/**
* 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.mahout.clustering.spectral.eigencuts;
import java.util.List;
import java.util.Map;
import com.google.common.collect.Lists;
import com.google.common.collect.Maps;
import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.fs.Path;
import org.apache.hadoop.io.IntWritable;
import org.apache.hadoop.io.Text;
import org.apache.hadoop.mapreduce.Mapper;
import org.apache.hadoop.mapreduce.Reducer;
import org.apache.mahout.clustering.spectral.common.VertexWritable;
import org.apache.mahout.clustering.spectral.eigencuts.EigencutsAffinityCutsJob.EigencutsAffinityCutsCombiner;
import org.apache.mahout.clustering.spectral.eigencuts.EigencutsAffinityCutsJob.EigencutsAffinityCutsMapper;
import org.apache.mahout.clustering.spectral.eigencuts.EigencutsAffinityCutsJob.EigencutsAffinityCutsReducer;
import org.apache.mahout.common.DummyRecordWriter;
import org.apache.mahout.common.MahoutTestCase;
import org.apache.mahout.math.DenseVector;
import org.apache.mahout.math.Vector;
import org.apache.mahout.math.VectorWritable;
import org.junit.Test;
/**
* <p>Tests the Eigencuts affinity matrix "cut" ability, the core functionality
* of the algorithm responsible for making the clusterings.</p>
*
* <p>Due to the complexity of this section, and the amount of data required,
* there are three steps: the mapper essentially reads in the affinity/cut
* matrices and creating "vertices" of points, the combiner performs the
* actual checks on the sensitivities and zeroes out the necessary affinities,
* and at last the reducer reforms the affinity matrix.</p>
*/
public class TestEigencutsAffinityCutsJob extends MahoutTestCase {
private final double [][] affinity = { {0, 10, 2, 1}, {10, 0, 2, 2},
{2, 2, 0, 10}, {1, 2, 10, 0} };
private final double [][] sensitivity = { {0, 0, 1, 1}, {0, 0, 1, 1},
{1, 1, 0, 0}, {1, 1, 0, 0} };
/**
* Testing the mapper is fairly straightforward: there are two matrices
* to be processed simultaneously (cut matrix of sensitivities, and the
* affinity matrix), and since both are symmetric, two entries from each
* will be grouped together with the same key (or, in the case of an
* entry along the diagonal, only two entries).
*
* The correct grouping of these quad or pair vertices is the only
* output of the mapper.
*
* @throws Exception
*/
@Test
public void testEigencutsAffinityCutsMapper() throws Exception {
EigencutsAffinityCutsMapper mapper = new EigencutsAffinityCutsMapper();
Configuration conf = new Configuration();
conf.setInt(EigencutsKeys.AFFINITY_DIMENSIONS, this.affinity.length);
// set up the writer
DummyRecordWriter<Text, VertexWritable> writer =
new DummyRecordWriter<Text, VertexWritable>();
Mapper<IntWritable, VectorWritable, Text, VertexWritable>.Context context =
DummyRecordWriter.build(mapper, conf, writer);
// perform the maps
for (int i = 0; i < this.affinity.length; i++) {
VectorWritable aff = new VectorWritable(new DenseVector(this.affinity[i]));
VectorWritable sens = new VectorWritable(new DenseVector(this.sensitivity[i]));
IntWritable key = new IntWritable(i);
mapper.map(key, aff, context);
mapper.map(key, sens, context);
}
// were the vertices constructed correctly? if so, then for two 4x4
// matrices, there should be 10 unique keys with 56 total entries
assertEquals("Number of keys", 10, writer.getKeys().size());
for (int i = 0; i < this.affinity.length; i++) {
for (int j = 0; j < this.affinity.length; j++) {
Text key = new Text(Math.max(i, j) + "_" + Math.min(i,j));
List<VertexWritable> values = writer.getValue(key);
// if we're on a diagonal, there should only be 2 entries
// otherwise, there should be 4
if (i == j) {
assertEquals("Diagonal entry", 2, values.size());
for (VertexWritable v : values) {
assertFalse("Diagonal values are zero", v.getValue() > 0);
}
} else {
assertEquals("Off-diagonal entry", 4, values.size());
if (i + j == 3) { // all have values greater than 0
for (VertexWritable v : values) {
assertTrue("Off-diagonal non-zero entries", v.getValue() > 0);
}
}
}
}
}
}
/**
* This is by far the trickiest step. However, an easy condition is if
* we have only two vertices - indicating vertices on the diagonal of the
* two matrices - then we simply exit (since the algorithm does not operate
* on the diagonal; it makes no sense to perform cuts by isolating data
* points from themselves).
*
* If there are four points, then first we must separate the two which
* belong to the affinity matrix from the two that are sensitivities. In theory,
* each pair should have exactly the same value (symmetry). If the sensitivity
* is below a certain threshold, then we set the two values of the affinity
* matrix to 0 (but not before adding the affinity values to the diagonal, so
* as to maintain the overall sum of the row of the affinity matrix).
*
* @throws Exception
*/
@Test
public void testEigencutsAffinityCutsCombiner() throws Exception {
Configuration conf = new Configuration();
Path affinity = new Path("affinity");
Path sensitivity = new Path("sensitivity");
conf.set(EigencutsKeys.AFFINITY_PATH, affinity.getName());
conf.setInt(EigencutsKeys.AFFINITY_DIMENSIONS, this.affinity.length);
// since we need the working paths to distinguish the vertex types,
// we can't use the mapper (since we have no way of manually setting
// the Context.workingPath() )
Map<Text, List<VertexWritable>> data = buildMapData(affinity, sensitivity, this.sensitivity);
// now, set up the combiner
EigencutsAffinityCutsCombiner combiner = new EigencutsAffinityCutsCombiner();
DummyRecordWriter<Text, VertexWritable> redWriter =
new DummyRecordWriter<Text, VertexWritable>();
Reducer<Text, VertexWritable, Text, VertexWritable>.Context
redContext = DummyRecordWriter.build(combiner, conf, redWriter, Text.class,
VertexWritable.class);
// perform the combining
for (Map.Entry<Text, List<VertexWritable>> entry : data.entrySet()) {
combiner.reduce(entry.getKey(), entry.getValue(), redContext);
}
// test the number of cuts, there should be 2
assertEquals("Number of cuts detected", 4,
redContext.getCounter(EigencutsAffinityCutsJob.CUTSCOUNTER.NUM_CUTS).getValue());
// loop through all the results; let's see if they match up to our
// affinity matrix (and all the cuts appear where they should
Map<Text, List<VertexWritable>> results = redWriter.getData();
for (Map.Entry<Text, List<VertexWritable>> entry : results.entrySet()) {
List<VertexWritable> row = entry.getValue();
IntWritable key = new IntWritable(Integer.parseInt(entry.getKey().toString()));
double calcDiag = 0.0;
double trueDiag = sumOfRowCuts(key.get(), this.sensitivity);
for (VertexWritable e : row) {
// should the value have been cut, e.g. set to 0?
if (key.get() == e.getCol()) {
// we have our diagonal
calcDiag += e.getValue();
} else if (this.sensitivity[key.get()][e.getCol()] == 0.0) {
// no, corresponding affinity should have same value as before
assertEquals("Preserved affinity value",
this.affinity[key.get()][e.getCol()], e.getValue(),EPSILON);
} else {
// yes, corresponding affinity value should be 0
assertEquals("Cut affinity value", 0.0, e.getValue(),EPSILON);
}
}
// check the diagonal has the correct sum
assertEquals("Diagonal sum from cuts", trueDiag, calcDiag,EPSILON);
}
}
/**
* Fairly straightforward: the task here is to reassemble the rows of the
* affinity matrix. The tricky part is that any specific element in the list
* of elements which does NOT lay on the diagonal will be so because it
* did not drop below the sensitivity threshold, hence it was not "cut".
*
* On the flip side, there will be many entries whose coordinate is now
* set to the diagonal, indicating they were previously affinity entries
* whose sensitivities were below the threshold, and hence were "cut" -
* set to 0 at their original coordinates, and had their values added to
* the diagonal entry (hence the numerous entries with the coordinate of
* the diagonal).
*
* @throws Exception
*/
@Test
public void testEigencutsAffinityCutsReducer() throws Exception {
Configuration conf = new Configuration();
Path affinity = new Path("affinity");
Path sensitivity = new Path("sensitivity");
conf.set(EigencutsKeys.AFFINITY_PATH, affinity.getName());
conf.setInt(EigencutsKeys.AFFINITY_DIMENSIONS, this.affinity.length);
// since we need the working paths to distinguish the vertex types,
// we can't use the mapper (since we have no way of manually setting
// the Context.workingPath() )
Map<Text, List<VertexWritable>> data = buildMapData(affinity, sensitivity, this.sensitivity);
// now, set up the combiner
EigencutsAffinityCutsCombiner combiner = new EigencutsAffinityCutsCombiner();
DummyRecordWriter<Text, VertexWritable> comWriter =
new DummyRecordWriter<Text, VertexWritable>();
Reducer<Text, VertexWritable, Text, VertexWritable>.Context
comContext = DummyRecordWriter.build(combiner, conf, comWriter, Text.class,
VertexWritable.class);
// perform the combining
for (Map.Entry<Text, List<VertexWritable>> entry : data.entrySet()) {
combiner.reduce(entry.getKey(), entry.getValue(), comContext);
}
// finally, set up the reduction writers
EigencutsAffinityCutsReducer reducer = new EigencutsAffinityCutsReducer();
DummyRecordWriter<IntWritable, VectorWritable> redWriter = new
DummyRecordWriter<IntWritable, VectorWritable>();
Reducer<Text, VertexWritable, IntWritable, VectorWritable>.Context
redContext = DummyRecordWriter.build(reducer, conf, redWriter,
Text.class, VertexWritable.class);
// perform the reduction
for (Text key : comWriter.getKeys()) {
reducer.reduce(key, comWriter.getValue(key), redContext);
}
// now, check that the affinity matrix is correctly formed
for (IntWritable row : redWriter.getKeys()) {
List<VectorWritable> results = redWriter.getValue(row);
// there should only be 1 vector
assertEquals("Only one vector with a given row number", 1, results.size());
Vector therow = results.get(0).get();
for (Vector.Element e : therow) {
// check the diagonal
if (row.get() == e.index()) {
assertEquals("Correct diagonal sum of cuts", sumOfRowCuts(row.get(),
this.sensitivity), e.get(),EPSILON);
} else {
// not on the diagonal...if it was an element labeled to be cut,
// it should have a value of 0. Otherwise, it should have kept its
// previous value
if (this.sensitivity[row.get()][e.index()] == 0.0) {
// should be what it was originally
assertEquals("Preserved element", this.affinity[row.get()][e.index()], e.get(), EPSILON);
} else {
// should be 0
assertEquals("Cut element", 0.0, e.get(), EPSILON);
}
}
}
}
}
/**
* Utility method for simulating the Mapper behavior.
* @param affinity
* @param sensitivity
* @param array
* @return
*/
private Map<Text, List<VertexWritable>> buildMapData(Path affinity,
Path sensitivity, double [][] array) {
Map<Text, List<VertexWritable>> map = Maps.newHashMap();
for (int i = 0; i < this.affinity.length; i++) {
for (int j = 0; j < this.affinity[i].length; j++) {
Text key = new Text(Math.max(i, j) + "_" + Math.min(i, j));
List<VertexWritable> toAdd = Lists.newArrayList();
if (map.containsKey(key)) {
toAdd = map.get(key);
map.remove(key);
}
toAdd.add(new VertexWritable(i, j, this.affinity[i][j], affinity.getName()));
toAdd.add(new VertexWritable(i, j, array[i][j], sensitivity.getName()));
map.put(key, toAdd);
}
}
return map;
}
/**
* Utility method for calculating the new diagonal on the specified row of the
* affinity matrix after a single iteration, given the specified cut matrix
* @param row
* @param cuts
* @return
*/
private double sumOfRowCuts(int row, double [][] cuts) {
double retval = 0.0;
for (int j = 0; j < this.affinity[row].length; j++) {
if (cuts[row][j] != 0.0) {
retval += this.affinity[row][j];
}
}
return retval;
}
}