基于hadoop的推荐算法-mahout版

来源：互联网发布：js和java做验签编辑：程序博客网时间：2024/04/29 08:13

http://blackproof.iteye.com/blog/2110877

基于hadoop的推荐算法，讲其中mahout实现的基于项目的推荐算法

分为4步：

1.获得人-物用户矩阵

输入为所有人对物品的评价或关联

map端输出key为人，value为物品+倾好度

reeduce端输出key为人，vallue为多个物品+倾好度

2.获得物-物项目矩阵

输入为“用户矩阵”，讲每一行人-物数据中的物品做笛卡尔积，生产成物-物的关联

map端输出为key为物，value为关联度

reduce端输出key为物，value为多个物的关联度

（可以根据各种规则生成项目相似度矩阵表，此处算法带过）

修改：

求项目相似矩阵是基于项目的协同过滤算法的核心

公式有很多种，核心是物品i和物品j相关用户的交集与并集的商

mahout使用的公式是1.dot(i,j) = sum(Pi(u)*Pi(u))

2.norms(i) = sum(Pi(u)^2)

3.simi(i,j) = 1/(1+(norms(i)-2*dot(i,j)+noorm(i))^1/2)

mahout的实现方法是

第一个job，用物品-人的矩阵，求得norms，即物品的用户平方和，输出是物-norms

第二个job，Map：用人-物的矩阵，求Pi(u)*Pi(u),即相同用户的物品的评价的乘机，输出物-多个对端物品的Pi(u)*Pi(u)

Reduce：用物-多个对端物品的Pi(u)*Pi(u)和物-norms，求得物品的相似矩阵（因为这个时候可以汇总所有和这个物品相关的物品的dot）

第三个job，补全物品的相似矩阵

3.获得用户-项目相似矩阵

输入为人-物用户矩阵和物-物项目矩阵

Map端输出key为物，value为类VectorOrPrefWritable，是包含物与人的倾好度，或是物与物的相似度

reduce端输出key为物，value为类VectorAndPrefWritable,是汇总当个物品到所有人的倾好度和到所有物品的相似度

4.获得用户推荐矩阵

输入为VectorAndPrefWritable

Map端输出为key：人，value：物+系数（map端根据单个物品贡献的系数生成推荐系数，也就是人到物品A的倾好度*物品A到其他物品的相似度）

reduce端输出为key：人，，value：推荐项目+系数（reduce端使用自定公式，汇总所有单物品贡献的四叔，求人到其他项目的倾好度，取topn作为当前用户的推荐项目）

再在这里贴几个mahout推荐算法分析的帖子：

http://eric-gcm.iteye.com/blog/1817822

http://eric-gcm.iteye.com/blog/1818033

http://eric-gcm.iteye.com/blog/1820060

以下是mahout代码：

ItemSimilarityJob类是mahout使用hadoop做推荐引擎的主要实现类，下面开始分析。

run()函数是启动函数：

Java代码  
public final class RecommenderJob extends AbstractJob {  
  
  public static final String BOOLEAN_DATA = "booleanData";  
  
  private static final int DEFAULT_MAX_SIMILARITIES_PER_ITEM = 100;  
  private static final int DEFAULT_MAX_PREFS_PER_USER = 1000;  
  private static final int DEFAULT_MIN_PREFS_PER_USER = 1;  
  
  @Override  
  public int run(String[] args) throws Exception {  
    //这里原来有大一堆代码，都是用来载入配置项，不用管它  
  
    //第一步：准备矩阵，将原始数据转换为一个矩阵，在PreparePreferenceMatrixJob这个类中完成  
    if (shouldRunNextPhase(parsedArgs, currentPhase)) {  
      ToolRunner.run(getConf(), new PreparePreferenceMatrixJob(), new String[]{  
              "--input", getInputPath().toString(),  
              "--output", prepPath.toString(),  
              "--maxPrefsPerUser", String.valueOf(maxPrefsPerUserInItemSimilarity),  
              "--minPrefsPerUser", String.valueOf(minPrefsPerUser),  
              "--booleanData", String.valueOf(booleanData),  
              "--tempDir", getTempPath().toString()});  
  
      numberOfUsers = HadoopUtil.readInt(new Path(prepPath, PreparePreferenceMatrixJob.NUM_USERS), getConf());  
    }  
  
    //第二步：计算协同矩阵  
    if (shouldRunNextPhase(parsedArgs, currentPhase)) {  
  
      /* special behavior if phase 1 is skipped */  
      if (numberOfUsers == -1) {  
        numberOfUsers = (int) HadoopUtil.countRecords(new Path(prepPath, PreparePreferenceMatrixJob.USER_VECTORS),  
                PathType.LIST, null, getConf());  
      }  
  
      /* Once DistributedRowMatrix uses the hadoop 0.20 API, we should refactor this call to something like 
       * new DistributedRowMatrix(...).rowSimilarity(...) */  
      //calculate the co-occurrence matrix  
      ToolRunner.run(getConf(), new RowSimilarityJob(), new String[]{  
              "--input", new Path(prepPath, PreparePreferenceMatrixJob.RATING_MATRIX).toString(),  
              "--output", similarityMatrixPath.toString(),  
              "--numberOfColumns", String.valueOf(numberOfUsers),  
              "--similarityClassname", similarityClassname,  
              "--maxSimilaritiesPerRow", String.valueOf(maxSimilaritiesPerItem),  
              "--excludeSelfSimilarity", String.valueOf(Boolean.TRUE),  
              "--threshold", String.valueOf(threshold),  
              "--tempDir", getTempPath().toString()});  
    }  
  
    //start the multiplication of the co-occurrence matrix by the user vectors  
    if (shouldRunNextPhase(parsedArgs, currentPhase)) {  
      Job prePartialMultiply1 = prepareJob(  
              similarityMatrixPath, prePartialMultiplyPath1, SequenceFileInputFormat.class,  
              SimilarityMatrixRowWrapperMapper.class, VarIntWritable.class, VectorOrPrefWritable.class,  
              Reducer.class, VarIntWritable.class, VectorOrPrefWritable.class,  
              SequenceFileOutputFormat.class);  
      boolean succeeded = prePartialMultiply1.waitForCompletion(true);  
      if (!succeeded)   
        return -1;  
      //continue the multiplication  
      Job prePartialMultiply2 = prepareJob(new Path(prepPath, PreparePreferenceMatrixJob.USER_VECTORS),  
              prePartialMultiplyPath2, SequenceFileInputFormat.class, UserVectorSplitterMapper.class, VarIntWritable.class,  
              VectorOrPrefWritable.class, Reducer.class, VarIntWritable.class, VectorOrPrefWritable.class,  
              SequenceFileOutputFormat.class);  
      if (usersFile != null) {  
        prePartialMultiply2.getConfiguration().set(UserVectorSplitterMapper.USERS_FILE, usersFile);  
      }  
      prePartialMultiply2.getConfiguration().setInt(UserVectorSplitterMapper.MAX_PREFS_PER_USER_CONSIDERED,  
              maxPrefsPerUser);  
      succeeded = prePartialMultiply2.waitForCompletion(true);  
      if (!succeeded)   
        return -1;  
      //finish the job  
      Job partialMultiply = prepareJob(  
              new Path(prePartialMultiplyPath1 + "," + prePartialMultiplyPath2), partialMultiplyPath,  
              SequenceFileInputFormat.class, Mapper.class, VarIntWritable.class, VectorOrPrefWritable.class,  
              ToVectorAndPrefReducer.class, VarIntWritable.class, VectorAndPrefsWritable.class,  
              SequenceFileOutputFormat.class);  
      setS3SafeCombinedInputPath(partialMultiply, getTempPath(), prePartialMultiplyPath1, prePartialMultiplyPath2);  
      succeeded = partialMultiply.waitForCompletion(true);  
      if (!succeeded)   
        return -1;  
    }  
  
    if (shouldRunNextPhase(parsedArgs, currentPhase)) {  
      //filter out any users we don't care about  
      /* convert the user/item pairs to filter if a filterfile has been specified */  
      if (filterFile != null) {  
        Job itemFiltering = prepareJob(new Path(filterFile), explicitFilterPath, TextInputFormat.class,  
                ItemFilterMapper.class, VarLongWritable.class, VarLongWritable.class,  
                ItemFilterAsVectorAndPrefsReducer.class, VarIntWritable.class, VectorAndPrefsWritable.class,  
                SequenceFileOutputFormat.class);  
        boolean succeeded = itemFiltering.waitForCompletion(true);  
        if (!succeeded)   
          return -1;  
      }  
  
      String aggregateAndRecommendInput = partialMultiplyPath.toString();  
      if (filterFile != null) {  
        aggregateAndRecommendInput += "," + explicitFilterPath;  
      }  
      //extract out the recommendations  
      Job aggregateAndRecommend = prepareJob(  
              new Path(aggregateAndRecommendInput), outputPath, SequenceFileInputFormat.class,  
              PartialMultiplyMapper.class, VarLongWritable.class, PrefAndSimilarityColumnWritable.class,  
              AggregateAndRecommendReducer.class, VarLongWritable.class, RecommendedItemsWritable.class,  
              TextOutputFormat.class);  
      Configuration aggregateAndRecommendConf = aggregateAndRecommend.getConfiguration();  
      if (itemsFile != null) {  
        aggregateAndRecommendConf.set(AggregateAndRecommendReducer.ITEMS_FILE, itemsFile);  
      }  
  
      if (filterFile != null) {  
        setS3SafeCombinedInputPath(aggregateAndRecommend, getTempPath(), partialMultiplyPath, explicitFilterPath);  
      }  
      setIOSort(aggregateAndRecommend);  
      aggregateAndRecommendConf.set(AggregateAndRecommendReducer.ITEMID_INDEX_PATH,  
              new Path(prepPath, PreparePreferenceMatrixJob.ITEMID_INDEX).toString());  
      aggregateAndRecommendConf.setInt(AggregateAndRecommendReducer.NUM_RECOMMENDATIONS, numRecommendations);  
      aggregateAndRecommendConf.setBoolean(BOOLEAN_DATA, booleanData);  
      boolean succeeded = aggregateAndRecommend.waitForCompletion(true);  
      if (!succeeded)   
        return -1;  
    }  
  
    return 0;  
  }  

第二步，计算协同矩阵，主要在RowSimilarityJob 这个类中完成

Java代码  
ToolRunner.run(getConf(), new RowSimilarityJob(), new String[]{  
              "--input", new Path(prepPath, PreparePreferenceMatrixJob.RATING_MATRIX).toString(),  
              "--output", similarityMatrixPath.toString(),  
              "--numberOfColumns", String.valueOf(numberOfUsers),  
              "--similarityClassname", similarityClassname,  
              "--maxSimilaritiesPerRow", String.valueOf(maxSimilaritiesPerItem),  
              "--excludeSelfSimilarity", String.valueOf(Boolean.TRUE),  
              "--threshold", String.valueOf(threshold),  
              "--tempDir", getTempPath().toString()});  
    }  

可以看到这个job的输入路径就是上一篇中，PreparePreferenceMatrixJob中最后一个reducer的输出路径。

下边详细分析RowSimilarityJob类的实现：

Java代码  
public class RowSimilarityJob extends AbstractJob {  
  
  
  @Override  
  public int run(String[] args) throws Exception {  
    //一大堆载入参数的代码，忽略  
      
    //第一个MapReduce  
    if (shouldRunNextPhase(parsedArgs, currentPhase)) {  
      Job normsAndTranspose = prepareJob(getInputPath(), weightsPath, VectorNormMapper.class, IntWritable.class,  
          VectorWritable.class, MergeVectorsReducer.class, IntWritable.class, VectorWritable.class);  
      normsAndTranspose.setCombinerClass(MergeVectorsCombiner.class);  
      Configuration normsAndTransposeConf = normsAndTranspose.getConfiguration();  
      normsAndTransposeConf.set(THRESHOLD, String.valueOf(threshold));  
      normsAndTransposeConf.set(NORMS_PATH, normsPath.toString());  
      normsAndTransposeConf.set(NUM_NON_ZERO_ENTRIES_PATH, numNonZeroEntriesPath.toString());  
      normsAndTransposeConf.set(MAXVALUES_PATH, maxValuesPath.toString());  
      normsAndTransposeConf.set(SIMILARITY_CLASSNAME, similarityClassname);  
      boolean succeeded = normsAndTranspose.waitForCompletion(true);  
      if (!succeeded) {  
        return -1;  
      }  
    }  
    //第二个MapReduce  
    if (shouldRunNextPhase(parsedArgs, currentPhase)) {  
      Job pairwiseSimilarity = prepareJob(weightsPath, pairwiseSimilarityPath, CooccurrencesMapper.class,  
          IntWritable.class, VectorWritable.class, SimilarityReducer.class, IntWritable.class, VectorWritable.class);  
      pairwiseSimilarity.setCombinerClass(VectorSumReducer.class);  
      Configuration pairwiseConf = pairwiseSimilarity.getConfiguration();  
      pairwiseConf.set(THRESHOLD, String.valueOf(threshold));  
      pairwiseConf.set(NORMS_PATH, normsPath.toString());  
      pairwiseConf.set(NUM_NON_ZERO_ENTRIES_PATH, numNonZeroEntriesPath.toString());  
      pairwiseConf.set(MAXVALUES_PATH, maxValuesPath.toString());  
      pairwiseConf.set(SIMILARITY_CLASSNAME, similarityClassname);  
      pairwiseConf.setInt(NUMBER_OF_COLUMNS, numberOfColumns);  
      pairwiseConf.setBoolean(EXCLUDE_SELF_SIMILARITY, excludeSelfSimilarity);  
      boolean succeeded = pairwiseSimilarity.waitForCompletion(true);  
      if (!succeeded) {  
        return -1;  
      }  
    }  
    //第三个MapReduce  
    if (shouldRunNextPhase(parsedArgs, currentPhase)) {  
      Job asMatrix = prepareJob(pairwiseSimilarityPath, getOutputPath(), UnsymmetrifyMapper.class,  
          IntWritable.class, VectorWritable.class, MergeToTopKSimilaritiesReducer.class, IntWritable.class,  
          VectorWritable.class);  
      asMatrix.setCombinerClass(MergeToTopKSimilaritiesReducer.class);  
      asMatrix.getConfiguration().setInt(MAX_SIMILARITIES_PER_ROW, maxSimilaritiesPerRow);  
      boolean succeeded = asMatrix.waitForCompletion(true);  
      if (!succeeded) {  
        return -1;  
      }  
    }  
  
    return 0;  
  }  

可以看到RowSimilityJob也是分成三个MapReduce过程：

1、Mapper ：VectorNormMapper类，输出 ( userid_index, <itemid_index, pref> )类型

Java代码  
public static class VectorNormMapper extends Mapper<IntWritable,VectorWritable,IntWritable,VectorWritable> {  
  
    @Override  
    protected void map(IntWritable row, VectorWritable vectorWritable, Context ctx)  
        throws IOException, InterruptedException {  
  
      Vector rowVector = similarity.normalize(vectorWritable.get());  
  
      int numNonZeroEntries = 0;  
      double maxValue = Double.MIN_VALUE;  
  
      Iterator<Vector.Element> nonZeroElements = rowVector.iterateNonZero();  
      while (nonZeroElements.hasNext()) {  
        Vector.Element element = nonZeroElements.next();  
        RandomAccessSparseVector partialColumnVector = new RandomAccessSparseVector(Integer.MAX_VALUE);  
        partialColumnVector.setQuick(row.get(), element.get());  
        //输出 ( userid_index, <itemid_index, pref> )类型  
        ctx.write(new IntWritable(element.index()), new VectorWritable(partialColumnVector));  
  
        numNonZeroEntries++;  
        if (maxValue < element.get()) {  
          maxValue = element.get();  
        }  
      }  
  
      if (threshold != NO_THRESHOLD) {  
        nonZeroEntries.setQuick(row.get(), numNonZeroEntries);  
        maxValues.setQuick(row.get(), maxValue);  
      }  
      norms.setQuick(row.get(), similarity.norm(rowVector));  
      //计算item的总数  
      ctx.getCounter(Counters.ROWS).increment(1);  
    }  
}  

Reduer : MergeVectorsReducer类，输入的是(userid_index, <itemid_index, pref>)，同一个userid_index在此进行合并，输出（ userid_index, vector<itemid_index, pref> )

Java代码  
  public static class MergeVectorsReducer extends Reducer<IntWritable,VectorWritable,IntWritable,VectorWritable> {  
  
    @Override  
    protected void reduce(IntWritable row, Iterable<VectorWritable> partialVectors, Context ctx)  
        throws IOException, InterruptedException {  
      Vector partialVector = Vectors.merge(partialVectors);  
  
      if (row.get() == NORM_VECTOR_MARKER) {  
        Vectors.write(partialVector, normsPath, ctx.getConfiguration());  
      } else if (row.get() == MAXVALUE_VECTOR_MARKER) {  
        Vectors.write(partialVector, maxValuesPath, ctx.getConfiguration());  
      } else if (row.get() == NUM_NON_ZERO_ENTRIES_VECTOR_MARKER) {  
        Vectors.write(partialVector, numNonZeroEntriesPath, ctx.getConfiguration(), true);  
      } else {  
        ctx.write(row, new VectorWritable(partialVector));  
      }  
    }  
  }  
}  

2、Mapper：CooccurrencesMapper类，对同一个userid_index下的vector<itemid_index ,pref>进行处理，

收集<item1, item2>对，输出为（ itemid_index, vector<itemid_index, value> ）

Java代码  
public static class CooccurrencesMapper extends Mapper<IntWritable,VectorWritable,IntWritable,VectorWritable> {  
  
    @Override  
    protected void map(IntWritable column, VectorWritable occurrenceVector, Context ctx)  
        throws IOException, InterruptedException {  
      Vector.Element[] occurrences = Vectors.toArray(occurrenceVector);  
      Arrays.sort(occurrences, BY_INDEX);  
  
      int cooccurrences = 0;  
      int prunedCooccurrences = 0;  
      for (int n = 0; n < occurrences.length; n++) {  
        Vector.Element occurrenceA = occurrences[n];  
        Vector dots = new RandomAccessSparseVector(Integer.MAX_VALUE);  
        for (int m = n; m < occurrences.length; m++) {  
          Vector.Element occurrenceB = occurrences[m];  
          if (threshold == NO_THRESHOLD || consider(occurrenceA, occurrenceB)) {  
            dots.setQuick(occurrenceB.index(), similarity.aggregate(occurrenceA.get(), occurrenceB.get()));  
            cooccurrences++;  
          } else {  
            prunedCooccurrences++;  
          }  
        }  
        ctx.write(new IntWritable(occurrenceA.index()), new VectorWritable(dots));  
      }  
      ctx.getCounter(Counters.COOCCURRENCES).increment(cooccurrences);  
      ctx.getCounter(Counters.PRUNED_COOCCURRENCES).increment(prunedCooccurrences);  
    }  
  }  

Reducer ：SimilarityReducer类，生成协同矩阵

Java代码  
public static class SimilarityReducer  
      extends Reducer<IntWritable,VectorWritable,IntWritable,VectorWritable> {  
  
    @Override  
    protected void reduce(IntWritable row, Iterable<VectorWritable> partialDots, Context ctx)  
        throws IOException, InterruptedException {  
      Iterator<VectorWritable> partialDotsIterator = partialDots.iterator();  
      //取一个vecotr作为该item的行向量  
      Vector dots = partialDotsIterator.next().get();  
      while (partialDotsIterator.hasNext()) {  
        Vector toAdd = partialDotsIterator.next().get();  
        Iterator<Vector.Element> nonZeroElements = toAdd.iterateNonZero();  
        while (nonZeroElements.hasNext()) {  
          Vector.Element nonZeroElement = nonZeroElements.next();  
          //nonZeroElement.index()为itemid，将另一个vecotr中itemid的value加进去  
          dots.setQuick(nonZeroElement.index(), dots.getQuick(nonZeroElement.index()) + nonZeroElement.get());  
        }  
      }  
      //最后得到的dots是协同矩阵中行号为row的一行，行中元素是item对其他的item的相似度  
      Vector similarities = dots.like();  
      double normA = norms.getQuick(row.get());  
      Iterator<Vector.Element> dotsWith = dots.iterateNonZero();  
      while (dotsWith.hasNext()) {  
        Vector.Element b = dotsWith.next();  
        double similarityValue = similarity.similarity(b.get(), normA, norms.getQuick(b.index()), numberOfColumns);  
        if (similarityValue >= treshold) {  
          similarities.set(b.index(), similarityValue);  
        }  
      }  
      if (excludeSelfSimilarity) {  
        similarities.setQuick(row.get(), 0);  
      }  
      ctx.write(row, new VectorWritable(similarities));  
    }  
  }  

3、Mapper：UnsymmetrifyMapper类，用来生成对称矩阵的。上一步得到的是非对称矩阵，首先将矩阵偏转，得到偏转矩阵，用原矩阵加上偏转矩阵，可以得到对称矩阵

Java代码  
public static class UnsymmetrifyMapper extends Mapper<IntWritable,VectorWritable,IntWritable,VectorWritable>  {  
  
    private int maxSimilaritiesPerRow;  
  
    @Override  
    protected void setup(Mapper.Context ctx) throws IOException, InterruptedException {  
      maxSimilaritiesPerRow = ctx.getConfiguration().getInt(MAX_SIMILARITIES_PER_ROW, 0);  
      Preconditions.checkArgument(maxSimilaritiesPerRow > 0, "Incorrect maximum number of similarities per row!");  
    }  
  
    @Override  
    protected void map(IntWritable row, VectorWritable similaritiesWritable, Context ctx)  
        throws IOException, InterruptedException {  
      Vector similarities = similaritiesWritable.get();  
      // For performance reasons moved transposedPartial creation out of the while loop and reusing the same vector  
      Vector transposedPartial = similarities.like();  
      TopK<Vector.Element> topKQueue = new TopK<Vector.Element>(maxSimilaritiesPerRow, Vectors.BY_VALUE);  
      Iterator<Vector.Element> nonZeroElements = similarities.iterateNonZero();  
      //这个地方用来生成偏转矩阵的，非对称矩阵，用原矩阵加上偏转矩阵，可以得到对称矩阵  
      while (nonZeroElements.hasNext()) {  
        Vector.Element nonZeroElement = nonZeroElements.next();  
        topKQueue.offer(new Vectors.TemporaryElement(nonZeroElement));  
          
        transposedPartial.setQuick(row.get(), nonZeroElement.get());  
        //偏转矩阵中的每一个元素  
        ctx.write(new IntWritable(nonZeroElement.index()), new VectorWritable(transposedPartial));  
          
        transposedPartial.setQuick(row.get(), 0.0);  
      }  
      Vector topKSimilarities = similarities.like();  
      for (Vector.Element topKSimilarity : topKQueue.retrieve()) {  
        topKSimilarities.setQuick(topKSimilarity.index(), topKSimilarity.get());  
      }  
      //这里只收集前maxSimilaritiesPerRow个得分最高的item，所以咱们最后的对称矩阵，实际上每行只有  
      //maxSimilaritiesPerRow个是对称的，其他的位置也不管了  
      ctx.write(row, new VectorWritable(topKSimilarities));  
    }  
  }  

Reducer：MergeToTopKSimilaritiesReducer类，就是将上面Map偏转的元素都收集起来，也就是完成了偏转矩阵和（截取了得分前maxSimilaritiesPerRow个）的原矩阵相加的过程，得到了对称矩阵

Java代码  
public static class MergeToTopKSimilaritiesReducer  
    extends Reducer<IntWritable,VectorWritable,IntWritable,VectorWritable> {  
  
  private int maxSimilaritiesPerRow;  
  
  @Override  
  protected void setup(Context ctx) throws IOException, InterruptedException {  
    maxSimilaritiesPerRow = ctx.getConfiguration().getInt(MAX_SIMILARITIES_PER_ROW, 0);  
    Preconditions.checkArgument(maxSimilaritiesPerRow > 0, "Incorrect maximum number of similarities per row!");  
  }  
  
  @Override  
  protected void reduce(IntWritable row, Iterable<VectorWritable> partials, Context ctx)  
      throws IOException, InterruptedException {  
    Vector allSimilarities = Vectors.merge(partials);  
    Vector topKSimilarities = Vectors.topKElements(maxSimilaritiesPerRow, allSimilarities);  
    ctx.write(row, new VectorWritable(topKSimilarities));  
  }  
}  

至此，RowSimilarityJob类的全部工作就完成，最终生成的是一个对称矩阵，也就是协同矩阵

Java代码  
//协同矩阵与用户向量相乘  
    //start the multiplication of the co-occurrence matrix by the user vectors  
    if (shouldRunNextPhase(parsedArgs, currentPhase)) {  
      //第一个MapReducer  
      Job prePartialMultiply1 = prepareJob(  
              similarityMatrixPath, prePartialMultiplyPath1, SequenceFileInputFormat.class,  
              SimilarityMatrixRowWrapperMapper.class, VarIntWritable.class, VectorOrPrefWritable.class,  
              Reducer.class, VarIntWritable.class, VectorOrPrefWritable.class,  
              SequenceFileOutputFormat.class);  
      boolean succeeded = prePartialMultiply1.waitForCompletion(true);  
      if (!succeeded)   
        return -1;  
      //第二个MapReduce  
      //continue the multiplication  
      Job prePartialMultiply2 = prepareJob(new Path(prepPath, PreparePreferenceMatrixJob.USER_VECTORS),  
              prePartialMultiplyPath2, SequenceFileInputFormat.class, UserVectorSplitterMapper.class, VarIntWritable.class,  
              VectorOrPrefWritable.class, Reducer.class, VarIntWritable.class, VectorOrPrefWritable.class,  
              SequenceFileOutputFormat.class);  
      if (usersFile != null) {  
        prePartialMultiply2.getConfiguration().set(UserVectorSplitterMapper.USERS_FILE, usersFile);  
      }  
      prePartialMultiply2.getConfiguration().setInt(UserVectorSplitterMapper.MAX_PREFS_PER_USER_CONSIDERED,  
              maxPrefsPerUser);  
      succeeded = prePartialMultiply2.waitForCompletion(true);  
      if (!succeeded)   
        return -1;  
      //finish the job  
      //第三个MapReduce  
      Job partialMultiply = prepareJob(  
              new Path(prePartialMultiplyPath1 + "," + prePartialMultiplyPath2), partialMultiplyPath,  
              SequenceFileInputFormat.class, Mapper.class, VarIntWritable.class, VectorOrPrefWritable.class,  
              ToVectorAndPrefReducer.class, VarIntWritable.class, VectorAndPrefsWritable.class,  
              SequenceFileOutputFormat.class);  
      setS3SafeCombinedInputPath(partialMultiply, getTempPath(), prePartialMultiplyPath1, prePartialMultiplyPath2);  
      succeeded = partialMultiply.waitForCompletion(true);  
      if (!succeeded)   
        return -1;  
    }  

下边也是同样分析一下这个三个MapReduce的细节：

1、Mapper： SimilarityMatrixRowWrapperMapper 类，将协同矩阵的一行拿出来，通过包装，封装成VectorOrPrefWritable类，与那边的UserVectorSplitterMapper 的输出类型一致

Java代码  
public final class SimilarityMatrixRowWrapperMapper extends  
    Mapper<IntWritable,VectorWritable,VarIntWritable,VectorOrPrefWritable> {  
    
  //将协同矩阵的一行拿出来，通过包装，封装成VectorOrPrefWritable类，与那边的UserVectorSplitterMapper  
  //的输出类型一致  
  @Override  
  protected void map(IntWritable key,  
                     VectorWritable value,  
                     Context context) throws IOException, InterruptedException {  
    Vector similarityMatrixRow = value.get();  
    /* remove self similarity */  
    similarityMatrixRow.set(key.get(), Double.NaN);  
    context.write(new VarIntWritable(key.get()), new VectorOrPrefWritable(similarityMatrixRow));  
  }  
  
}  

2、Mapper：UserVectorSplitterMapper类

Java代码  
//输入格式： theUserID：<itemid_index1,pref1>,<itemid_index2,pref2>........<itemid_indexN,prefN>  
  //输出格式：  itemid1：<theUserID,pref1>  
  //          itemid2：<theUserID,pref2>  
  //          itemid3：<theUserID,pref3>  
  //          ......  
  //          itemidN：<theUserID,prefN>  

Java代码  
public final class UserVectorSplitterMapper extends  
    Mapper<VarLongWritable,VectorWritable, VarIntWritable,VectorOrPrefWritable> {  
    
  @Override  
  protected void map(VarLongWritable key,  
                     VectorWritable value,  
                     Context context) throws IOException, InterruptedException {  
    long userID = key.get();  
    if (usersToRecommendFor != null && !usersToRecommendFor.contains(userID)) {  
      return;  
    }  
    Vector userVector = maybePruneUserVector(value.get());  
    Iterator<Vector.Element> it = userVector.iterateNonZero();  
    VarIntWritable itemIndexWritable = new VarIntWritable();  
    VectorOrPrefWritable vectorOrPref = new VectorOrPrefWritable();  
    while (it.hasNext()) {  
      Vector.Element e = it.next();  
      itemIndexWritable.set(e.index());  
      vectorOrPref.set(userID, (float) e.get());  
      context.write(itemIndexWritable, vectorOrPref);  
    }  
  }  

3、Reduce：ToVectorAndPrefReducer类，收集协同矩阵为itemid的一行，并且收集评价过该item的用户和评分，最后的输出是 itemid_index,VectorAndPrefsWritable(vector,List<userid>,List<pref>)

Java代码  
public final class ToVectorAndPrefReducer extends  
    Reducer<VarIntWritable,VectorOrPrefWritable,VarIntWritable,VectorAndPrefsWritable> {  
  
  //收集所有key为itemid的  
  @Override  
  protected void reduce(VarIntWritable key,  
                        Iterable<VectorOrPrefWritable> values,  
                        Context context) throws IOException, InterruptedException {  
  
    List<Long> userIDs = Lists.newArrayList();  
    List<Float> prefValues = Lists.newArrayList();  
    Vector similarityMatrixColumn = null;  
    for (VectorOrPrefWritable value : values) {  
      if (value.getVector() == null) {  
        // Then this is a user-pref value  
        userIDs.add(value.getUserID());  
        prefValues.add(value.getValue());  
      } else {  
        // Then this is the column vector  
        //协同矩阵的一个行（行号为itemid的一行）  
        if (similarityMatrixColumn != null) {  
          throw new IllegalStateException("Found two similarity-matrix columns for item index " + key.get());  
        }  
        similarityMatrixColumn = value.getVector();  
      }  
    }  
  
    if (similarityMatrixColumn == null) {  
      return;  
    }  
    //收集协同矩阵为itemid的一行，并且手机评价过该item的用户和评分  
    VectorAndPrefsWritable vectorAndPrefs = new VectorAndPrefsWritable(similarityMatrixColumn, userIDs, prefValues);  
    context.write(key, vectorAndPrefs);  
  }  
  
}  

第四步，协同矩阵和用户向量相乘，得到推荐结果

Java代码  
//extract out the recommendations  
     Job aggregateAndRecommend = prepareJob(  
             new Path(aggregateAndRecommendInput), outputPath, SequenceFileInputFormat.class,  
             PartialMultiplyMapper.class, VarLongWritable.class, PrefAndSimilarityColumnWritable.class,  
             AggregateAndRecommendReducer.class, VarLongWritable.class, RecommendedItemsWritable.class,  
             TextOutputFormat.class);  
     Configuration aggregateAndRecommendConf = aggregateAndRecommend.getConfiguration();  

Mapper：PartialMultiplyMapper类

Java代码  
//输入类型：( itemid_index, <userid的数组，pref的数组，协同矩阵行号为itemid_index的行> )  
//输出类型： userid，<该用户对itemid_index1的评分，协同矩阵行号为itemid_index1的行> )  
//        userid，<该用户对itemid_index2的评分，协同矩阵行号为itemid_index2的行> )  
//                       .....    
//                       .....  
//          userid，<该用户对itemid_indexN的评分，协同矩阵行号为itemid_indexN的行> )  

Java代码  
public final class PartialMultiplyMapper extends  
    Mapper<VarIntWritable,VectorAndPrefsWritable,VarLongWritable,PrefAndSimilarityColumnWritable> {  
  
  @Override  
  protected void map(VarIntWritable key,  
                     VectorAndPrefsWritable vectorAndPrefsWritable,  
                     Context context) throws IOException, InterruptedException {  
  
    Vector similarityMatrixColumn = vectorAndPrefsWritable.getVector();  
    List<Long> userIDs = vectorAndPrefsWritable.getUserIDs();  
    List<Float> prefValues = vectorAndPrefsWritable.getValues();  
  
    VarLongWritable userIDWritable = new VarLongWritable();  
    PrefAndSimilarityColumnWritable prefAndSimilarityColumn = new PrefAndSimilarityColumnWritable();  
  
    for (int i = 0; i < userIDs.size(); i++) {  
      long userID = userIDs.get(i);  
      float prefValue = prefValues.get(i);  
      if (!Float.isNaN(prefValue)) {  
        prefAndSimilarityColumn.set(prefValue, similarityMatrixColumn);  
        userIDWritable.set(userID);  
        context.write(userIDWritable, prefAndSimilarityColumn);  
      }  
    }  
  }  
  
}  

Reducer：AggregateAndRecommendReducer类，Reducer中进行PartialMultiply，按乘积得到的推荐度的大小取出最大的几个item。对于非booleanData，是用pref和相似度矩阵的PartialMultiply得到推荐度的值来进行排序。
而booleanData的pref值都是1.0f，所以去计算矩阵相乘的过程没有意义，直接累加相似度的值即可。
用这个数据排序就可得到推荐结果

Java代码  
public final class AggregateAndRecommendReducer extends  
    Reducer<VarLongWritable,PrefAndSimilarityColumnWritable,VarLongWritable,RecommendedItemsWritable> {  
 @Override  
  protected void reduce(VarLongWritable userID,  
                        Iterable<PrefAndSimilarityColumnWritable> values,  
                        Context context) throws IOException, InterruptedException {  
    if (booleanData) {  
      reduceBooleanData(userID, values, context);  
    } else {  
      reduceNonBooleanData(userID, values, context);  
    }  
  }  
  
  private void reduceBooleanData(VarLongWritable userID,  
                                 Iterable<PrefAndSimilarityColumnWritable> values,  
                                 Context context) throws IOException, InterruptedException {  
    /* having boolean data, each estimated preference can only be 1, 
     * however we can't use this to rank the recommended items, 
     * so we use the sum of similarities for that. */  
    Vector predictionVector = null;  
    for (PrefAndSimilarityColumnWritable prefAndSimilarityColumn : values) {  
      predictionVector = predictionVector == null  
          ? prefAndSimilarityColumn.getSimilarityColumn()  
          : predictionVector.plus(prefAndSimilarityColumn.getSimilarityColumn());  
    }  
    writeRecommendedItems(userID, predictionVector, context);  
  }  
  
  private void reduceNonBooleanData(VarLongWritable userID,  
                        Iterable<PrefAndSimilarityColumnWritable> values,  
                        Context context) throws IOException, InterruptedException {  
    /* each entry here is the sum in the numerator of the prediction formula */  
    Vector numerators = null;  
    /* each entry here is the sum in the denominator of the prediction formula */  
    Vector denominators = null;  
    /* each entry here is the number of similar items used in the prediction formula */  
    Vector numberOfSimilarItemsUsed = new RandomAccessSparseVector(Integer.MAX_VALUE, 100);  
  
    for (PrefAndSimilarityColumnWritable prefAndSimilarityColumn : values) {  
      Vector simColumn = prefAndSimilarityColumn.getSimilarityColumn();  
      float prefValue = prefAndSimilarityColumn.getPrefValue();  
      /* count the number of items used for each prediction */  
      Iterator<Vector.Element> usedItemsIterator = simColumn.iterateNonZero();  
      while (usedItemsIterator.hasNext()) {  
        int itemIDIndex = usedItemsIterator.next().index();  
        numberOfSimilarItemsUsed.setQuick(itemIDIndex, numberOfSimilarItemsUsed.getQuick(itemIDIndex) + 1);  
      }  
      //vector.times(float) 是向量乘于一个数，也就是向量的每一个值都乘以这个数  
      //vector.plus(vector) 是两个向量相加，每一个位置上的值相加  
        
      //numerators是一个vecotr，每一个元素是这样的  
      /* 
                例如index为item1的元素的值为： 
       simility(item1, item_2)*pref(userid, item_2) 
      + simility(item_1, item_3)*pref(userid, item_3) 
      + simility(item1, item_4)*pref(userid, item_4) 
      + ……  
      + simility(item_1, item_2)*pref(userid, item_N) 
      */  
      // 注：其中simility(item1, item2)代表物品item1和物品item2的相似度 ，pref(userid, item)代表用于userid对item打分分值   
       
      numerators = numerators == null  
          ? prefValue == BOOLEAN_PREF_VALUE ? simColumn.clone() : simColumn.times(prefValue)  
          : numerators.plus(prefValue == BOOLEAN_PREF_VALUE ? simColumn : simColumn.times(prefValue));  
        
        
        
      simColumn.assign(ABSOLUTE_VALUES);  
      //denominators是一个vecotr，每一个元素是这样的  
      /* 
                例如index为item1的元素的值为： 
       simility(item1, item_2)+ simility(item_1, item_3)+ …… + simility(item_1, item_2)*pref(userid, item_N) 
      */  
      // 注：其中simility(item1, item2)代表物品item1和物品item2的相似度  
      denominators = denominators == null ? simColumn : denominators.plus(simColumn);  
    }  
  
    if (numerators == null) {  
      return;  
    }  
  
    Vector recommendationVector = new RandomAccessSparseVector(Integer.MAX_VALUE, 100);  
    Iterator<Vector.Element> iterator = numerators.iterateNonZero();  
    while (iterator.hasNext()) {  
      Vector.Element element = iterator.next();  
      int itemIDIndex = element.index();  
      /* preference estimations must be based on at least 2 datapoints */  
      if (numberOfSimilarItemsUsed.getQuick(itemIDIndex) > 1) {  
        /* compute normalized prediction */  
        //计算归一化预测值  
        double prediction = element.get() / denominators.getQuick(itemIDIndex);  
        recommendationVector.setQuick(itemIDIndex, prediction);  
      }  
    }  
    writeRecommendedItems(userID, recommendationVector, context);  
  }  
}  

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