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k-均值聚類（Kmeans）算法是非常基礎且被大量使用的聚類算法。

算法基本原理：以空間中k個點為中心進行聚類，對最靠近它們的點進行歸類。通過迭代的方法，逐次更新各聚類中心的值，直至得到最好的聚類結果。

將樣本集分為k個類別的算法描述如下：

適當選擇k個類的初始中心。
在第i次迭代中，對任意一個樣本，求其到k個中心的距離，將該樣本歸到距離最短的中心所在的類。
利用均值等方法更新該類的中心值。
對于所有的k個聚類中心，如果利用上兩步的迭代法更新后，值保持不變或者小于某個閾值，則迭代結束，否則繼續迭代。

代碼示例

K-均值聚類算法的代碼，如下所示。

import java.io.DataInput;
import java.io.DataOutput;
import java.io.IOException;

import org.apache.log4j.Logger;

import com.aliyun.odps.io.WritableRecord;
import com.aliyun.odps.graph.Aggregator;
import com.aliyun.odps.graph.ComputeContext;
import com.aliyun.odps.graph.GraphJob;
import com.aliyun.odps.graph.GraphLoader;
import com.aliyun.odps.graph.MutationContext;
import com.aliyun.odps.graph.Vertex;
import com.aliyun.odps.graph.WorkerContext;
import com.aliyun.odps.io.DoubleWritable;
import com.aliyun.odps.io.LongWritable;
import com.aliyun.odps.io.NullWritable;
import com.aliyun.odps.data.TableInfo;
import com.aliyun.odps.io.Text;
import com.aliyun.odps.io.Tuple;
import com.aliyun.odps.io.Writable;

public class Kmeans {
  private final static Logger LOG = Logger.getLogger(Kmeans.class);

  public static class KmeansVertex extends
      Vertex<Text, Tuple, NullWritable, NullWritable> {

    @Override
    public void compute(
        ComputeContext<Text, Tuple, NullWritable, NullWritable> context,
        Iterable<NullWritable> messages) throws IOException {
      context.aggregate(getValue());
    }

  }

  public static class KmeansVertexReader extends
      GraphLoader<Text, Tuple, NullWritable, NullWritable> {
    @Override
    public void load(LongWritable recordNum, WritableRecord record,
        MutationContext<Text, Tuple, NullWritable, NullWritable> context)
        throws IOException {
      KmeansVertex vertex = new KmeansVertex();
      vertex.setId(new Text(String.valueOf(recordNum.get())));
      vertex.setValue(new Tuple(record.getAll()));
      context.addVertexRequest(vertex);
    }

  }

  public static class KmeansAggrValue implements Writable {

    Tuple centers = new Tuple();
    Tuple sums = new Tuple();
    Tuple counts = new Tuple();

    @Override
    public void write(DataOutput out) throws IOException {
      centers.write(out);
      sums.write(out);
      counts.write(out);
    }

    @Override
    public void readFields(DataInput in) throws IOException {
      centers = new Tuple();
      centers.readFields(in);
      sums = new Tuple();
      sums.readFields(in);
      counts = new Tuple();
      counts.readFields(in);
    }

    @Override
    public String toString() {
      return "centers " + centers.toString() + ", sums " + sums.toString()
          + ", counts " + counts.toString();
    }

  }

  public static class KmeansAggregator extends Aggregator<KmeansAggrValue> {

    @SuppressWarnings("rawtypes")
    @Override
    public KmeansAggrValue createInitialValue(WorkerContext context)
        throws IOException {
      KmeansAggrValue aggrVal = null;
      if (context.getSuperstep() == 0) {
        aggrVal = new KmeansAggrValue();
        aggrVal.centers = new Tuple();
        aggrVal.sums = new Tuple();
        aggrVal.counts = new Tuple();

        byte[] centers = context.readCacheFile("centers");
        String lines[] = new String(centers).split("\n");

        for (int i = 0; i < lines.length; i++) {
          String[] ss = lines[i].split(",");
          Tuple center = new Tuple();
          Tuple sum = new Tuple();
          for (int j = 0; j < ss.length; ++j) {
            center.append(new DoubleWritable(Double.valueOf(ss[j].trim())));
            sum.append(new DoubleWritable(0.0));
          }
          LongWritable count = new LongWritable(0);
          aggrVal.sums.append(sum);
          aggrVal.counts.append(count);
          aggrVal.centers.append(center);
        }
      } else {
        aggrVal = (KmeansAggrValue) context.getLastAggregatedValue(0);
      }

      return aggrVal;
    }

    @Override
    public void aggregate(KmeansAggrValue value, Object item) {
      int min = 0;
      double mindist = Double.MAX_VALUE;
      Tuple point = (Tuple) item;

      for (int i = 0; i < value.centers.size(); i++) {
        Tuple center = (Tuple) value.centers.get(i);
        // use Euclidean Distance, no need to calculate sqrt
        double dist = 0.0d;
        for (int j = 0; j < center.size(); j++) {
          double v = ((DoubleWritable) point.get(j)).get()
              - ((DoubleWritable) center.get(j)).get();
          dist += v * v;
        }
        if (dist < mindist) {
          mindist = dist;
          min = i;
        }
      }

      // update sum and count
      Tuple sum = (Tuple) value.sums.get(min);
      for (int i = 0; i < point.size(); i++) {
        DoubleWritable s = (DoubleWritable) sum.get(i);
        s.set(s.get() + ((DoubleWritable) point.get(i)).get());
      }
      LongWritable count = (LongWritable) value.counts.get(min);
      count.set(count.get() + 1);
    }

    @Override
    public void merge(KmeansAggrValue value, KmeansAggrValue partial) {
      for (int i = 0; i < value.sums.size(); i++) {
        Tuple sum = (Tuple) value.sums.get(i);
        Tuple that = (Tuple) partial.sums.get(i);
        for (int j = 0; j < sum.size(); j++) {
          DoubleWritable s = (DoubleWritable) sum.get(j);
          s.set(s.get() + ((DoubleWritable) that.get(j)).get());
        }
      }

      for (int i = 0; i < value.counts.size(); i++) {
        LongWritable count = (LongWritable) value.counts.get(i);
        count.set(count.get() + ((LongWritable) partial.counts.get(i)).get());
      }
    }

    @SuppressWarnings("rawtypes")
    @Override
    public boolean terminate(WorkerContext context, KmeansAggrValue value)
        throws IOException {

      // compute new centers
      Tuple newCenters = new Tuple(value.sums.size());
      for (int i = 0; i < value.sums.size(); i++) {
        Tuple sum = (Tuple) value.sums.get(i);
        Tuple newCenter = new Tuple(sum.size());
        LongWritable c = (LongWritable) value.counts.get(i);
        for (int j = 0; j < sum.size(); j++) {

          DoubleWritable s = (DoubleWritable) sum.get(j);
          double val = s.get() / c.get();
          newCenter.set(j, new DoubleWritable(val));

          // reset sum for next iteration
          s.set(0.0d);
        }
        // reset count for next iteration
        c.set(0);
        newCenters.set(i, newCenter);
      }

      // update centers
      Tuple oldCenters = value.centers;
      value.centers = newCenters;

      LOG.info("old centers: " + oldCenters + ", new centers: " + newCenters);

      // compare new/old centers
      boolean converged = true;
      for (int i = 0; i < value.centers.size() && converged; i++) {
        Tuple oldCenter = (Tuple) oldCenters.get(i);
        Tuple newCenter = (Tuple) newCenters.get(i);
        double sum = 0.0d;
        for (int j = 0; j < newCenter.size(); j++) {
          double v = ((DoubleWritable) newCenter.get(j)).get()
              - ((DoubleWritable) oldCenter.get(j)).get();
          sum += v * v;
        }
        double dist = Math.sqrt(sum);
        LOG.info("old center: " + oldCenter + ", new center: " + newCenter
            + ", dist: " + dist);
        // converge threshold for each center: 0.05
        converged = dist < 0.05d;
      }

      if (converged || context.getSuperstep() == context.getMaxIteration() - 1) {
        // converged or reach max iteration, output centers
        for (int i = 0; i < value.centers.size(); i++) {
          context.write(((Tuple) value.centers.get(i)).toArray());
        }
        // true means to terminate iteration
        return true;
      }

      // false means to continue iteration
      return false;
    }
  }

  private static void printUsage() {
    System.out.println("Usage: <in> <out> [Max iterations (default 30)]");
    System.exit(-1);
  }

  public static void main(String[] args) throws IOException {
    if (args.length < 2)
      printUsage();

    GraphJob job = new GraphJob();

    job.setGraphLoaderClass(KmeansVertexReader.class);
    job.setRuntimePartitioning(false);
    job.setVertexClass(KmeansVertex.class);
    job.setAggregatorClass(KmeansAggregator.class);
    job.addInput(TableInfo.builder().tableName(args[0]).build());
    job.addOutput(TableInfo.builder().tableName(args[1]).build());

    // default max iteration is 30
    job.setMaxIteration(30);
    if (args.length >= 3)
      job.setMaxIteration(Integer.parseInt(args[2]));

    long start = System.currentTimeMillis();
    job.run();
    System.out.println("Job Finished in "
        + (System.currentTimeMillis() - start) / 1000.0 + " seconds");
  }
}

上述代碼說明如下：

第26行：定義KmeansVertex類，compute()方法非常簡單，只是調用上下文對象的aggregate方法，傳入當前點的取值（Tuple類型，向量表示）。
第38行：定義KmeansVertexReader類，加載圖，將表中每一條記錄解析為一個點，點標識無關緊要，這里取傳入的recordNum序號作為標識，點值為記錄的所有列組成的Tuple。
第83行：定義KmeansAggregator類，這個類封裝了Kmeans算法的主要邏輯，其中：
- createInitialValue為每一輪迭代創建的初始值（k類中心點）。如果是第一輪迭代（superstep=0），該取值為初始中心點，否則取值為上一輪結束時的新中心點。
- aggregate方法為每個點計算其到各個類中心的距離，并歸為距離最短的類，并更新該類的sum和count。
- merge方法合并來自各個Worker收集的sum和count。
- terminate方法根據各個類的sum和count計算新的中心點。如果新中心點與之前的中心點距離小于某個閾值或者迭代次數到達最大迭代次數設置，則終止迭代（返回False），寫最終的中心點到結果表。
第236行：主程序（main函數），定義GraphJob類，指定Vertex、GraphLoader、Aggregator等的實現，以及最大迭代次數（默認30），并指定輸入輸出表。
第243行：job.setRuntimePartitioning(false)，對于Kmeans算法，加載圖不需要進行點的分發。設置RuntimePartitioning為False，以提升加載圖時的性能。

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代碼示例