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index.html
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index.html
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<!doctype html>
<html>
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<title>Community Detection in Social Networks</title>
<link rel="stylesheet" href="css/reveal.css">
<link rel="stylesheet" href="css/theme/league.css">
<!-- Theme used for syntax highlighting of code -->
<!-- <link rel="stylesheet" href="lib/css/zenburn.css"> -->
<link rel="stylesheet" href="lib/css/agate.css">
<!-- Printing and PDF exports -->
<script>
var link = document.createElement( 'link' );
link.rel = 'stylesheet';
link.type = 'text/css';
link.href = window.location.search.match( /print-pdf/gi ) ? 'css/print/pdf.css' : 'css/print/paper.css';
document.getElementsByTagName( 'head' )[0].appendChild( link );
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<script src="https://d3js.org/d3.v4.min.js"></script>
</head>
<body>
<div class="reveal">
<div class="slides">
<section>
<h1>Détection de communautés dans les réseaux sociaux</h1>
<h6>Teven Le Scao, Dimitri Lozeve</h6>
</section>
<section data-state="sbm">
<h2>Détection de communautés : le problème</h2>
<div id="sbm"></div>
</section>
<section>
<h1>Plan</h1>
<ol>
<li> <b>Visualisation d'une méthode : la méthode de Louvain</b>
<li> <b>Stochastic Block Model</b>
<li> <b>Le problème de la recommandation : Prestashop</b>
</ol>
</section>
<section>
<h1>Visualisation d'une méthode : la méthode de Louvain</h1>
</section>
<section>
<h2>Modularité</h2>
$$ Q = \frac{1}{2m} \sum_{i,j} \left( A_{ij} - \frac{k_i k_j}{2m} \right) \delta(C_i, C_j) $$
</section>
<section>
<iframe width="1120" height="630" src="https://www.youtube.com/embed/dGa-TXpoPz8" frameborder="0" allowfullscreen></iframe>
</section>
<section>
<h2>Intérêts de la méthode de Louvain</h2>
<img src="dendrogram.png" alt="dendrogram">
</section>
<section>
<h2>Intérêts de la méthode de Louvain</h2>
<font size="+15">$$ \mathcal{O}(n \log n) $$</font>
vs
$$ \mathcal{O}(n \log^2 n) $$
vs
$$ \mathcal{O}(n^2) $$
</section>
<section>
<section data-state="ringofcliques">
<h2>Limitations de la modularité</h2>
<div id="ringofcliques"></div>
</section>
<section>
<h2>Modularité</h2>
$$ Q = \frac{1}{2m} \sum_{i,j} \left( A_{ij} - \frac{k_i k_j}{2m} \right) \delta(C_i, C_j) $$
</section>
</section>
<section>
<h1>Stochastic Block Model</h1>
</section>
<section>
<section data-state="erdosrenyi">
<h2>Modèles de graphes aléatoires</h2>
<h5>Erdös-Rényi</h5>
<div id="erdosrenyi"></div>
</section>
<section data-state="sbm2">
<h5>Stochastic Block Model</h5>
<div id="sbm2"></div>
</section>
</section>
<section>
Test standard pour les méthodes de clustering
<br/>
$\longrightarrow$ Remise en cause
</section>
<section>
$$ \deg(x) = \sum_{j=1}^k X_j $$
où $\;\; X_j = \mathrm{Binom}\left(\left|B_j\right|, P_{ij}\right) $
</section>
<section>
<img style="background-color:white" src="youtubedegree.png" alt="youtubedegree">
</section>
<section>
<h1>Le problème de la recommandation : Prestashop</h1>
</section>
<section>
<img src="users.png" alt="users" />
</section>
<section>
<img src="degreeusers.png" alt="degreeusers" />
</section>
<section>
<h2>Validation croisée</h2>
<ol>
<li>Masquer une partie des arêtes
<li>Appliquer une méthode de clustering sur le réseau
"train"
<li>Mesurer la proportion d'arêtes "test" dont les deux
extrémités sont à l'intérieur d'un cluster
</ol>
</section>
<section data-state="induced">
<h2>Graphe des blocs</h2>
<div id="induced"></div>
</section>
</div>
</div>
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.data(graph.links)
.enter().append("line")
.attr("stroke", "lightgray")
.attr("stroke-width", function(d) { return Math.sqrt(d.value); });
var node = svg.append("g")
.attr("class", "nodes")
.selectAll("circle")
.data(graph.nodes)
.enter().append("circle")
.attr("r", 5)
.attr("fill", function(d) { return color(d.group); })
.call(d3.drag()
.on("start", dragstarted)
.on("drag", dragged)
.on("end", dragended));
node.append("title")
.text(function(d) { return d.id; });
simulation
.nodes(graph.nodes)
.on("tick", ticked);
simulation.force("link")
.links(graph.links);
function ticked() {
link
.attr("x1", function(d) { return d.source.x; })
.attr("y1", function(d) { return d.source.y; })
.attr("x2", function(d) { return d.target.x; })
.attr("y2", function(d) { return d.target.y; });
node
.attr("cx", function(d) { return d.x; })
.attr("cy", function(d) { return d.y; });
}
});
function dragstarted(d) {
if (!d3.event.active) simulation.alphaTarget(0.3).restart();
d.fx = d.x;
d.fy = d.y;
}
function dragged(d) {
d.fx = d3.event.x;
d.fy = d3.event.y;
}
function dragended(d) {
if (!d3.event.active) simulation.alphaTarget(0);
d.fx = null;
d.fy = null;
}
})
</script>
<script type="text/javascript">
Reveal.addEventListener( 'induced', function() {
var width=960, height=600;
var svg = d3.select("#induced").selectAll('svg').data([0]).enter().append("svg")
.attr("width", width)
.attr("height", height);
var color = d3.scaleOrdinal(d3.schemeCategory20);
var simulation = d3.forceSimulation()
.force("link", d3.forceLink().id(function(d) { return d.id; }))
.force("charge", d3.forceManyBody())
.force("center", d3.forceCenter(width / 2, height / 2));
d3.json("induced.json", function(error, graph) {
if (error) throw error;
var link = svg.append("g")
.attr("class", "links")
.selectAll("line")
.data(graph.links)
.enter().append("line")
.attr("stroke", "lightgray")
.attr("stroke-width", function(d) { return Math.sqrt(d.value); });
var node = svg.append("g")
.attr("class", "nodes")
.selectAll("circle")
.data(graph.nodes)
.enter().append("circle")
.attr("r", 5)
.attr("fill", function(d) { return color(d.group); })
.call(d3.drag()
.on("start", dragstarted)
.on("drag", dragged)
.on("end", dragended));
node.append("title")
.text(function(d) { return d.id; });
simulation
.nodes(graph.nodes)
.on("tick", ticked);
simulation.force("link")
.links(graph.links);
function ticked() {
link
.attr("x1", function(d) { return d.source.x; })
.attr("y1", function(d) { return d.source.y; })
.attr("x2", function(d) { return d.target.x; })
.attr("y2", function(d) { return d.target.y; });
node
.attr("cx", function(d) { return d.x; })
.attr("cy", function(d) { return d.y; });
}
});
function dragstarted(d) {
if (!d3.event.active) simulation.alphaTarget(0.3).restart();
d.fx = d.x;
d.fy = d.y;
}
function dragged(d) {
d.fx = d3.event.x;
d.fy = d3.event.y;
}
function dragended(d) {
if (!d3.event.active) simulation.alphaTarget(0);
d.fx = null;
d.fy = null;
}
})
</script>
</body>
</html>