[SPARK-6517][MLLIB] Implement the Algorithm of Hierarchical Clustering

I implemented a hierarchical clustering algorithm again.  This PR doesn't include examples, documentation and spark.ml APIs. I am going to send another PRs later.
https://issues.apache.org/jira/browse/SPARK-6517

- This implementation based on a bi-sectiong K-means clustering.
    - It derives from the freeman-lab 's implementation
- The basic idea is not changed from the previous version. (#2906)
    - However, It is 1000x faster than the previous version through parallel processing.

Thank you for your great cooperation, RJ Nowling(rnowling), Jeremy Freeman(freeman-lab), Xiangrui Meng(mengxr) and Sean Owen(srowen).

Author: Yu ISHIKAWA <yuu.ishikawa@gmail.com>
Author: Xiangrui Meng <meng@databricks.com>
Author: Yu ISHIKAWA <yu-iskw@users.noreply.github.com>

Closes #5267 from yu-iskw/new-hierarchical-clustering.

1 files changed, 182 insertions, 0 deletions

diff --git a/mllib/src/test/scala/org/apache/spark/mllib/clustering/BisectingKMeansSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/clustering/BisectingKMeansSuite.scala
new file mode 100644
index 0000000000..41b9d5c0d9
--- /dev/null
+++ b/mllib/src/test/scala/org/apache/spark/mllib/clustering/BisectingKMeansSuite.scala
@@ -0,0 +1,182 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.mllib.clustering
+
+import org.apache.spark.SparkFunSuite
+import org.apache.spark.mllib.linalg.Vectors
+import org.apache.spark.mllib.util.MLlibTestSparkContext
+import org.apache.spark.mllib.util.TestingUtils._
+
+class BisectingKMeansSuite extends SparkFunSuite with MLlibTestSparkContext {
+
+  test("default values") {
+    val bkm0 = new BisectingKMeans()
+    assert(bkm0.getK === 4)
+    assert(bkm0.getMaxIterations === 20)
+    assert(bkm0.getMinDivisibleClusterSize === 1.0)
+    val bkm1 = new BisectingKMeans()
+    assert(bkm0.getSeed === bkm1.getSeed, "The default seed should be constant.")
+  }
+
+  test("setter/getter") {
+    val bkm = new BisectingKMeans()
+
+    val k = 10
+    assert(bkm.getK !== k)
+    assert(bkm.setK(k).getK === k)
+    val maxIter = 100
+    assert(bkm.getMaxIterations !== maxIter)
+    assert(bkm.setMaxIterations(maxIter).getMaxIterations === maxIter)
+    val minSize = 2.0
+    assert(bkm.getMinDivisibleClusterSize !== minSize)
+    assert(bkm.setMinDivisibleClusterSize(minSize).getMinDivisibleClusterSize === minSize)
+    val seed = 10L
+    assert(bkm.getSeed !== seed)
+    assert(bkm.setSeed(seed).getSeed === seed)
+
+    intercept[IllegalArgumentException] {
+      bkm.setK(0)
+    }
+    intercept[IllegalArgumentException] {
+      bkm.setMaxIterations(0)
+    }
+    intercept[IllegalArgumentException] {
+      bkm.setMinDivisibleClusterSize(0.0)
+    }
+  }
+
+  test("1D data") {
+    val points = Vectors.sparse(1, Array.empty, Array.empty) +:
+      (1 until 8).map(i => Vectors.dense(i))
+    val data = sc.parallelize(points, 2)
+    val bkm = new BisectingKMeans()
+      .setK(4)
+      .setMaxIterations(1)
+      .setSeed(1L)
+    // The clusters should be
+    // (0, 1, 2, 3, 4, 5, 6, 7)
+    //   - (0, 1, 2, 3)
+    //     - (0, 1)
+    //     - (2, 3)
+    //   - (4, 5, 6, 7)
+    //     - (4, 5)
+    //     - (6, 7)
+    val model = bkm.run(data)
+    assert(model.k === 4)
+    // The total cost should be 8 * 0.5 * 0.5 = 2.0.
+    assert(model.computeCost(data) ~== 2.0 relTol 1e-12)
+    val predictions = data.map(v => (v(0), model.predict(v))).collectAsMap()
+    Range(0, 8, 2).foreach { i =>
+      assert(predictions(i) === predictions(i + 1),
+        s"$i and ${i + 1} should belong to the same cluster.")
+    }
+    val root = model.root
+    assert(root.center(0) ~== 3.5 relTol 1e-12)
+    assert(root.height ~== 2.0 relTol 1e-12)
+    assert(root.children.length === 2)
+    assert(root.children(0).height ~== 1.0 relTol 1e-12)
+    assert(root.children(1).height ~== 1.0 relTol 1e-12)
+  }
+
+  test("points are the same") {
+    val data = sc.parallelize(Seq.fill(8)(Vectors.dense(1.0, 1.0)), 2)
+    val bkm = new BisectingKMeans()
+      .setK(2)
+      .setMaxIterations(1)
+      .setSeed(1L)
+    val model = bkm.run(data)
+    assert(model.k === 1)
+  }
+
+  test("more desired clusters than points") {
+    val data = sc.parallelize(Seq.tabulate(4)(i => Vectors.dense(i)), 2)
+    val bkm = new BisectingKMeans()
+      .setK(8)
+      .setMaxIterations(2)
+      .setSeed(1L)
+    val model = bkm.run(data)
+    assert(model.k === 4)
+  }
+
+  test("min divisible cluster") {
+    val data = sc.parallelize(
+      Seq.tabulate(16)(i => Vectors.dense(i)) ++ Seq.tabulate(4)(i => Vectors.dense(-100.0 - i)),
+      2)
+    val bkm = new BisectingKMeans()
+      .setK(4)
+      .setMinDivisibleClusterSize(10)
+      .setMaxIterations(1)
+      .setSeed(1L)
+    val model = bkm.run(data)
+    assert(model.k === 3)
+    assert(model.predict(Vectors.dense(-100)) === model.predict(Vectors.dense(-97)))
+    assert(model.predict(Vectors.dense(7)) !== model.predict(Vectors.dense(8)))
+
+    bkm.setMinDivisibleClusterSize(0.5)
+    val sameModel = bkm.run(data)
+    assert(sameModel.k === 3)
+  }
+
+  test("larger clusters get selected first") {
+    val data = sc.parallelize(
+      Seq.tabulate(16)(i => Vectors.dense(i)) ++ Seq.tabulate(4)(i => Vectors.dense(-100.0 - i)),
+      2)
+    val bkm = new BisectingKMeans()
+      .setK(3)
+      .setMaxIterations(1)
+      .setSeed(1L)
+    val model = bkm.run(data)
+    assert(model.k === 3)
+    assert(model.predict(Vectors.dense(-100)) === model.predict(Vectors.dense(-97)))
+    assert(model.predict(Vectors.dense(7)) !== model.predict(Vectors.dense(8)))
+  }
+
+  test("2D data") {
+    val points = Seq(
+      (11, 10), (9, 10), (10, 9), (10, 11),
+      (11, -10), (9, -10), (10, -9), (10, -11),
+      (0, 1), (0, -1)
+    ).map { case (x, y) =>
+      if (x == 0) {
+        Vectors.sparse(2, Array(1), Array(y))
+      } else {
+        Vectors.dense(x, y)
+      }
+    }
+    val data = sc.parallelize(points, 2)
+    val bkm = new BisectingKMeans()
+      .setK(3)
+      .setMaxIterations(4)
+      .setSeed(1L)
+    val model = bkm.run(data)
+    assert(model.k === 3)
+    assert(model.root.center ~== Vectors.dense(8, 0) relTol 1e-12)
+    model.root.leafNodes.foreach { node =>
+      if (node.center(0) < 5) {
+        assert(node.size === 2)
+        assert(node.center ~== Vectors.dense(0, 0) relTol 1e-12)
+      } else if (node.center(1) > 0) {
+        assert(node.size === 4)
+        assert(node.center ~== Vectors.dense(10, 10) relTol 1e-12)
+      } else {
+        assert(node.size === 4)
+        assert(node.center ~== Vectors.dense(10, -10) relTol 1e-12)
+      }
+    }
+  }
+}