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