[SPARK-1212] Adding sparse data support and update KMeans

Continue our discussions from https://github.com/apache/incubator-spark/pull/575

This PR is WIP because it depends on a SNAPSHOT version of breeze.

Per previous discussions and benchmarks, I switched to breeze for linear algebra operations. @dlwh and I made some improvements to breeze to keep its performance comparable to the bare-bone implementation, including norm computation and squared distance. This is why this PR needs to depend on a SNAPSHOT version of breeze.

@fommil , please find the notice of using netlib-core in `NOTICE`. This is following Apache's instructions on appropriate labeling.

I'm going to update this PR to include:

1. Fast distance computation: using `\|a\|_2^2 + \|b\|_2^2 - 2 a^T b` when it doesn't introduce too much numerical error. The squared norms are pre-computed. Otherwise, computing the distance between the center (dense) and a point (possibly sparse) always takes O(n) time.

2. Some numbers about the performance.

3. A released version of breeze. @dlwh, a minor release of breeze will help this PR get merged early. Do you mind sharing breeze's release plan? Thanks!

Author: Xiangrui Meng <meng@databricks.com>

Closes #117 from mengxr/sparse-kmeans and squashes the following commits:

67b368d [Xiangrui Meng] fix SparseVector.toArray
5eda0de [Xiangrui Meng] update NOTICE
67abe31 [Xiangrui Meng] move ArrayRDDs to mllib.rdd
1da1033 [Xiangrui Meng] remove dependency on commons-math3 and compute EPSILON directly
9bb1b31 [Xiangrui Meng] optimize SparseVector.toArray
226d2cd [Xiangrui Meng] update Java friendly methods in Vectors
238ba34 [Xiangrui Meng] add VectorRDDs with a converter from RDD[Array[Double]]
b28ba2f [Xiangrui Meng] add toArray to Vector
e69b10c [Xiangrui Meng] remove examples/JavaKMeans.java, which is replaced by mllib/examples/JavaKMeans.java
72bde33 [Xiangrui Meng] clean up code for distance computation
712cb88 [Xiangrui Meng] make Vectors.sparse Java friendly
27858e4 [Xiangrui Meng] update breeze version to 0.7
07c3cf2 [Xiangrui Meng] change Mahout to breeze in doc use a simple lower bound to avoid unnecessary distance computation
6f5cdde [Xiangrui Meng] fix a bug in filtering finished runs
42512f2 [Xiangrui Meng] Merge branch 'master' into sparse-kmeans
d6e6c07 [Xiangrui Meng] add predict(RDD[Vector]) to KMeansModel
42b4e50 [Xiangrui Meng] line feed at the end
a4ace73 [Xiangrui Meng] Merge branch 'fast-dist' into sparse-kmeans
3ed1a24 [Xiangrui Meng] add doc to BreezeVectorWithSquaredNorm
0107e19 [Xiangrui Meng] update NOTICE
87bc755 [Xiangrui Meng] tuned the KMeans code: changed some for loops to while, use view to avoid copying arrays
0ff8046 [Xiangrui Meng] update KMeans to use fastSquaredDistance
f355411 [Xiangrui Meng] add BreezeVectorWithSquaredNorm case class
ab74f67 [Xiangrui Meng] add fastSquaredDistance for KMeans
4e7d5ca [Xiangrui Meng] minor style update
07ffaf2 [Xiangrui Meng] add dense/sparse vector data models and conversions to/from breeze vectors use breeze to implement KMeans in order to support both dense and sparse data

NOTICE

@@ -3,3 +3,12 @@ Copyright 2014 The Apache Software Foundation.
 
 This product includes software developed at
 The Apache Software Foundation (http://www.apache.org/).
+
+In addition, this product includes:
+
+- JUnit (http://www.junit.org) is a testing framework for Java. We included it
+  under the terms of the Eclipse Public License v1.0.
+
+- JTransforms (https://sites.google.com/site/piotrwendykier/software/jtransforms)
+  provides fast transforms in Java. It is tri-licensed, and we included it under 
+  the terms of the Mozilla Public License v1.1.

examples/src/main/java/org/apache/spark/mllib/examples/JavaKMeans.java

@@ -17,32 +17,33 @@
 
 package org.apache.spark.mllib.examples;
 
+import java.util.regex.Pattern;
+
 import org.apache.spark.api.java.JavaRDD;
 import org.apache.spark.api.java.JavaSparkContext;
 import org.apache.spark.api.java.function.Function;
 
 import org.apache.spark.mllib.clustering.KMeans;
 import org.apache.spark.mllib.clustering.KMeansModel;
-
-import java.util.Arrays;
-import java.util.regex.Pattern;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
 
 /**
  * Example using MLLib KMeans from Java.
  */
 public final class JavaKMeans {
 
-  static class ParsePoint implements Function<String, double[]> {
+  private static class ParsePoint implements Function<String, Vector> {
     private static final Pattern SPACE = Pattern.compile(" ");
 
     @Override
-    public double[] call(String line) {
+    public Vector call(String line) {
       String[] tok = SPACE.split(line);
       double[] point = new double[tok.length];
       for (int i = 0; i < tok.length; ++i) {
         point[i] = Double.parseDouble(tok[i]);
       }
-      return point;
+      return Vectors.dense(point);
     }
   }
 
@@ -65,15 +66,15 @@ public static void main(String[] args) {
 
     JavaSparkContext sc = new JavaSparkContext(args[0], "JavaKMeans",
         System.getenv("SPARK_HOME"), JavaSparkContext.jarOfClass(JavaKMeans.class));
-    JavaRDD<String> lines = sc.textFile(args[1]);
+    JavaRDD<String> lines = sc.textFile(inputFile);
 
-    JavaRDD<double[]> points = lines.map(new ParsePoint());
+    JavaRDD<Vector> points = lines.map(new ParsePoint());
 
-    KMeansModel model = KMeans.train(points.rdd(), k, iterations, runs);
+    KMeansModel model = KMeans.train(points.rdd(), k, iterations, runs, KMeans.K_MEANS_PARALLEL());
 
     System.out.println("Cluster centers:");
-    for (double[] center : model.clusterCenters()) {
-      System.out.println(" " + Arrays.toString(center));
+    for (Vector center : model.clusterCenters()) {
+      System.out.println(" " + center);
     }
     double cost = model.computeCost(points.rdd());
     System.out.println("Cost: " + cost);

mllib/pom.xml

@@ -60,6 +60,11 @@
       <artifactId>jblas</artifactId>
       <version>1.2.3</version>
     </dependency>
+    <dependency>
+      <groupId>org.scalanlp</groupId>
+      <artifactId>breeze_${scala.binary.version}</artifactId>
+      <version>0.7</version>
+    </dependency>
     <dependency>
       <groupId>org.scalatest</groupId>
       <artifactId>scalatest_${scala.binary.version}</artifactId>

mllib/src/main/scala/org/apache/spark/mllib/api/python/PythonMLLibAPI.scala

@@ -16,14 +16,16 @@
  */
 
 package org.apache.spark.mllib.api.python
+
+import java.nio.{ByteBuffer, ByteOrder}
+
 import org.apache.spark.api.java.JavaRDD
-import org.apache.spark.mllib.regression._
 import org.apache.spark.mllib.classification._
 import org.apache.spark.mllib.clustering._
+import org.apache.spark.mllib.linalg.Vectors
 import org.apache.spark.mllib.recommendation._
+import org.apache.spark.mllib.regression._
 import org.apache.spark.rdd.RDD
-import java.nio.ByteBuffer
-import java.nio.ByteOrder
 
 /**
  * The Java stubs necessary for the Python mllib bindings.
@@ -205,10 +207,10 @@ class PythonMLLibAPI extends Serializable {
   def trainKMeansModel(dataBytesJRDD: JavaRDD[Array[Byte]], k: Int,
       maxIterations: Int, runs: Int, initializationMode: String):
       java.util.List[java.lang.Object] = {
-    val data = dataBytesJRDD.rdd.map(xBytes => deserializeDoubleVector(xBytes))
+    val data = dataBytesJRDD.rdd.map(xBytes => Vectors.dense(deserializeDoubleVector(xBytes)))
     val model = KMeans.train(data, k, maxIterations, runs, initializationMode)
     val ret = new java.util.LinkedList[java.lang.Object]()
-    ret.add(serializeDoubleMatrix(model.clusterCenters))
+    ret.add(serializeDoubleMatrix(model.clusterCenters.map(_.toArray)))
     ret
   }