function(i){
+ var _i = i;
+ $(this).find('img').each(function(){
+ var alt = this.alt;
+
+ if (alt != ''){
+ $(this).after(''+alt+' ');
+ }
+
+ $(this).wrap('∞ "; // because IE date parsing isn't fun.
+ }
+ var say = {
+ just_now: " now",
+ minute_ago: "1m",
+ minutes_ago: "m",
+ hour_ago: "1h",
+ hours_ago: "h",
+ yesterday: "1d",
+ days_ago: "d",
+ last_week: "1w",
+ weeks_ago: "w"
+ };
+
+ var current_date = new Date(),
+ current_date_time = current_date.getTime(),
+ current_date_full = current_date_time + (1 * 60000),
+ date = new Date(time),
+ diff = ((current_date_full - date.getTime()) / 1000),
+ day_diff = Math.floor(diff / 86400);
+
+ if (isNaN(day_diff) || day_diff < 0) { return "∞ "; }
+
+ return day_diff === 0 && (
+ diff < 60 && say.just_now ||
+ diff < 120 && say.minute_ago ||
+ diff < 3600 && Math.floor(diff / 60) + say.minutes_ago ||
+ diff < 7200 && say.hour_ago ||
+ diff < 86400 && Math.floor(diff / 3600) + say.hours_ago) ||
+ day_diff === 1 && say.yesterday ||
+ day_diff < 7 && day_diff + say.days_ago ||
+ day_diff === 7 && say.last_week ||
+ day_diff > 7 && Math.ceil(day_diff / 7) + say.weeks_ago;
+}
+
+function linkifyTweet(text, url) {
+ // Linkify urls, usernames, hashtags
+ text = text.replace(/(https?:\/\/)([\w\-:;?&=+.%#\/]+)/gi, '$2 ')
+ .replace(/(^|\W)@(\w+)/g, '$1@$2 ')
+ .replace(/(^|\W)#(\w+)/g, '$1#$2 ');
+
+ // Use twitter's api to replace t.co shortened urls with expanded ones.
+ for (var u in url) {
+ if(url[u].expanded_url != null){
+ var shortUrl = new RegExp(url[u].url, 'g');
+ text = text.replace(shortUrl, url[u].expanded_url);
+ var shortUrl = new RegExp(">"+(url[u].url.replace(/https?:\/\//, '')), 'g');
+ text = text.replace(shortUrl, ">"+url[u].display_url);
+ }
+ }
+ return text
+}
+
+function showTwitterFeed(tweets, twitter_user) {
+ var timeline = document.getElementById('tweets'),
+ content = '';
+
+ for (var t in tweets) {
+ content += ''+''+''+prettyDate(tweets[t].created_at)+' '+linkifyTweet(tweets[t].text.replace(/\n/g, '
'+' ';
+ }
+ timeline.innerHTML = content;
+}
+
+function getTwitterFeed(user, count, replies) {
+ count = parseInt(count, 10);
+ $.ajax({
+ url: "https://api.twitter.com/1/statuses/user_timeline/" + user + ".json?trim_user=true&count=" + (count + 20) + "&include_entities=1&exclude_replies=" + (replies ? "0" : "1") + "&callback=?"
+ , type: 'jsonp'
+ , error: function (err) { $('#tweets li.loading').addClass('error').text("Twitter's busted"); }
+ , success: function(data) { showTwitterFeed(data.slice(0, count), user); }
+ })
+}
diff --git a/source/projects/deep-learn.markdown b/source/projects/deep-learn.markdown
new file mode 100644
index 0000000..6259f09
--- /dev/null
+++ b/source/projects/deep-learn.markdown
@@ -0,0 +1,381 @@
+---
+layout: page
+title: "Deep Learning for Image Classification"
+date: December 15, 2014 22:20:12 -0700
+comments: false
+sharing: true
+footer: true
+---
+
+
+Finding good features is an important yet challenging task in most machine learning applications. For computer vision tasks, deep learning techniques, based on multi-layer neural networks, are effective in extracting good learning representations from image data. Although powerful, deep neural networks are prone to overfitting. In this project, I studied different regularization techniques that mitigate overfitting. Precisely, I present the basic model of feed-forward neural networks. Next, I will present the procedures for fitting the network to the training data. In particular, the backpropagation algorithm, which is used to compute the network weights, is derived for the case of multi-label classification. Next, we will show how different optimization procedures can be built on top of the backpropagation algorithm to minimize the training error. In addition, a prototype neural network library is implemented in the [Julia programming language](http://julialang.org/) and applied to image classification of hand-written digits with the [MNIST datasets](http://yann.lecun.com/exdb/mnist/). Note that classifying hand-written digits can be a difficult task for a machine. As shown below, it can be challenging to distinguish between a digit to another.
+
+{% img ../images/neural/errors.png %}
+
+## Deep Neural Networks
+
+Neural networks are biologically inspired machine learning models that offer lots of flexibility in modeling a target function. It is composed of multiple layers of neurons and was shown to be a universal approximation[1]. It can be used for both regression and classification problems. Although flexible, neural network can easily overfit. Therefore, regularization techniques are needed to train neural networks. The focus of the project is to investigate different regularization techniques.
+
+
+### Feed-forward Neural Network Model
+
+
+Let’s start by describing the architecture of the neural network. As illustrated in the following figure, it consists of \\(L\\) layers of connected neurons or units. The layers are index as \\(l = 1, . . . ,L\\), in which the first \\(L − 1\\) layers are hidden and the last layer \\(l = L\\) is the output layer.
+
+{% img ../images/neural/net.png %}
+
+The input data \\(x = [1, x_1, . . . ,x_p]\\), which has p raw features, enters the network from the leftmost units. It then flows through the network towards the output nodes on the right. Each layer \\(l\\) has \\(d^{(l)}\\) neurons and a bias node. The bias node outputs a constant value 1, which corresponds to an intercept term. On the other hand, a neuron transforms the input, also called activation, to an output using a nonlinear operation \\(\theta\\). The resulting output is called the activity of the neuron.
+
+Except for the bias node, all nodes between two consecutive layers are connected by arrows. In particular, the arrow between node \\(i\\) of layer \\(l\\) and node \\(j\\) of the next layer multiplies the activity \\(x^{(l)}_i\\) of layer \\(l\\) by the weight \\(w(l)_{ij}\\) and passes the result to node \\(j\\). All activities of layer \\(l\\) that goes into node \\(j\\) is combined to obtain the activation \\(s^{(l)}_j\\) as follows:
+
+$$
+s_{j}^{\left(l\right)}=\sum_{i=0}^{d^{\left(l\right)}}w_{ij}x_{i}^{\left(l\right)},\ \forall j=1,\ldots,d^{\left(l\right)}
+$$
+
+This later is then transformed to an activation that is passed to all nodes of the next layer:
+
+$$
+x_{j}^{\left(l+1\right)}=\theta\left(s_{j}^{\left(l\right)}\right),\ \forall j=1,\ldots,d^{\left(l\right)}
+$$
+
+By concatenating all activation inputs and outputs (including the bias nodes’), the above operations can be concisely described in vector notations:
+
+$$
+\begin{align}
+\mathbf{s}^{\left(l\right)} & =\left(\mathbf{W}^{\left(l\right)}\right)^{\top}\mathbf{x}^{\left(l\right)},\ \forall l=1,\ldots,L\label{eq:s_to_x}\\
+\mathbf{x}^{\left(l+1\right)} & =\left[\begin{array}{c}
+1\\
+\theta\left(\mathbf{s}^{\left(l\right)}\right)
+\end{array}\right],\qquad\forall l=1,\ldots,L\label{eq:x_to_s}
+\end{align}
+$$
+
+For classification tasks, the dimension \\(d^{(L)}\\) of the network output vector \\(x^{(L+1)}\\) is equal to the number of class labels \\(C\\). In fact, \\(x^{(L+1)}\\) models the posterior probabilities that a sample belongs to each class given the feature data \\(x^{(1)}\\). To enforce that the outputs sum to one, we use the softmax activation function:
+
+$$
+\begin{equation}
+\mathbf{x}_{j}^{\left(L+1\right)}=\frac{\exp\left(s_{j}^{\left(L\right)}\right)}{\sum_{m=1}^{C}\exp\left(s_{m}^{\left(L\right)}\right)},\ \forall j=1,\ldots,C
+\end{equation}
+$$
+
+For the hidden layers, we instead use the hyperbolic tangent function:
+
+$$
+\mathbf{x}_{j}^{\left(l+1\right)}=\tanh\left(s_{j}^{\left(l\right)}\right),\ \forall j=2,\ldots,d^{\left(l\right)}+1
+$$
+
+Unlike x(L+1), the output vectors x(l) of the hidden layers all include a bias \\(x^{(l)}_1 = 1\\). Thus, \\(x^{(l)}\\) has \\(d^{(l)} + 1\\) elements for all \\(l = 1, . . . ,L\\). These moving parts of a neural network are summarized in the Table 1 and the chain of transformations from input to output is illustrated below:
+
+In summary, a neural network is characterized by:
+
+- the total number of layers
+- the input and output dimensions
+- the number of units at each __hidden layer__ (i.e. layer between input and output)
+- an activation function at each neuron or node
+- a set of weights matrices that relate the input and output between layers.
+
+In Julia, we can define a neural network by the following data type:
+
+```julia
+##----------------------------------------------------------------------
+## Neural Network structure
+type NeuralNet
+ numLayers::Int # Number of layers (excluding input)
+ numInputs::Int # Input dimension (no bias node)
+ numOutputs::Int # Output dimension
+ numHidden::Array{Int} # Number of units at each hidden layer
+ activFunc::String # Activation function of hidden units
+ weights # Weight matrices
+end
+```
+
+#### Predicting the class of test samples
+
+{% img ../images/neural/forward.png %}
+
+Given these parameters, the relationship between the inputs and the outputs of the network is determined by a process called __*forward propagation*__. When predicting the class label of a new test sample \\(\mathbf{x} \\) the corresponding outputs \\(h_k(\mathbf{x}) = x^{(L+1)}_k\\) \\(k = 1, . . . C\\) are calculated using the chain of transformations previously described. Implementing the prediction is very simple. All we need to do is to run the forward propagation algorithm with the new sample `xnew`:
+
+
+```julia
+##----------------------------------------------------------------------
+## predict: predict the labels of new samples using forward propagation
+## Inputs:
+## - Neural network structure
+## - New samples of size N x p
+## Output: a vector of pairs containing:
+## - Maximum posterior probability of predicted class
+## - Label of predicted class ∈ {1,...,C}
+##----------------------------------------------------------------------
+function predict(net::NeuralNet, xnew)
+ x,s = forwardPropagate(net, xnew)
+ prob, class = findmax(x[end])
+end
+```
+
+The implementation of forward propagation follows directly from the above equations as follows:
+
+```julia
+##----------------------------------------------------------------------
+## Forward propagation subroutine
+## Inputs:
+## - Training example: xn
+## - Neural network structure: number of layers, number of units
+## Outputs:
+## - L+1 output vectors x[l] (including input vector x[1] = xn)
+## - L input vectors s[l]
+##----------------------------------------------------------------------
+function forwardPropagate(nn::NeuralNet, xn::Array{Float64})
+ # println("Forward propagation..")
+ # Network topology
+ L = nn.numLayers # number of all layers excluding input
+ C = nn.numOutputs
+
+ # Cells containg L input vectors and L+1 output vectors
+ s = cell(L,1) # inputs of all layers
+ x = cell(L+1,1) # outputs of all layers
+
+ # Compute input s[l] and output x[l+1] at each layer
+ # Input vector x[1] has no bias node
+ x[1] = xn
+ # Hidden layers
+ for l in 1:L-1
+ W = (nn.weights[l])
+ s[l] = W'*x[l]
+ x[l+1] = [1, map(tanh, s[l])] # use tanh
+ end
+ # Output layer
+ s[L] = (nn.weights[L])' * x[L]
+ x[L+1] = if C == 1
+ logit(s[L])
+ else
+ softmax(s[L])
+ end
+
+ # return output and input vectors
+ x, s
+end
+```
+
+
+## Model fitting using backpropagation
+
+Previously, we assumed that the neural network model is already trained, i.e. the set of weight matrices are pre-configured. But how do we set these weight matrices \\(W^{(l)}, l=1,...,L\\)? In the following, we answer that question using another procedure called _**backpropagation**_ in conjunction with forward propagation. A related question is how big and how deep should the network be. Since, it is computationally prohibitive to find the optimal size and depth of the network, a good choice is conventionally found by trial-and-error. However, we will later present an efficient technique called _**dropout**_ to generate and average the predictions of many network configurations. In this section, we will focus on finding the optimal weight parameter \(w given a configuration and training data.
+
+The next thing we need is an error measure for the multi-label classification task. Assuming the class conditional distribution of the training data is multinomial, we employ the negative likelihood as the error function:
+
+$$
+E\left(\mathbf{w}\right)=-\sum_{n=1}^{N}e_{n}\left(h\left(\mathbf{x}_{n};\mathbf{w}\right),\mathbf{y}_{n}\right)=\sum_{n=1}^{N}\sum_{k=1}^{C}y_{nk}\ln\left(h_{k}\left(\mathbf{x}_{n};\mathbf{w}\right)\right)\label{eq:cross-entropy-error}
+$$
+
+where \\(x_n\\) is a feature input vector and \\(y_n\\) is a \\(C\\) by \\(1\\) vector that encodes the class label using _one-of-C rule_. The function \\(h\\) is parameterized by the weights \\(w\\). In (4), we can identify \\(E\\) as a cross-entropy error function that measures the “distance” between the estimated MAP (_Maximum-a-Posteriori_) probabilities \\(h(x_n;w)\\) and the true label vector \\(y_n\\).
+
+The error surface \\(E\\) is not convex w.r.t. the weights \\(w\\). Nonetheless, its derivatives are still useful for finding directions towards a good local optimum. In fact, finding the global optimum is not only computationally prohibitive here, but also it can be harmful. We will discuss more about this issue later and emphasize the importance to stopping our search early to avoid overfitting. In any case, we always need a way to cheaply compute all partial derivatives. Fortunately, there is a clever algorithm, called the _**backpropagation**_ [3] that does it with \\(O(M)\\) runtime complexity. Here, \\(M\\) is the total number of weights in the network.
+
+The implementation of the model training or fitting function is shown below:
+
+```julia
+##----------------------------------------------------------------------
+## Fit: train the neural network model
+## Inputs:
+## - Neural network structure
+## - Matrix of features X with dimension N x p
+## - Class label vector of dimension N x 1 (yn ∈ {1,...,C})
+## - fitting options
+## - maximum number of optimization iterations
+##----------------------------------------------------------------------
+function fit!(nn::NeuralNet, X, y, options::FitOptions, maxIter::Int)
+
+ # assume trainData if preprocessed to make learning faster
+ # e.g. successive examples come from different classes
+ L = nn.numLayers
+ C = nn.numOutputs
+ N = size(X,1)
+ d = [nn.numInputs, reshape(nn.numHidden, length(nn.numHidden),1), nn.numOutputs]
+
+ # Initialize weights
+ initWeights!(nn, X)
+
+ # Iteration of whole batch training
+ for i = 1:maxIter
+ if i % 10 == 0 tic; println("Pass data Iteration: $i") end
+ for n = 1:N
+ if n % 50 == 0 println("Samples: $n") end
+ # Local variables within scope of each iteration
+ xn, yn = X[n,:]', y[n]
+
+ # Compute output vectors x(l), l = 1,...,L+1
+ x, s = forwardPropagate(nn, xn)
+
+ # Compute sensitivity matrices Δ[l], l = 1,...,L
+ local Δ = backPropagate(nn, x)
+
+ # Update the weights
+ updateWeights!(nn, Δ, x, yn)
+ end
+ if i % 10 == 0 toc end
+ end
+
+ # return in-sample error (optionally)
+end
+```
+
+Basically, the training is performed after multiple iterations of both the forward and backward propagations. Through these rounds, the neural network is trained to model the right relationship between the input and the output. The backward propagation computes the sensisitivy matrices \\(\Delta\\) as follows:
+
+```julia
+##----------------------------------------------------------------------
+## Backpropagation subroutine
+## Inputs:
+## - L+1 output vectors x[l] (including input vector x[1] = xn)
+## - L input vectors s[l]
+## Outputs:
+## - Sensitivity matrices Δ[l] for all layer l = 1,...,L
+##----------------------------------------------------------------------
+function backPropagate(nn::NeuralNet, x)
+ # println("Back propagation..")
+ # Network topology
+ L = nn.numLayers # number of all layers excluding input
+ C = nn.numOutputs
+ d = [nn.numInputs, reshape(nn.numHidden, length(nn.numHidden),1), nn.numOutputs]
+ Δ = cell(L,1)
+
+ # Output vector
+ h = x[L+1]
+
+ # Sensitivity matrix for output layer
+ Δ[L] = [ h[i]*(δ(i,j) - h[j]) for i in 1:C, j in 1:C ]
+
+ # Sensitivity matrix for inner layers
+ for l = L-1:-1:1
+ Δ[l] = zeros(Float64, C, d[l+1])
+ W = nn.weights[l+1]
+ for k in 1:C
+ for j in 1:d[l+1]
+ # assuming tanh activation function at hidden units
+ Δ[l][k,j] = (1 - h[k]^2) * (W[j,:] * Δ[l+1][k,:]')[1]
+ end
+ end
+ end
+
+ # return sensitivity matrices for all layers ∀l = L,...,1
+ Δ
+end
+```
+
+## Optimizing the network weights
+
+After the sensitivity matrices are calculated by the weight matrices, the weight matrices are optimized. There are two general strategies for doing this:
+
+1. Batch gradient descent update the weights using the gradient of the error contributed by all training examples. This is done after a single pass through all the examples.
+2. Stochastic gradient descent (SGD) is a more efficient method as it immediately updates the weights after seeing each training example[4]. Another advantage of the stochastic approach is that it takes advantage of randomization to escape poor local optimum. The overall SGD algorithm is presented in Table 2.
+
+{% img right ../images/neural/table2.png %}
+
+Different acceleration techniques have also been proposed to speed up the training procedure of neural networks. These include Nesterov’s method, conjugate gradient descent (which only works for batch mode) as well as Newton-type methods. Due to the computational hurdles with training large neural networks, first-order methods such as SGD are more practical. The implementation of simple SGD method is displayed below:
+
+
+```julia
+##----------------------------------------------------------------------
+## updateWeights: update and return the weight matrices at each iteration
+## Inputs:
+## - Neural network structure
+## - Sensitivity matrices Δ[l], ∀l ∈ {1,..,L}
+## - Output vectors x[l], ∀l ∈ {1,..,L+1}
+## - Class label of example: yn
+## Output:
+## - weights matrices
+##----------------------------------------------------------------------
+function updateWeights!(nn::NeuralNet, Δ, x, yn)
+
+ L = nn.numLayers
+ C = nn.numOutputs
+ d = [nn.numInputs, reshape(nn.numHidden, length(nn.numHidden),1), nn.numOutputs]
+
+ # Softmax output
+ h = x[L+1]
+
+ # Step size
+ μ = 0.1
+
+ # yn is encoded as one-of-C vector
+ yv = mask(ones(C), yn)
+
+ # Gradient of error w.r.t softmax output vector
+ ∇e_h = - vec(yv ./ h)
+
+ # Gradient of error w.r.t weight matrix W[L]
+ # assuming softmax output activation and cross-entropy error
+ ∇e_WL = zeros(Float64, d[L]+1,C)
+ for i in 1:d[L]+1
+ for j in 1:C
+ ∇e_WL[i,j] = x[L][i] * (h[j] - yv[j])
+ end
+ end
+ # SGD update of weight matrix W[L]
+ nn.weights[L] = nn.weights[L] - μ * ∇e_WL
+
+ # Gradient of error w.r.t weight matrix @ input W[1]
+ # Input has no bias node: W1 is d[1] x d[2] matrix
+ ∇e_W1 = zeros(Float64, d[1],d[2])
+ for i in 1:d[1]
+ for j in 1:C
+ ∇e_W1[i,j] = x[1][i] * dot(∇e_h, vec(Δ[1][:,j]))
+ end
+ end
+
+ # SGD update of weight matrix W[1]
+ nn.weights[1] = nn.weights[1] - μ * ∇e_W1
+
+ # Gradient of error w.r.t weight matrices of hidden layers
+ for l = 2:L-1
+ # Gradient of error w.r.t weight matrix Wl
+ # x[l] has bias node: Wl is (d[l]+1) x d[l+1] matrix
+ ∇e_Wl = zeros(Float64, d[l]+1, d[l+1])
+ for i in 1:d[l]+1
+ for j in 1:d[l+1]
+ ∇e_Wl[i,j] = x[l][i] * dot(∇e_h, vec(Δ[l][:,j]))
+ end
+ end
+
+ # SGD update the weight matrices
+ nn.weights[l] = nn.weights[l] - μ * ∇e_Wl
+ end
+ nn.weights
+end
+```
+
+What is most attractive about deep learning models is that they learn the feature automatically. In constrast, classic supervised model such as logistic regression or classification trees require the user to select the features. In neural networks, the features are represented by the states of the neurons in the hidden layers. For the digit classification application, the figure below shows such learned features.
+
+{% img right ../images/neural/featuresminst.png %}
+
+
+## Regularization techniques
+Neural networks offer a considerable flexibility to the extent that they can approximate any function with abritrary complexity. However, they can also easily overfit the data and fail to generalize to give accurate predictions when presented with new data samples. To prevent this, we can use three types of regularization methods: weight decay, early stopping and dropout.
+
+#### Weight decay
+Weight decay is a classic regularization technique [5] that is used in different problems, including linear ridge regression. The basic idea is to penalize models that are too complex by adding a quadratic penalty terms to the error loss function and the weight update becomes:
+Precisely, it seeks to shrink the weights towards zero.
+
+#### Early stopping
+The second regularization method avoids overfitting using a validation set approach. Precisely, we monitor the prediction error of the validation set at each iteration of the weight optimization. Although the optimization seeks to minimize the training error, we stop as early as the validation error increases with the iterations. This is a good indication that the model starts to overfit.
+
+#### Dropout
+Dropout is another regularization technique that was recently proposed in [6]. The key idea is to randomly drop the units during training with a probability p. When a unit is dropped, all its incoming and outgoing connections are also temporarily removed. For each training point, we sample the network by droping units randomly to produce a “thinned” network. This is usually done within a mini-batch and the weight of each arrow becomes average over the points in the mini-batch. If for one point, the unit connecting the arrow was dropped, its weight counts as zero. At test time, the entire network is used but the weights are scaled by the probability p.
+
+{% img right ../images/neural/dropout.png %}
+
+Simulation results show that the use of dropout to regularize the network help against overfitting. The out-of-sample classification can be reduced to 1% with dropout on the MNISTN dataset as shown in the figure below.
+
+{% img left ../images/neural/result.png %}
+
+
+## References
+
+1. R Ramamonjison. Training deep neural networks for multi-label classification, UBC Tech. Report, 2014.
+1. K Murphy. Machine Learning: A Probabilistic Perspective. The MIT Press, 2012.
+2. C Bishop. Neural Networks for Pattern Recognition. Oxford University Press, Inc., New York, NY, USA, 1995.
+3. D Rumelhart, G E Hinton, and R J Williams. Learning representations by back-propagating errors. Nature, 323(6088):533–536, 1986.
+4. L Bottou. Stochastic gradient learning in neural networks. In In Proceedings of Neuro-Nimes. EC2, 1991.
+5. A Tikhonov. Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl., 4:1035–1038, 1963.
+6. N Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research, 15:1929–1958, 2014.
+7. M Schmidt, N Le Roux, and F Bach. Minimizing finite sums with the stochastic average gradient. CoRR, abs/1309.2388, 2013.
+
diff --git a/source/projects/index.markdown b/source/projects/index.markdown
new file mode 100644
index 0000000..f297fb1
--- /dev/null
+++ b/source/projects/index.markdown
@@ -0,0 +1,45 @@
+---
+layout: page
+title: "projects"
+date: 2015-07-15 13:36
+comments: true
+sharing: true
+footer: true
+---
+
+Below is a list of the projects I have been working on recently.
+
+### Anomaly detection (Mitacs research internship)
+
+Anomaly detection is an important analytics problem for business applications. It helps an organization in detecting operation bottlenecks and in reducing risks. However, when the number of metrics to monitor are large, it is crucial to develop efficient machine learning algorithms that are optimized for parallel processing. In this research project, I have been investigating parallel algorithms to enable fast and scalable predictive analytics.
+
+I developed new techniques for detecting data points in time series data that deviate from a normal behavior. In particular, I designed and implemented algorithms using time series decomposition, smoothing methods and robust statistics. The algorithms were prototyped in Matlab and implemented in Haskell. The benefits of these algorithms are that they are computationally efficient and can work on time series data that may exhibit seasonality and trend. In addition, they lead naturally to parallelization. Thus, they can be used for monitoring discrepancies in most time-series data. This project was generously supported by D&B Cloud Innovation center and by the [Mitacs Accelerate](https://www.mitacs.ca/en/programs/accelerate) program.
+
+
+### Apache Spark projects
+
+[Apache Spark](http://spark.apache.org/) is a cluster computing framework originally developed in the AMPLab at UC Berkeley. In contrast to Hadoop's MapReduce paradigm, Spark's in-memory processing provides performance up to 100 times faster for certain applications. By allowing user programs to load data into a cluster's memory and query it repeatedly, Spark is well-suited to various data applications such as machine learning, graph processing and real-time data analysis.
+
+As the most active open-source project in Big Data, Spark has a large and diverse community. I have been involved with Spark since it was in incubation stage. The following list is a sample of my projects and contributions to this exciting project:
+
+- I created and co-organize the local [**Vancouver Spark Meetups**](http://www.meetup.com/Vancouver-Spark/), which now has over 300 members.
+- I also wrote a book on **Spark Graph Processing**. While waiting for its release, you can access a [**chapter preview here**](http://giocode.github.io/projects/spark-graph.html).
+- **CPSC 546 - Optimization course project:** "_Distributed algorithms for training recommendation systems_"
+- Some Spark tutorials that I taught include:
+ - [IEEE Summer School on Signal Processing and Machine Learning for Big Data](https://sites.google.com/site/s3pbigdata2014/lecturers)
+ - [Workshop on Distributed Machine Learning and Computing with Spark](http://www.meetup.com/Vancouver-Spark/events/178126142/) at SAP.
+
+
+### Deep learning for image classification (CPSC 540)
+
+Deep learning and neural networks is a exciting subject not only for researchers but also for A.I. community in general. Google's acquisition of [DeepMind](http://deepmind.com/) is only one of the interesting developments in this field. Traditional approaches to machine learning have been based on having engineers build or select the right features for a learning problem. After extracting the features, the learning model needs to be trained with a large amount of labeled datasets. Feature extraction is a hard topic especially for machine vision problem such as image classification. In contrast, neural networks can learn the features during the training - by themselves. However, care must be taken not overfit the model! In fact, neural networks are known to easily overfit since they can virtually approximate any function.
+
+In my [machine learning course](http://www.cs.ubc.ca/~schmidtm/Courses/540-W16/) project, I investigated regularizations methods to prevent overfitting when training neural networks. Following this project, I wrote a [**compact and accessible tutorial**](http://giocode.github.io/projects/deep-learn.html) on this subject. It includes just the important math and contains illustrative code written in Julia language to explain the main concepts.
+
+
+### Mobile app development
+
+In my free time, I had the chance to learn and build mobile applications on both iOS and Android platform. In particular, I have published the [Hashter mobile app](https://play.google.com/store/apps/details?id=com.highhay.hashtag.free) for creating gorgeous social media posters.
+
+
+
diff --git a/source/projects/spark-graph.markdown b/source/projects/spark-graph.markdown
new file mode 100644
index 0000000..cedc77e
--- /dev/null
+++ b/source/projects/spark-graph.markdown
@@ -0,0 +1,753 @@
+---
+layout: page
+title: "Sabermetrics with Apache Spark"
+date: May 24, 2015
+comments: true
+sharing: true
+footer: true
+---
+
+
+It is no secret analytics have made a big impact in sports. The quest for an objective understanding of the game has even a name: "sabermetrics". Analytics have proven invaluable in many aspects: from [building dream teams under tight cap constraints](http://www.sfgate.com/warriors/article/Golden-State-Warriors-at-the-forefront-of-NBA-5753776.php), to [selecting game-specific strategies](https://en.wikipedia.org/wiki/Moneyball) to actively [engaging with fans](http://www.nhl.com/ice/news.htm?id=754184) and so on. No matter what the goal is, gaining useful insights requires a quick ability to process big data and handle its complexities. In the following, we analyze NCAA Men's college basketball game stats gathered during one season. As sports-data experts, we are going to leverage Spark's graph processing library to answer several questions for retrospection.
+
+[__Apache Spark__](http://spark.apache.org/) is a fast and general-purpose technology, which greatly simplify the parallel processing of large data that is distributed over a computing cluster. While Spark handles different types of processing, here we will focus on its graph processing capability. In particular, our goal is to expose the powerful yet generic graph-aggregation operator of Spark:`aggregateMessages`. We can think of this operator as a version of MapReduce for aggregating the neighborhood information in graphs.
+
+In fact, many graph processing algorithms such as PageRank rely on iteratively accessing the properties of neighbouring vertices and adjacent edges. By applying `aggregateMessages` on the NCAA College Basketball datasets, we will:
+
+- identify the basic mechanisms and undersand the patterns for using `aggregateMessages`
+- apply `aggregateMessages` to create custom graph aggregation operations
+- optimize the performance and efficiency of `aggregateMessages`
+
+## NCAA College Basketball datasets
+
+As an illustrative example, the [NCAA College Basketball](http://www.ncaa.com/sports/basketball-men) datasets consist of two CSV datasets. This first one `teams.csv` contains the list of all college teams that played in NCAA Division I competition. Each team is associated with a 4 digit id number. The second dataset `stats.csv` contains the score and statistics of every game played during the 2014-2015 regular season.
+
+### Loading team data into RDDs
+
+To start, we parse and load these datasets into RDDs (__Resilient Distributed Datasets__), which are the core Spark abstraction for any data that is distributed and stored over a cluster. First, we create a class `GameStats` that records a team's statistics during a game.
+
+```scala
+case class GameStats(
+ val score: Int,
+ val fieldGoalMade: Int,
+ val fieldGoalAttempt: Int,
+ val threePointerMade: Int,
+ val threePointerAttempt: Int,
+ val threeThrowsMade: Int,
+ val threeThrowsAttempt: Int,
+ val offensiveRebound: Int,
+ val defensiveRebound: Int,
+ val assist: Int,
+ val turnOver: Int,
+ val steal: Int,
+ val block: Int,
+ val personalFoul: Int
+)
+```
+
+### Loading game stats into RDDs
+
+We also add the following methods to `GameStats` in order to know how efficient a team's offense was:
+
+```scala
+// Field Goal percentage
+def fgPercent: Double = 100.0 * fieldGoalMade / fieldGoalAttempt
+
+// Three Point percentage
+def tpPercent: Double = 100.0 * threePointerMade / threePointerAttempt
+
+// Free throws percentage
+def ftPercent: Double = 100.0 * threeThrowsMade / threeThrowsAttempt
+override def toString: String = "Score: " + score
+```
+
+Next, we create a couple of classes for the games' result.
+
+```scala
+abstract class GameResult(
+ val season: Int,
+ val day: Int,
+ val loc: String
+)
+
+
+case class FullResult(
+ override val season: Int,
+ override val day: Int,
+ override val loc: String,
+ val winnerStats: GameStats,
+ val loserStats: GameStats
+) extends GameResult(season, day, loc)
+```
+
+`FullResult` has the year and day of the season, the location where the game was played and the game statistics of both the winning and losing teams.
+
+Next, we will create a statistics graph of the regular seasons. In this graph, the nodes are the teams whereas each edge corresponds to a specific game. To create the graph, let us parse the CSV file `teams.csv` into the RDD `teams` :
+
+```scala
+val teams: RDD[(VertexId, String)] =
+ sc.textFile("./data/teams.csv").
+ filter(! _.startsWith("#")).
+ map {line =>
+ val row = line split ','
+ (row(0).toInt, row(1))
+ }
+```
+
+We can check the first few teams in this new RDD:
+
+```scala
+scala> teams.take(3).foreach{println}
+(1101,Abilene Chr)
+(1102,Air Force)
+(1103,Akron)
+```
+
+We do the same thing to obtain an RDD of the game results, which will have a type `RDD[Edge[FullResult]]`. We just parse `stats.csv` and record the fields that we need: (1) the ID of the winning team, (2) the ID of the losing team, and (3) the game statistics of both teams:
+
+```scala
+val detailedStats: RDD[Edge[FullResult]] =
+ sc.textFile("./data/stats.csv").
+ filter(! _.startsWith("#")).
+ map {line =>
+ val row = line split ','
+ Edge(row(2).toInt, row(4).toInt,
+ FullResult(
+ row(0).toInt, row(1).toInt,
+ row(6),
+ GameStats(
+ score = row(3).toInt,
+ fieldGoalMade = row(8).toInt,
+ fieldGoalAttempt = row(9).toInt,
+ threePointerMade = row(10).toInt,
+ threePointerAttempt = row(11).toInt,
+ threeThrowsMade = row(12).toInt,
+ threeThrowsAttempt = row(13).toInt,
+ offensiveRebound = row(14).toInt,
+ defensiveRebound = row(15).toInt,
+ assist = row(16).toInt,
+ turnOver = row(17).toInt,
+ steal = row(18).toInt,
+ block = row(19).toInt,
+ personalFoul = row(20).toInt
+ ),
+ GameStats(
+ score = row(5).toInt,
+ fieldGoalMade = row(21).toInt,
+ fieldGoalAttempt = row(22).toInt,
+ threePointerMade = row(23).toInt,
+ threePointerAttempt = row(24).toInt,
+ threeThrowsMade = row(25).toInt,
+ threeThrowsAttempt = row(26).toInt,
+ offensiveRebound = row(27).toInt,
+ defensiveRebound = row(28).toInt,
+ assist = row(20).toInt,
+ turnOver = row(30).toInt,
+ steal = row(31).toInt,
+ block = row(32).toInt,
+ personalFoul = row(33).toInt
+ )
+ )
+ )
+ }
+```
+
+We could avoid typing all that by using the nice [spark-csv package](http://spark-packages.org/package/databricks/spark-csv) that reads CSV files into `SchemaRDD`. Let's check what we got:
+
+```scala
+scala> detailedStats.take(3).foreach(println)
+Edge(1165,1384,FullResult(2006,8,N,Score: 75-54))
+Edge(1393,1126,FullResult(2006,8,H,Score: 68-37))
+Edge(1107,1324,FullResult(2006,9,N,Score: 90-73))
+```
+
+We then create our score graph using the collection of teams (of type `RDD[(VertexId, String)]`) as vertices and the collection `detailedStats` (of type `RDD[(VertexId, String)]`) as edges:
+
+```scala
+scala> val scoreGraph = Graph(teams, detailedStats)
+```
+
+For curiosity, let's see which team has won against the 2015 NCAA national champ Duke during regular season. It seems Duke has lost only four games during the regular season:
+
+```scala
+scala> scoreGraph.triplets.filter(_.dstAttr == "Duke").foreach(println)
+((1274,Miami FL),(1181,Duke),FullResult(2015,71,A,Score: 90-74))
+((1301,NC State),(1181,Duke),FullResult(2015,69,H,Score: 87-75))
+((1323,Notre Dame),(1181,Duke),FullResult(2015,86,H,Score: 77-73))
+((1323,Notre Dame),(1181,Duke),FullResult(2015,130,N,Score: 74-64))
+```
+
+
+## Aggregating Game Stats
+
+Having our graph ready, let's start aggregating the stats data in `scoreGraph`. In Spark, `aggregateMessages` is the operator for that kind of jobs.
+For example, let's find out the average field goals made per game by the winners. In other words, the games that a team lost will not be counted. To get the average for each team, we first need to have the number of games won by the team and the total field goals that the team made in those games:
+
+```scala
+// Aggregate the total field goals made by winning teams
+type Msg = (Int, Int)
+type Context = EdgeContext[String, FullResult, Msg]
+val winningFieldGoalMade: VertexRDD[Msg] = scoreGraph aggregateMessages(
+ // sendMsg
+ (ec: Context) => ec.sendToSrc(1, ec.attr.winnerStats.fieldGoalMade),
+
+ // mergeMsg
+ (x: Msg, y: Msg) => (x._1 + y._1, x._2+ y._2)
+)
+```
+
+### AggregateMessage operator
+
+There is a lot going on in the above call to `aggregateMessages`. So let's see it working in slow motion. When we called `aggregateMessages` on the `scoreGraph`, we had to pass two functions as arguments.
+
+#### SendMsg
+The first function has a signature `EdgeContext[VD, ED, Msg] => Unit`. It takes an `EdgeContext` as input. Since it does not return anything, its return type is `Unit`. This function is needed for sending message between nodes.
+
+Ok, but what is that `EdgeContext` type? `EdgeContext` represents an edge along with its neighboring nodes. It can access both the edge attribute and the source and destination nodes' attributes. In addition, `EdgeContext` has two methods to send messages along the edge to its source node or to its destination node. These methods are `sendToSrc` and `sendToDst` respectively. Then, the type of messages being sent through the graph is defined by `Msg`. Similar to vertex and edge types, we can defined the concrete type that `Msg` takes as we wish.
+
+#### Merge
+In addition to `sendMsg`, the second function that we need to pass to `aggregateMessages` is a `mergeMsg` function with the following signature `(Msg, Msg) => Msg`. As its name implies, `mergeMsg` is used to merge two messages received at each node into a new one. Its output must also be of type `Msg`. Using these two functions, `aggregateMessages` returns the aggregated messages inside a `VertexRDD[Msg]`.
+
+#### Example
+In our example, we need to aggregate the number of games played and the number of field goals made. Therefore, `Msg` is simply a pair of `Int`. Furthermore, each edge context needs to send a message to only its source node, i.e. the winning team. This is because we want to compute the total field goals made by each team for only the games that it won. The actual message sent to each "winner" node is the pair of integers `(1, ec.attr.winnerStats.fieldGoalMade)`. Here, `1` serves as a counter for the number of games won by the source node. The second integer, which is the number of field goals in one game, is extracted from the edge attribute.
+
+As we set out to compute the average field goals per winning game for all teams, we need to apply the `mapValues` operator to the output of `aggregateMessages` as follows:
+
+```scala
+// Average field goals made per Game by the winning teams
+val avgWinningFieldGoalMade: VertexRDD[Double] =
+ winningFieldGoalMade mapValues (
+ (id: VertexId, x: Msg) => x match {
+ case (count: Int, total: Int) => total.toDouble/count
+})
+
+scala> avgWinningFieldGoalMade.take(5).foreach(println)
+(1260,24.71641791044776)
+(1410,23.56578947368421)
+(1426,26.239436619718308)
+(1166,26.137614678899084)
+(1434,25.34285714285714)
+```
+
+## Abstracting out the aggregation
+
+That was kind of cool! We can surely do the same thing for the average points per game scored by winning teams:
+
+```scala
+// Aggregate the points scored by winning teams
+val winnerTotalPoints: VertexRDD[(Int, Int)] = scoreGraph.aggregateMessages(
+ // sendMsg
+ triplet => triplet.sendToSrc(1, triplet.attr.winnerStats.score),
+ // mergeMsg
+ (x, y) => (x._1 + y._1, x._2+ y._2)
+)
+
+// Average field goals made per Game by winning teams
+var winnersPPG: VertexRDD[Double] =
+ winnerTotalPoints mapValues (
+ (id: VertexId, x: (Int, Int)) => x match {
+ case (count: Int, total: Int) => total.toDouble/count
+ })
+
+scala> winnersPPG.take(5).foreach(println)
+(1260,71.19402985074628)
+(1410,71.11842105263158)
+(1426,76.30281690140845)
+(1166,76.89449541284404)
+(1434,74.28571428571429)
+```
+
+What if the coach wants to know the top 5 teams with the highest average three pointer made per winning game? By the way, he might also ask which teams are the most efficient in three pointers.
+
+### Keeping things DRY
+
+We can copy and modify the previous code but that would be quite repetitive. Instead, let's abstract out the average aggregation operator so that it can work on any statistics that the coach needs. Luckily, Scala's higher-order functions are there to help in this task.
+
+Let's define functions that take a team's `GameStats` as input and returns specific statistic that we are interested in. For now, we will need the number of three pointer made and the average three pointer percentage:
+
+```scala
+// Getting individual stats
+def threePointMade(stats: GameStats) = stats.threePointerMade
+def threePointPercent(stats: GameStats) = stats.tpPercent
+```
+
+Then, we create a generic function that takes as inputs a stats graph and one of the functions defined above, which has a signature `GameStats => Double`.
+
+```scala
+// Generic function for stats averaging
+def averageWinnerStat(graph: Graph[String, FullResult])(getStat: GameStats => Double): VertexRDD[Double] = {
+ type Msg = (Int, Double)
+ val winningScore: VertexRDD[Msg] = graph.aggregateMessages[Msg](
+ // sendMsg
+ triplet => triplet.sendToSrc(1, getStat(triplet.attr.winnerStats)),
+ // mergeMsg
+ (x, y) => (x._1 + y._1, x._2+ y._2)
+ )
+ winningScore mapValues (
+ (id: VertexId, x: Msg) => x match {
+ case (count: Int, total: Double) => total/count
+ })
+}
+```
+
+Now, we can get the average stats by passing the functions `threePointMade` and `threePointPercent` to `averageWinnerStat`:
+
+```scala
+val winnersThreePointMade = averageWinnerStat(scoreGraph)(threePointMade)
+val winnersThreePointPercent = averageWinnerStat(scoreGraph)(threePointPercent)
+```
+
+With little efforts, we can tell coach which five winning teams score the highest number of threes per game:
+
+```scala
+scala> winnersThreePointMade.sortBy(_._2,false).take(5).foreach(println)
+(1440,11.274336283185841)
+(1125,9.521929824561404)
+(1407,9.008849557522124)
+(1172,8.967441860465117)
+(1248,8.915384615384616)
+```
+While we are at it, let's find out the five most efficient teams in three pointers:
+
+```scala
+scala> winnersThreePointPercent.sortBy(_._2,false).take(5).foreach(println)
+(1101,46.90555728464225)
+(1147,44.224282479431224)
+(1294,43.754532434101534)
+(1339,43.52308905887638)
+(1176,43.080814169045105)
+```
+Interestingly, the teams that made the most three pointers per winning game are not always the one who are the most efficient at it. But it is ok because at least, they won those games.
+
+### Coach wants more numbers
+
+Coach seems to argue against that argument. He asks us to get the same statistics but he wants the average over all games that each team has played.
+
+We then have to aggregate the information at all nodes, and not only at the destination nodes. To make our previous abstraction more flexible, let's create the following types:
+
+```scala
+trait Teams
+case class Winners extends Teams
+case class Losers extends Teams
+case class AllTeams extends Teams
+```
+
+We modify the previous higher-order function to have a extra argument `Teams`, which will help us specify at which nodes we want to collect and aggregate the required game stats. The new function becomes:
+
+```scala
+def averageStat(graph: Graph[String, FullResult])(getStat: GameStats => Double, tms: Teams): VertexRDD[Double] = {
+ type Msg = (Int, Double)
+ val aggrStats: VertexRDD[Msg] = graph.aggregateMessages[Msg](
+ // sendMsg
+ tms match {
+ case _ : Winners => t => t.sendToSrc((1, getStat(t.attr.winnerStats)))
+ case _ : Losers => t => t.sendToDst((1, getStat(t.attr.loserStats)))
+ case _ => t => {
+ t.sendToSrc((1, getStat(t.attr.winnerStats)))
+ t.sendToDst((1, getStat(t.attr.loserStats)))
+ }
+ }
+ ,
+ // mergeMsg
+ (x, y) => (x._1 + y._1, x._2+ y._2)
+ )
+
+ aggrStats mapValues (
+ (id: VertexId, x: Msg) => x match {
+ case (count: Int, total: Double) => total/count
+ })
+ }
+```
+
+Now, `aggregateStat` allows us to choose whether we want to aggregate the stats for winners only, for losers only or for all teams. Since coach wants the overall stats averaged over all games played, we aggregate the stats by passing the `AllTeams()` flag in `aggregateStat`. In this case, we define the `sendMsg` argument in `aggregateMessages` to send the required stats to both the source (the winner) and to the destination (the loser) using `EdgeContext`'s `sendToSrc` and `sendToDst` functions respectively. This mechanism is pretty straightforward. We just need make sure we send the right information to the right node. In this case, we send the `winnerStats` to the winner and the `loserStats`to the loser.
+
+Ok, you got the idea now. So, let's apply it to please our coach. Here are the teams with the overall highest three pointers per page:
+
+```scala
+// Average Three Point Made Per Game for All Teams
+val allThreePointMade = averageStat(scoreGraph)(threePointMade, AllTeams())
+scala> allThreePointMade.sortBy(_._2, false).take(5).foreach(println)
+(1440,10.180811808118081)
+(1125,9.098412698412698)
+(1172,8.575657894736842)
+(1184,8.428571428571429)
+(1407,8.411149825783973)
+```
+
+And here are the five most efficient teams overall in three pointers per Game:
+
+```scala
+// Average Three Point Percent for All Teams
+val allThreePointPercent = averageStat(scoreGraph)(threePointPercent, AllTeams())
+
+scala> allThreePointPercent.sortBy(_._2,false).take(5).foreach(println)
+(1429,38.8351815824302)
+(1323,38.522819895594)
+(1181,38.43052051444854)
+(1294,38.41227053353959)
+(1101,38.097896464168954)
+```
+
+Actually, there is only a 2% difference between the most efficient team and the one in 50th position. Most NCAA teams are therefore pretty efficient behind the line. I bet coach knew that already!
+
+### Average Points Per Game
+
+We can also reuse the `averageStat` function to get the average points per game for the winners. In particular, let's take a look at the two teams that won games with the highest and lowest scores:
+
+```
+// Winning teams
+val winnerAvgPPG = averageStat(scoreGraph)(score, Winners())
+
+scala> winnerAvgPPG.max()(Ordering.by(_._2))
+res36: (org.apache.spark.graphx.VertexId, Double) = (1322,90.73333333333333)
+
+scala> winnerAvgPPG.min()(Ordering.by(_._2))
+res39: (org.apache.spark.graphx.VertexId, Double) = (1197,60.5)
+```
+Apparently, the most defensive team can win game by scoring only 60 points whereas the most offensive team can score an average of 90 points.
+
+Next, let us average the points per game for all games played and look at the two teams with the best and worst offense during the 2015 season:
+
+```scala
+// Average Points Per Game of All Teams
+val allAvgPPG = averageStat(scoreGraph)(score, AllTeams())
+
+scala> allAvgPPG.max()(Ordering.by(_._2))
+res42: (org.apache.spark.graphx.VertexId, Double) = (1322,83.81481481481481)
+
+scala> allAvgPPG.min()(Ordering.by(_._2))
+res43: (org.apache.spark.graphx.VertexId, Double) = (1212,51.111111111111114)
+
+```
+
+To no surprise, the best offensive team is the same as the one who scores most in winning games. To win games, 50 points is not enough in average for a team to win games.
+
+## Defense Stats: The D matters as in Direction
+
+Above, we obtained some statistics such as field goals or three point percentage that a team achieves. What if we want to aggregate instead the average points or rebounds that each team concedes to their opponents? To compute that, we define a new higher-order function `averageConcededStat`. Compared to `averageStat`, this function needs to send the `loserStats` to the winning team and the `winnerStats` to the losing team. To make things more interesting, we are going to make the team name as part of the message `Msg`.
+
+```scala
+def averageConcededStat(graph: Graph[String, FullResult])(getStat: GameStats => Double, rxs: Teams): VertexRDD[(String, Double)] = {
+ type Msg = (Int, Double, String)
+ val aggrStats: VertexRDD[Msg] = graph.aggregateMessages[Msg](
+ // sendMsg
+ rxs match {
+ case _ : Winners => t => t.sendToSrc((1, getStat(t.attr.loserStats), t.srcAttr))
+ case _ : Losers => t => t.sendToDst((1, getStat(t.attr.winnerStats), t.dstAttr))
+ case _ => t => {
+ t.sendToSrc((1, getStat(t.attr.loserStats),t.srcAttr))
+ t.sendToDst((1, getStat(t.attr.winnerStats),t.dstAttr))
+ }
+ }
+ ,
+ // mergeMsg
+ (x, y) => (x._1 + y._1, x._2+ y._2, x._3)
+ )
+
+ aggrStats mapValues (
+ (id: VertexId, x: Msg) => x match {
+ case (count: Int, total: Double, name: String) => (name, total/count)
+ })
+}
+
+```
+
+With that, we can calculate the average points conceded by winning and losing teams as follows:
+
+```scala
+val winnersAvgConcededPoints = averageConcededStat(scoreGraph)(score, Winners())
+val losersAvgConcededPoints = averageConcededStat(scoreGraph)(score, Losers())
+
+scala> losersAvgConcededPoints.min()(Ordering.by(_._2))
+res: (VertexId, (String, Double)) = (1101,(Abilene Chr,74.04761904761905))
+
+scala> winnersAvgConcededPoints.min()(Ordering.by(_._2))
+res: (org.apache.spark.graphx.VertexId, (String, Double)) = (1101,(Abilene Chr,74.04761904761905))
+
+scala> losersAvgConcededPoints.max()(Ordering.by(_._2))
+res: (VertexId, (String, Double)) = (1464,(Youngstown St,78.85714285714286))
+
+scala> winnersAvgConcededPoints.max()(Ordering.by(_._2))
+res: (VertexId, (String, Double)) = (1464,(Youngstown St,71.125))
+```
+
+The above tells us that Abilene Christian University is the most defensive team. They concede the least points whether they win a game or not. On the other hand, Youngstown has the worst defense.
+
+
+## Joining Aggregated Stats into Graphs
+
+The previous example shows us how flexible the `aggregateMessages` operator is. We can define the type `Msg` of the messages to be aggregated to fit our needs. Moreover, we can select which nodes receive the messages. Finally, we can also define how we want to merge the messages.
+
+As a final example, let us aggregate many statistics about each team and join this information into the nodes of the graph. To start, we create its own class for the team stats:
+
+```scala
+// Average Stats of All Teams
+case class TeamStat(
+ wins: Int = 0 // Number of wins
+ ,losses: Int = 0 // Number of losses
+ ,ppg: Int = 0 // Points per game
+ ,pcg: Int = 0 // Points conceded per game
+ ,fgp: Double = 0 // Field goal percentage
+ ,tpp: Double = 0 // Three point percentage
+ ,ftp: Double = 0 // Free Throw percentage
+ ){
+ override def toString = wins + "-" + losses
+}
+```
+
+Then, we collect the average stats for all teams using `aggregateMessages` below. For that, we define the type of the message to be an 8-element tuple that holds the counter for games played, wins, losses and other statistics that will be stored in `TeamStat` as listed above.
+
+```scala
+type Msg = (Int, Int, Int, Int, Int, Double, Double, Double)
+
+val aggrStats: VertexRDD[Msg] = scoreGraph.aggregateMessages(
+ // sendMsg
+ t => {
+ t.sendToSrc(( 1,
+ 1, 0,
+ t.attr.winnerStats.score,
+ t.attr.loserStats.score,
+ t.attr.winnerStats.fgPercent,
+ t.attr.winnerStats.tpPercent,
+ t.attr.winnerStats.ftPercent
+ ))
+ t.sendToDst(( 1,
+ 0, 1,
+ t.attr.loserStats.score,
+ t.attr.winnerStats.score,
+ t.attr.loserStats.fgPercent,
+ t.attr.loserStats.tpPercent,
+ t.attr.loserStats.ftPercent
+ ))
+ }
+ ,
+ // mergeMsg
+ (x, y) => ( x._1 + y._1, x._2 + y._2,
+ x._3 + y._3, x._4 + y._4,
+ x._5 + y._5, x._6 + y._6,
+ x._7 + y._7, x._8 + y._8
+ )
+ )
+```
+
+Given the aggregate message `aggrStats`, we map them into a collection of `TeamStat`
+
+```scala
+val teamStats: VertexRDD[TeamStat] = aggrStats mapValues {
+ (id: VertexId, m: Msg) => m match {
+ case ( count: Int,
+ wins: Int,
+ losses: Int,
+ totPts: Int,
+ totConcPts: Int,
+ totFG: Double,
+ totTP: Double,
+ totFT: Double) => TeamStat( wins, losses,
+ totPts/count,
+ totConcPts/count,
+ totFG/count,
+ totTP/count,
+ totFT/count)
+
+ }
+}
+```
+
+Next, let us join the `teamStats` into the graph. For that, we first create a class `Team` as a new type for the vertex attribute. `Team` will have the name and the `TeamStat`:
+
+```scala
+case class Team(name: String, stats: Option[TeamStat]) {
+ override def toString = name + ": " + stats
+}
+```
+
+Next, we use the `joinVertices` operator that we have seen in the previous chapter:
+
+```scala
+// Joining the average stats to vertex attributes
+def addTeamStat(id: VertexId, t: Team, stats: TeamStat) = Team(t.name, Some(stats))
+
+val statsGraph: Graph[Team, FullResult] =
+ scoreGraph.mapVertices((_, name) => Team(name, None)).
+ joinVertices(teamStats)(addTeamStat)
+```
+
+We can see that the join has worked well by printing the first three vertices in the new graph `statsGraph`:
+
+```scala
+scala> statsGraph.vertices.take(3).foreach(println)
+(1260,Loyola-Chicago: Some(17-13))
+(1410,TX Pan American: Some(7-21))
+(1426,UT Arlington: Some(15-15))
+```
+
+To conclude this task, let us find out the top 10 teams in the regular seasons. To do so, we define an `Ordering` for `Option[TeamStat]` as follows:
+
+```scala
+import scala.math.Ordering
+object winsOrdering extends Ordering[Option[TeamStat]] {
+ def compare(x: Option[TeamStat], y: Option[TeamStat]) = (x, y) match {
+ case (None, None) => 0
+ case (Some(a), None) => 1
+ case (None, Some(b)) => -1
+ case (Some(a), Some(b)) => if (a.wins == b.wins) a.losses compare b.losses
+ else a.wins compare b.wins
+ }
+}
+```
+
+Finally!
+
+```scala
+import scala.reflect.classTag
+import scala.reflect.ClassTag
+scala> statsGraph.vertices.sortBy(v => v._2.stats,false)(winsOrdering, classTag[Option[TeamStat]]).
+ | take(10).foreach(println)
+(1246,Kentucky: Some(34-0))
+(1437,Villanova: Some(32-2))
+(1112,Arizona: Some(31-3))
+(1458,Wisconsin: Some(31-3))
+(1211,Gonzaga: Some(31-2))
+(1320,Northern Iowa: Some(30-3))
+(1323,Notre Dame: Some(29-5))
+(1181,Duke: Some(29-4))
+(1438,Virginia: Some(29-3))
+(1268,Maryland: Some(27-6))
+```
+
+Note that the `ClassTag` parameter is required in `sortBy` to make use of Scala's reflection. That is why we had the above imports.
+
+
+## Performance optimization with TripletFields
+
+
+In addition to the `sendMsg` and `mergeMsg`, `aggregateMessages` can also take an optional argument `tripletsFields` which indicates what data is accessed in the EdgeContext. The main reason for explicitly specifying such information is to help optimize the performance of the `aggregateMessages` operation.
+
+In fact, `TripletFields` represents a subset of the fields of an _EdgeTriplet_ and it enables GraphX to populate only those fields when necessary.
+
+The default value is TripletFields.All which means that the `sendMsg` function may access any of the fields in the EdgeContext. Otherwise, the tripletFields argument is used to tell GraphX that only part of the EdgeContext will be required so that an efficient join strategy can be used. All possible options for the tripletsFields are listed below:
+
+- `TripletFields.All`: expose all the fields (source, edge, and destination).
+- `TripletFields.Dst`: expose the destination and edge fields but not the source field.
+- `TripletFields.EdgeOnly`: expose only the edge field.
+- `TripletFields.None`: None of the triplet fields are exposed.
+- `TripletFields.Src`: expose the source and edge fields but not the destination field.
+
+Using our previous example, if we are interested in computing the total number of wins and losses for each team, we will not need to access any field of the `EdgeContext`. In this case, we should use `TripletFields.None` to indicate so:
+
+```scala
+// Number of wins of the teams
+val numWins: VertexRDD[Int] = scoreGraph.aggregateMessages(
+ triplet => {
+ triplet.sendToSrc(1) // No attribute is passed but an integer
+ },
+ (x, y) => x + y,
+ TripletFields.None
+)
+
+// Number of losses of the teams
+val numLosses: VertexRDD[Int] = scoreGraph.aggregateMessages(
+ triplet => {
+ triplet.sendToDst(1) // No attribute is passed but an integer
+ },
+ (x, y) => x + y,
+ TripletFields.None
+)
+```
+
+To see, that this works, let's print the top 5 and bottom 5 teams:
+
+```scala
+scala> numWins.sortBy(_._2,false).take(5).foreach(println)
+(1246,34)
+(1437,32)
+(1112,31)
+(1458,31)
+(1211,31)
+
+scala> numLosses.sortBy(_._2, false).take(5).foreach(println)
+(1363,28)
+(1146,27)
+(1212,27)
+(1197,27)
+(1263,27)
+```
+
+Should you want the name of the top 5 teams, you need to access the `srcAttr` attribute. In this case, we need to set the `tripletFields` to `TripletFields.Src`:
+
+Kentucky as undefeated team in regular season:
+
+```scala
+val numWinsOfTeams: VertexRDD[(String, Int)] = scoreGraph.aggregateMessages(
+ t => {
+ t.sendToSrc(t.srcAttr, 1) // Pass source attribute only
+ },
+ (x, y) => (x._1, x._2 + y._2),
+ TripletFields.Src
+)
+```
+
+Et voila!
+
+```scala
+scala> numWinsOfTeams.sortBy(_._2._2, false).take(5).foreach(println)
+(1246,(Kentucky,34))
+(1437,(Villanova,32))
+(1112,(Arizona,31))
+(1458,(Wisconsin,31))
+(1211,(Gonzaga,31))
+
+scala> numWinsOfTeams.sortBy(_._2._2).take(5).foreach(println)
+(1146,(Cent Arkansas,2))
+(1197,(Florida A&M,2))
+(1398,(Tennessee St,3))
+(1263,(Maine,3))
+(1420,(UMBC,4))
+```
+
+Kentucky has not lost any of its 34 games during the regular season. Too bad that they could not make it into the championship final.
+
+
+## Warning about MapReduceTriplets operator
+
+Prior to Spark 1.2, there was no `aggregateMessages` method in `Graph`. Instead, the now deprecated `mapReduceTriplets` was the primary aggregation operator. The API for `mapReduceTriplets` is:
+
+```scala
+class Graph[VD, ED] {
+ def mapReduceTriplets[Msg](
+ map: EdgeTriplet[VD, ED] => Iterator[(VertexId, Msg)],
+ reduce: (Msg, Msg) => Msg)
+ : VertexRDD[Msg]
+}
+```
+
+Compared to `mapReduceTriplets`, the new operator `aggregateMessages` is more expressive as it employs the message passing mechanism instead of returning an iterator of messages as `mapReduceTriplets` does. In addition, `aggregateMessages` explicitly requires the user to specify the TripletFields object for performance improvement as we explained above. In addition to API improvements, `aggregateMessages` is optimized for performance.
+
+
+Because `mapReduceTriplets` is now deprecated, we will not discuss it further. If you have to use it with earlier versions of Spark, you can refer to the Spark programming guide.
+
+
+## Summary
+
+In brief, AggregateMessages is a useful and generic operator that provides a functional abstraction for aggregating neighbourhood information in Spark graphs. Its definition is summarized below:
+
+```scala
+class Graph[VD, ED] {
+ def aggregateMessages[Msg: ClassTag](
+ sendMsg: EdgeContext[VD, ED, Msg] => Unit,
+ mergeMsg: (Msg, Msg) => Msg,
+ tripletFields: TripletFields = TripletFields.All)
+ : VertexRDD[Msg]
+}
+```
+
+This operator applies a user defined `sendMsg` function to each edge in the graph using an `EdgeContext`. Each `EdgeContext` access the required information about the edge and passes that information to its source node and/or destination node using the `sendToSrc` and/or `sendToDst` respectively. After all messages are received by the nodes, the `mergeMsg` function is used to aggregate those messages at each node.
+
+## Some interesting reads
+
+1. [Six keys to sports analytics.](http://newsoffice.mit.edu/2015/mit-sloan-sports-analytics-conference-0302)
+2. [Moneyball: The Art Of Winning An Unfair Game](https://en.wikipedia.org/wiki/Moneyball)
+3. [Golden State Warriors at the forefront of NBA data analysis](http://www.sfgate.com/warriors/article/Golden-State-Warriors-at-the-forefront-of-NBA-5753776.php)
+4. [How Data and Analytics Have Changed 'The Beautiful Game'](http://www.huffingtonpost.com/travis-korte/soccer-analytics-data_b_5512271.html)
+5. [NHL, SAP partnership to lead statistical revolution](http://www.nhl.com/ice/news.htm?id=754184)
+
diff --git a/source/projects/spark-ml.markdown b/source/projects/spark-ml.markdown
new file mode 100644
index 0000000..54b15a6
--- /dev/null
+++ b/source/projects/spark-ml.markdown
@@ -0,0 +1,8 @@
+---
+layout: page
+title: "spark-ml"
+date: 2015-08-01 13:46
+comments: true
+sharing: true
+footer: true
+---
diff --git a/source/projects/time-series-decomposition.markdown b/source/projects/time-series-decomposition.markdown
new file mode 100644
index 0000000..c2d44e5
--- /dev/null
+++ b/source/projects/time-series-decomposition.markdown
@@ -0,0 +1,287 @@
+---
+layout: page
+title: "Time Series: trend analysis, smoothing and anomaly detection"
+date: 2015-08-10 19:54
+comments: true
+sharing: true
+footer: true
+---
+
+
+## Forecasting
+
+Forecasting is an important tool for making effective decisions, planning efficiently and reducing risks.
+
+Forecasting is useful in many situations when uncertain quantity or event must and can be predicted. In other words, we must have data that allows to forecast the quantity or event accurately. Then, we need to build a model that can tell the difference between a random fluctuation and a existing pattern in the data. A good forecasting model should capture such patterns with a minimum out-of-sample error.
+
+
+### Time series forecasting
+
+Time series forecasting is concerned with only one question. Can we predict future values by looking at past ones? We are not attempting to identify factors that help explain the future. Instead, we want to accurately estimate how the historical data series will continue into the future. Thus, we want to find a functional relationship of the following form:
+
+$$
+Y_{t+1} = f(Y_t, Y_{t-1}, Y_{t-2}, ... , Y_{t-n}, \text{error})
+$$
+
+Such relationship is described by a time series model.
+
+### Basic forecasting steps
+
+There are in general four tasks that must be undertaken in forecasting.
+
+1. **Define the problem.** This is the most difficult task as we need to determine what exactly to forecast, within what time horizon and how frequently.
+2. **Gather data.** It is primordial to find and collect historical data to construct a model with which we can forecast the future. For time series, this can be anything that are observed sequentially over time.
+3. **Building and choosing models.** This step involves choosing and fitting several forecasting models. Each model has parameters that must be fitted based on the known historical data.
+4. **Selecting and using the best model.** We select the model that provides the most accurate predictions on the test data samples, i.e. data that were held out and not used for building the models. With the selected model, we can then predict future values and determine some prediction intervals.
+
+
+### Time series patterns
+
+Before building any forecasting model, it often helps to explore time series data by simply plotting them. This help to understand the behavior of the series data and the patterns that exist in the data. There exist four types of time series data patterns:
+
+1. A **stationary _horizontal_ pattern (H)** exists when the data values clearly fluctuate around a constant mean.
+2. A **_seasonal_ pattern (S)** exists because of the effects of seasonal factors (e.g. beginning of fiscal year, financial reporting quarters, weekends, days of the week, holidays, etc.) Note that such patterns need not to be exactly periodic.
+3. A **_cyclical_ pattern (C)** is present when the data values show a sequence of rises and falls that are not of a fixed period. Typical examples of a cyclical pattern are business cycles that impact the quantity of sales over a longer period of time.
+4. A **_trend_ (T)** is a long-term increase or decrease in the data. For instance, stock prices of high-growth companies usually exhibit a strong upward trend over a long period of time.
+
+A time series can have many of these four components at the same time. Sometimes, it is more convenient to combine H, C and T as a cycle-trend pattern that represents long-term changes in the time series. As a result, we will think of time series as a function of three components: the trend, the seasonality and the random error:
+
+$$
+\text{Time Series} = f(\text{Trend-Cycle}, \text{Seasonality}, \text{error})
+$$
+
+Most forecasting models explicitly assume that the random error is always present and try to minimize this error during model fitting. Depending on the actual time series, the functional relationship above can be additive or multiplicative. For example, we have the following with an additive decomposition model:
+
+$$
+\text{Time Series} = \text{Trend-Cycle} + \text{Seasonality} + \text{error}
+$$
+
+For a multiplicative model, the time series decomposes as follows:
+
+$$
+\text{Time Series} = \text{Trend-Cycle} \times \text{Seasonality} \times \text{error}
+$$
+
+In Haskell, we can for instance define a `TimeSeries` type as follows:
+
+```haskell
+data TimeSeries = TimeSeries [TimeStamp] [Float]
+type TS = TimeSeries
+```
+
+Let's suppose that we can appropriately define addition, substraction and multiplication over `TimeSeries`:
+
+```haskell
+(+) :: TS -> TS -> TS
+(-) :: TS -> TS -> TS
+(*) :: TS -> TS -> TS
+```
+
+Additionally, we need convenience functions for creating lagged version of a time series or for extracting data points that are within a given window of the series:
+
+```haskell
+lag :: TS -> Time -> TS
+window :: TS -> Time -> Time -> TS
+```
+
+
+## Time series decomposition
+
+In principle, if we want to further analyze the time series, we can use decomposition methods that extract these individual patterns. Decomposition methods are useful for forecasting as the trend-cycle can be used to extrapolate future values. This is the idea of **smoothing techniques**, which _smooth_ the series by eliminating the random fluctuations. Decomposition method is also needed when we want to detect anomalies such as outliers in the time series. We will cover about this topic later.
+
+
+### Basic decomposition method:
+
+A simple decomposition method consists of the following steps:
+
+1. The trend-cycle is computed using a Moving Average or LOESS method.
+2. The de-trended series is computed by removing the trend component from the time series.
+3. The seasonality component is extracted by averaging the values of the seasonal points over multiple periods (e.g. the values corresponding to same month for a monthly time series data)
+4. We obtain the residual errors by subtracting the previously estimated components from the time series.
+
+In Haskell, a decomposition method takes an input time series and return its three components:
+
+```haskell
+decompose :: TS -> (TS, TS, TS)
+decompose timeseries = (trendcycle, seasonality, residual)
+```
+
+Next, let's see these specific techniques in more details.
+
+
+### Seasonal effects adjustment
+
+We have seen that a decomposition method fully decomposes the series. Sometimes, we may just need to adjust time series to seasonal effects. In that case, we only need to remove its seasonality component. For example, the seasonal variation may be irrelevant and even lead to false conclusions to our analysis objectives. For an additive model, the _seasonally adjusted series_ is obtained after removing the seasonal pattern:
+
+$$
+\text{Seasonally Adjusted Series} = \text{Time Series} - \text{Seasonality} = \text{Trend-Cycle} + \text{error}
+$$
+
+For that, we can define function that decomposes a time series into its seasonality component and a seasonally adjusted series:
+
+```haskell
+seasonAdjust :: TS -> (TS, TS)
+seasonAdjust ts = (seas, adjusted)
+ where adjusted = ts - seas
+ (_, seas, _) = decompose ts
+```
+
+### Moving averages
+
+The Trend-Cycle component can be estimated by _smoothing_ the seasonally adjusted series. In other words, we reduce the random error fluctuations after removing the seasonality. The easiest way to do this is with a simple _moving average_. In the following, let's consider several moving average methods.
+
+#### Simple moving averages
+
+Moving average is based on the idea that values that are nearby in time are likely to be close. Hence, taking an average of neighboring points of each data point will yield a good estimate of the trend at that point. Local averaging smooths out the randomness in the data. There are two design parameters to consider:
+
+1. How many data points do we include in each average?
+2. How much weight do we put for each neighboring point involved in the average?
+
+The simplest MA smoother averages an odd number of observations around each data point and put equal weights to them. For instance, a MA smoother of order 3 centered at a time `t` is:
+
+$$
+T_t = \frac{1}{3} (Y_{t-1} + Y_{t} + Y_{t+1})
+$$
+
+Then, the estimate at time $$t+1$$ is obtained by dropping the oldest observation $$Y_{t-1}$$ and by including the next observation $$Y_{t-2}$$. Hence, the term _moving average_ describes this procedure.
+
+> The number of points involved in the average, or the order of the MA, affects the smoothness of the estimate. More points lead to a smoother trend. The drawback of MA is that it is impossible to estimate the trend-cycle close to the beginning and end of the series. The higher the order, the more points we miss at the front and back of the series.
+
+In summary, the movies averages takes two parameters: the number of points involved in each average and the weights of each point:
+
+```haskell
+movingAverage :: Int -> [Float] -> TS -> TS
+movingAverage numPoints weights timeSeries = trend
+ where trend = ...
+```
+
+
+### Double moving averages:
+
+Moving averages can be combined by smoothing an already smoothed series. For example, a $$3 \times 3$$ MA is a 3 MA of a 3 MA. When each 3 MA uses equal weights, the result is equivalent to a 5-period weighted moving average with the weigths 0.111, 0.222, 0.333, 0.222 and 0.111.
+
+Thus, the following double moving average
+
+```haskell
+simpleAverage :: TS -> TS
+simpleAverage = movingAverage 3 [0.333, 0.333, 0.333]
+doubleMovingAverage = simpleAverage . simpleAverage
+```
+
+is equivalent to:
+
+```haskell
+doubleMovingAverage :: TS -> TS
+doubleMovingAverage = movingAverage 5 [0.111, 0.222, 0.333, 0.222, 0.111]
+```
+
+### Weighted moving averages:
+
+In general, a weighted MA with order $$k$$ can be written as:
+
+$$
+T_t = \sum_{j=-\frac{k-1}{2}}^{\frac{k-1}{2}} w_j Y_{t+j}
+$$
+
+### LOESS smoothing
+
+Alternatively, we can use a local linear regression technique to determine the trend of a time series. Precisely, we can fit a straight line through the observations near each data point. Then, the estimate of the trend at each point is given by each fitted line. For the data point at time $$t$$, the estimated trend-cycle $$T$$ is given by:
+
+$$
+T_t = a + bt
+$$
+
+where the parameters $a$ and $b$ are determined for each point at time $t$ by minimizing the sum of squared error:
+
+$$
+\sum{j=-\frac{k-1}{2}}^{\frac{k-1}{2}} w_j(Y_{t+j} - a - b(t+j))^2
+$$
+
+
+Another question is how much weight $$w_j$$ we give to each point. Actually, Cleveland and his colleagues at Bell Labs propose a version of LOESS that is robust against outliers or unusual observations in the data. Their algorithm performs three things in each iteration:
+
+1. Run a local weighted regression smoothing (_see above_) for given weights
+2. Compute the error residuals using the fitted curve
+3. Adjust the weights so that large errors receive smaller weights
+
+A loess function is thus defined as follows:
+
+```haskell
+loess :: TS -> [Float] -> TS
+loess series weights = trend
+ where trend = ... -- run recursive of smoothing and weight adjustment
+```
+
+> Note that the LOESS is more computationally intensive than MA methods since a different value of $a$ and $b$ needs to be computed for every observation at a time $t$. For that, a different line is fitted at each data point using least squares. The number of points used in the local regression should not be too large to avoid underfitting and not too small to produce the desired smoothing.
+
+### STL decomposition
+
+The STL decomposition method literally stands for "Seasonal-Trend decomposition procedure based on Loess". It iteratively apply a LOESS smoother to give a decomposition that is robust against outliers. Another benefit of STL is that it has a flexibility to handle seasonality with abritrary length. The seasonality length just needs to be greater than one, which is usually satisfied in most applications. STL is flexible as it can handle trends of varying smoothness, missing values and seasonality of period other than quartlerly and monthly.
+
+
+STL consists of the following two recursive procedures:
+
+1. **Inner loop.** In each iteration of the inner loop, the seasonal and trend-cycle components are updated once.
+2. **Outer loop.** An iteration of outer loop consists of one or two iterations of the inner loop. At the end of each outer loop iteration, outliers are detected. Future iterations of the inner loop puts smaller weights to these outliers in the LOESS regression.
+
+More details about the operations performed in these two loops are described below. Although STL works with arbitrary cycle length, let us simply assume that we have a monthly time series data. This will simplify the explanations.
+
+#### Inner Loop procedure:
+
+We start the procedure by assuming the trend-cycle component is zero. Then, each iteration of the inner loop does the following two things:
+
+1. *Seasonal smoothing*: updates the seasonality component
+2. *Trend-cycle smoothing*: updates the trend-cycle smoothing
+
+**Seasonal smoothing**
+
+To obtain the seasonality component, we perform the following tasks in sequence:
+
+1. De-trend the series by removing the current trend-cycle estimate
+2. Collect the de-trended values for each month. As a result, we will get 12 separate sub-series.
+3. Smooth each of these sub-series with a LOESS smoother.
+4. Glue back the sub-series together to obtain a preliminary seasonality component.
+5. Extrapolate the Loess smoother to estimate the seasonal component for a few months before and after the observed data.
+6. Run a $$3 × 12 × 12$$ moving average on the resulting seasonality component.
+7. Follow with a LOESS smoothing of length 13 (one more than the seasonal period length). The loss of values at the beginning and end due to the moving average was anticipated and overcome by the extrapolation in **Task 5** above. This step also checks any possible trend component in the seasonality.
+8. Compute the seasonality component as difference between the results of step 6 and step 7.
+
+**Trend-cycle smoothing**
+
+Given the seasonality component, get the trend-cycle with two simple steps:
+
+1. Calculate the seasonally adjusted time series by substracting the seasonality from the original series.
+2. Smooth the adjusted time series with LOESS.
+
+#### Outer Loop:
+
+The outer loop consists of the following steps:
+
+1. Run one or two inner loop iterations to get the trend-cycle and seasonality.
+2. Calculate the error residuals by subtracting the trend-cycle and seasonality from the time series.
+3. Identify the observations with unusually large residual values. These could be outliers!
+4. Adjust the weights used for LOESS by downweighting the outliers.
+
+Note that in the STL procedure, all future inner iterations of inner loop begin with the trend component from the previous iteration rather than starter from zero as in the very first iteration of the inner loop.
+
+
+### STL-based Anomaly detection in time series
+
+Proposed by Vallis and his colleagues at Twitter, STL decomposition can be used to detect outliers in long-term time series data with seasonality and trend-cycle. Their proposed method is piece-wise in the sense that a long-term time series is broken down into multiple windows of time series.
+
+For each window, the following **median-based outlier detection** method is performed:
+
+1. Extract the seasonality component $$S$$ using STL decomposition.
+2. Compute the median $$\tilde{Y}$$
+3. Compute the residual $$R = Y - S - \tilde{Y}$$
+4. Run a standard outlier detection on the residuals (e.g. using median absolute deviation)
+
+## Summary
+
+We have presented an overview of time series analysis and forecasting. Time series can be decomposed into three components: a trend-cycle, a seasonality and the error residual. To extract the trend-cycle, we can employe moving average and LOESS techniques. The seasonality component can be obtained from the de-trended series using the STL decomposition procedure, which is flexible and robust against outliers. The STL decomposition method is also a key ingredient for detecting anomalies and outliers in time series data.
+
+## Further reading:
+
+- Makridakis, S., S. Wheelwright, R. Hyndman, and Y. Chang. Forecasting Methods and Applications. 3rd ed. New York: John Wiley & Sons, 1998.
+- Cleveland, R.B, Cleveland, W.S, Mcrae, J.E, and Terpenning, I. STL: A Seasonal-Trend decomposition procedure based on loess. Journal of Official Statistics, 6(1):3–73, 1990.
+- Vallis, O., Hochenbaum, J. and Kejariwal, A., (2014) “A Novel Technique for Long-Term Anomaly Detection in the Cloud”, 6th USENIX Workshop on Hot Topics in Cloud Computing, Philadelphia, PA.
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