Mahout推荐算法之ItemBased

Mahout推荐之ItemBased

一、 算法原理

(一) 基本原理

如下图评分矩阵所示：行为user，列为item.



图（1）

该算法的原理：

1. 计算Item之间的相似度。

2. 对用户U做推荐



公式(一)
Map tmp ;

Map tmp1 ;



for(item a in userRatedItems){

rate =userforItemRate(a)

ListsimItem =getSimItem(a);

For(Jin simItem){

Item b =j;

Simab=sim(a,b);

Tmp.add(b,Tmp .get(b)+simab*rate)

tmp1.add(b, tmp1.get(b)+simab)



}

}

Maptmp2=temp/temp1

Sortbyval(tmp2)

return topK(tmp2,k)


(二) 相似度计算

1. Cos相似度



公式（二）
2. 皮尔逊相似度



公式（三）
3. 调整的cos相似度



公式（四）
(三) 采样
计算全量的itemPair之间的相似度耗费大量的时间，也是没有必要的，所以需要采样,减小计算量。

二、 单机模式实现

(一) 候选Item搜索

计算所有Item Pair之间的相似度在单机模式下是不现实的，需要在海量的候选集中搜索出一部分最有可能的候选集用于计算。Mahout提供了4中候选Item选择策略。

1. AllSimilarItemsCandidateItemsStrategy

@Override FastIDSet doGetCandidateItems(long[] preferredItemIDs, DataModel dataModel) throws TasteException { FastIDSet candidateItemIDs = new FastIDSet(); for (long itemID : preferredItemIDs) { candidateItemIDs.addAll(similarity.allSimilarItemIDs(itemID)); } candidateItemIDs.removeAll(preferredItemIDs); return candidateItemIDs; }

2. AllUnknownItemsCandidateItemsStrategy

@Override protected FastIDSet doGetCandidateItems(long[] preferredItemIDs, DataModel dataModel) throws TasteException { FastIDSet possibleItemIDs = new FastIDSet(dataModel.getNumItems()); LongPrimitiveIterator allItemIDs = dataModel.getItemIDs(); while (allItemIDs.hasNext()) { possibleItemIDs.add(allItemIDs.nextLong()); } possibleItemIDs.removeAll(preferredItemIDs); return possibleItemIDs; }

3. PreferredItemsNeighborhoodCandidateItemsStrategy

@Override protected FastIDSet doGetCandidateItems(long[] preferredItemIDs, DataModel dataModel) throws TasteException { FastIDSet possibleItemsIDs = new FastIDSet(); for (long itemID : preferredItemIDs) { PreferenceArray itemPreferences = dataModel.getPreferencesForItem(itemID); int numUsersPreferringItem = itemPreferences.length(); for (int index = 0; index < numUsersPreferringItem; index++) { possibleItemsIDs.addAll(dataModel.getItemIDsFromUser(itemPreferences.getUserID(index))); } } possibleItemsIDs.removeAll(preferredItemIDs); return possibleItemsIDs; }

4. SamplingCandidateItemsStrategy

private static int computeMaxFrom(int factor, int numThings) { if (factor == NO_LIMIT_FACTOR) { return MAX_LIMIT; } long max = (long) (factor * (1.0 + Math.log(numThings) / LOG2)); return max > MAX_LIMIT ? MAX_LIMIT : (int) max; } @Override protected FastIDSet doGetCandidateItems(long[] preferredItemIDs, DataModel dataModel) throws TasteException { LongPrimitiveIterator preferredItemIDsIterator = new LongPrimitiveArrayIterator(preferredItemIDs); if (preferredItemIDs.length > maxItems) { double samplingRate = (double) maxItems / preferredItemIDs.length; // log.info("preferredItemIDs.length {}, samplingRate {}", preferredItemIDs.length, samplingRate); preferredItemIDsIterator = new SamplingLongPrimitiveIterator(preferredItemIDsIterator, samplingRate); } FastIDSet possibleItemsIDs = new FastIDSet(); while (preferredItemIDsIterator.hasNext()) { long itemID = preferredItemIDsIterator.nextLong(); PreferenceArray prefs = dataModel.getPreferencesForItem(itemID); int prefsLength = prefs.length(); if (prefsLength > maxUsersPerItem) { Iterator<Preference> sampledPrefs = new FixedSizeSamplingIterator<Preference>(maxUsersPerItem, prefs.iterator()); while (sampledPrefs.hasNext()) { addSomeOf(possibleItemsIDs, dataModel.getItemIDsFromUser(sampledPrefs.next().getUserID())); } } else { for (int i = 0; i < prefsLength; i++) { addSomeOf(possibleItemsIDs, dataModel.getItemIDsFromUser(prefs.getUserID(i))); } } } possibleItemsIDs.removeAll(preferredItemIDs); return possibleItemsIDs; } private void addSomeOf(FastIDSet possibleItemIDs, FastIDSet itemIDs) { if (itemIDs.size() > maxItemsPerUser) { LongPrimitiveIterator it = new SamplingLongPrimitiveIterator(itemIDs.iterator(), (double) maxItemsPerUser / itemIDs.size()); while (it.hasNext()) { possibleItemIDs.add(it.nextLong()); } } else { possibleItemIDs.addAll(itemIDs); } }

(二) 估值

protected float doEstimatePreference(long userID, PreferenceArray preferencesFromUser, long itemID) throws TasteException { double preference = 0.0; double totalSimilarity = 0.0; int count = 0; double[] similarities = similarity.itemSimilarities(itemID, preferencesFromUser.getIDs()); for (int i = 0; i < similarities.length; i++) { double theSimilarity = similarities[i]; if (!Double.isNaN(theSimilarity)) { // Weights can be negative! preference += theSimilarity * preferencesFromUser.getValue(i); totalSimilarity += theSimilarity; count++; } } // Throw out the estimate if it was based on no data points, of course, but also if based on // just one. This is a bit of a band-aid on the 'stock' item-based algorithm for the moment. // The reason is that in this case the estimate is, simply, the user's rating for one item // that happened to have a defined similarity. The similarity score doesn't matter, and that // seems like a bad situation. if (count <= 1) { return Float.NaN; } float estimate = (float) (preference / totalSimilarity); if (capper != null) { estimate = capper.capEstimate(estimate); } return estimate; }

(三) 推荐

1. 根据历史评分列表推荐

这种推荐方式根据用户之前产生过评分的item做推荐，推荐结果按照估计值的大小排序。

@Override public List<RecommendedItem> recommend(long userID, int howMany, IDRescorer rescorer) throws TasteException { Preconditions.checkArgument(howMany >= 1, "howMany must be at least 1"); log.debug("Recommending items for user ID '{}'", userID); PreferenceArray preferencesFromUser = getDataModel().getPreferencesFromUser(userID); if (preferencesFromUser.length() == 0) { return Collections.emptyList(); } FastIDSet possibleItemIDs = getAllOtherItems(userID, preferencesFromUser); TopItems.Estimator<Long> estimator = new Estimator(userID, preferencesFromUser); List<RecommendedItem> topItems = TopItems.getTopItems(howMany, possibleItemIDs.iterator(), rescorer, estimator); log.debug("Recommendations are: {}", topItems); return topItems; }

2. Because推荐

这种推荐方式用于实时推荐。

@Override public List<RecommendedItem> recommendedBecause(long userID, long itemID, int howMany) throws TasteException { Preconditions.checkArgument(howMany >= 1, "howMany must be at least 1"); DataModel model = getDataModel(); TopItems.Estimator<Long> estimator = new RecommendedBecauseEstimator(userID, itemID); PreferenceArray prefs = model.getPreferencesFromUser(userID); int size = prefs.length(); FastIDSet allUserItems = new FastIDSet(size); for (int i = 0; i < size; i++) { allUserItems.add(prefs.getItemID(i)); } allUserItems.remove(itemID); return TopItems.getTopItems(howMany, allUserItems.iterator(), null, estimator); } //估值方法 @Override public double estimate(Long itemID) throws TasteException { Float pref = getDataModel().getPreferenceValue(userID, itemID); if (pref == null) { return Float.NaN; } double similarityValue = similarity.itemSimilarity(recommendedItemID, itemID); return (1.0 + similarityValue) * pref; }

三、 MapReduce模式实现

(一) 将偏好文件转换成评分矩阵(PreparePreferenceMatrixJob)

(二) 计算共现矩阵相似度（RowSimilarityJob）

(三) 挑选最相似的K个Item

(四) 用户偏好向量和相似降维后的共现矩阵做乘法

(五) 过滤制定的user\titem

(六) 生成最终的推荐结果

四、 实例演示

1. 单机模式

1) 批量推荐

DataModel dataModel = new FileDataModel(new File("p/pereference")); ItemSimilarity similarity = new PearsonCorrelationSimilarity(dataModel); ItemBasedRecommender recommender = new GenericItemBasedRecommender(dataModel,similarity ); System.out.println(recommender.recommend(10, 10));

2) Because推荐

DataModel dataModel = new FileDataModel(new File("p/pereference")); ItemSimilarity similarity = new PearsonCorrelationSimilarity(dataModel); ItemBasedRecommender recommender = new GenericItemBasedRecommender(dataModel,similarity ); System.out.println(recommender.recommendedBecause(10, 10328, 100));

2. MapReduce模式

API

org.apache.mahout.cf.taste.hadoop.item.RecommenderJob.main(args)
--input	偏好数据路径，文本文件。格式 userid\t itemid\t preference
--output	推荐结果路径
-- numRecommendations	推荐个数
--usersFile	需要做出推荐的user，默认全部做推荐
--itemsFile	需要做出推荐的item，默认全部做推荐
--filterFile	文件格式文本，userid\itemid 。目的是给userid的用户不要推荐itemid的item
--booleanData	是否是布尔数据
--maxPrefsPerUser	最大偏好值
--minPrefsPerUser	最小偏好值
--maxSimilaritiesPerItem	给每一个Item计算最多的相似item数目
--maxPrefsPerUserInItemSimilarity	ItemSimilarity估计item相似度时，对每一个user最多偏好数目
--similarityClassname	SIMILARITY_PEARSON_CORRELATION、SIMILARITY_COOCCURRENCE、SIMILARITY_LOGLIKELIHOOD、SIMILARITY_TANIMOTO_COEFFICIENT、SIMILARITY_CITY_BLOCK、SIMILARITY_COSINE、SIMILARITY_EUCLIDEAN_DISTANCE
--threshold	删除低于该阈值的item对
--outputPathForSimilarityMatrix	指定生成的item相似矩阵路径,文本文件，格式为 itemA \t itemB \t 相似值

实例

String [] args ={"--input","p", "--output","recommender", "--numRecommendations","10", "--outputPathForSimilarityMatrix","simMatrix", "--similarityClassname","SIMILARITY_PEARSON_CORRELATION"} org.apache.mahout.cf.taste.hadoop.item.RecommenderJob.main(args);

五、 参考文献

1. M.Deshpandeand G. Karypis. Item-based top-n recommendation algorithms.

2. B.M.Sarwar, G. Karypis, J.A. Konstan, and J. Reidl. Item-based collaborativefiltering recommendation algorithms.

3. Item-based collaborative filtering

4. Accuratelycomputing running variance