推荐系统原始数据

input/16.RecommendedSystem/ml-1m/README

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+SUMMARY
+================================================================================
+
+These files contain 1,000,209 anonymous ratings of approximately 3,900 movies 
+made by 6,040 MovieLens users who joined MovieLens in 2000.
+
+USAGE LICENSE
+================================================================================
+
+Neither the University of Minnesota nor any of the researchers
+involved can guarantee the correctness of the data, its suitability
+for any particular purpose, or the validity of results based on the
+use of the data set.  The data set may be used for any research
+purposes under the following conditions:
+
+     * The user may not state or imply any endorsement from the
+       University of Minnesota or the GroupLens Research Group.
+
+     * The user must acknowledge the use of the data set in
+       publications resulting from the use of the data set, and must
+       send us an electronic or paper copy of those publications.
+
+     * The user may not redistribute the data without separate
+       permission.
+
+     * The user may not use this information for any commercial or
+       revenue-bearing purposes without first obtaining permission
+       from a faculty member of the GroupLens Research Project at the
+       University of Minnesota.
+
+If you have any further questions or comments, please contact GroupLens
+<grouplens-info@cs.umn.edu>. 
+
+ACKNOWLEDGEMENTS
+================================================================================
+
+Thanks to Shyong Lam and Jon Herlocker for cleaning up and generating the data
+set.
+
+FURTHER INFORMATION ABOUT THE GROUPLENS RESEARCH PROJECT
+================================================================================
+
+The GroupLens Research Project is a research group in the Department of 
+Computer Science and Engineering at the University of Minnesota. Members of 
+the GroupLens Research Project are involved in many research projects related 
+to the fields of information filtering, collaborative filtering, and 
+recommender systems. The project is lead by professors John Riedl and Joseph 
+Konstan. The project began to explore automated collaborative filtering in 
+1992, but is most well known for its world wide trial of an automated 
+collaborative filtering system for Usenet news in 1996. Since then the project 
+has expanded its scope to research overall information filtering solutions, 
+integrating in content-based methods as well as improving current collaborative 
+filtering technology.
+
+Further information on the GroupLens Research project, including research 
+publications, can be found at the following web site:
+        
+        http://www.grouplens.org/
+
+GroupLens Research currently operates a movie recommender based on 
+collaborative filtering:
+
+        http://www.movielens.org/
+
+RATINGS FILE DESCRIPTION
+================================================================================
+
+All ratings are contained in the file "ratings.dat" and are in the
+following format:
+
+UserID::MovieID::Rating::Timestamp
+
+- UserIDs range between 1 and 6040 
+- MovieIDs range between 1 and 3952
+- Ratings are made on a 5-star scale (whole-star ratings only)
+- Timestamp is represented in seconds since the epoch as returned by time(2)
+- Each user has at least 20 ratings
+
+USERS FILE DESCRIPTION
+================================================================================
+
+User information is in the file "users.dat" and is in the following
+format:
+
+UserID::Gender::Age::Occupation::Zip-code
+
+All demographic information is provided voluntarily by the users and is
+not checked for accuracy.  Only users who have provided some demographic
+information are included in this data set.
+
+- Gender is denoted by a "M" for male and "F" for female
+- Age is chosen from the following ranges:
+
+	*  1:  "Under 18"
+	* 18:  "18-24"
+	* 25:  "25-34"
+	* 35:  "35-44"
+	* 45:  "45-49"
+	* 50:  "50-55"
+	* 56:  "56+"
+
+- Occupation is chosen from the following choices:
+
+	*  0:  "other" or not specified
+	*  1:  "academic/educator"
+	*  2:  "artist"
+	*  3:  "clerical/admin"
+	*  4:  "college/grad student"
+	*  5:  "customer service"
+	*  6:  "doctor/health care"
+	*  7:  "executive/managerial"
+	*  8:  "farmer"
+	*  9:  "homemaker"
+	* 10:  "K-12 student"
+	* 11:  "lawyer"
+	* 12:  "programmer"
+	* 13:  "retired"
+	* 14:  "sales/marketing"
+	* 15:  "scientist"
+	* 16:  "self-employed"
+	* 17:  "technician/engineer"
+	* 18:  "tradesman/craftsman"
+	* 19:  "unemployed"
+	* 20:  "writer"
+
+MOVIES FILE DESCRIPTION
+================================================================================
+
+Movie information is in the file "movies.dat" and is in the following
+format:
+
+MovieID::Title::Genres
+
+- Titles are identical to titles provided by the IMDB (including
+year of release)
+- Genres are pipe-separated and are selected from the following genres:
+
+	* Action
+	* Adventure
+	* Animation
+	* Children's
+	* Comedy
+	* Crime
+	* Documentary
+	* Drama
+	* Fantasy
+	* Film-Noir
+	* Horror
+	* Musical
+	* Mystery
+	* Romance
+	* Sci-Fi
+	* Thriller
+	* War
+	* Western
+
+- Some MovieIDs do not correspond to a movie due to accidental duplicate
+entries and/or test entries
+- Movies are mostly entered by hand, so errors and inconsistencies may exist

src/python/16.RecommendedSystem/evaluation_model.py

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+
+def SplitData(data, M, k, seed):
+    test = []
+    train = []
+    random.seed(seed)
+    for user, item in data:
+        if random.randint(0,M) == k:
+            test.append([user,item])
+        else:
+            train.append([user,item])
+    return train, test
+
+
+# 准确率
+def Precision(train, test, N):
+    hit = 0
+    all = 0
+    for user in train.keys():
+        tu = test[user]
+        rank = GetRecommendation(user, N)
+        for item, pui in rank:
+            if item in tu:
+                hit += 1
+        all += N
+    return hit / (all * 1.0)
+
+
+# 召回率
+def Recall(train, test, N):
+    hit = 0
+    all = 0
+    for user in train.keys():
+        tu = test[user]
+        rank = GetRecommendation(user, N)
+        for item, pui in rank:
+            if item in tu:
+                hit += 1
+        all += len(tu)
+    return hit / (all * 1.0)
+
+
+# 覆盖率
+def Coverage(train, test, N):
+    recommend_items = set()
+    all_items = set()
+    for user in train.keys():
+        for item in train[user].keys():
+            all_items.add(item)
+        rank = GetRecommendation(user, N)
+        for item, pui in rank:
+            recommend_items.add(item)
+    return len(recommend_items) / (len(all_items) * 1.0)
+
+
+# 新颖度
+def Popularity(train, test, N):
+    item_popularity = dict()
+    for user, items in train.items():
+        for item in items.keys():
+            if item not in item_popularity:
+                item_popularity[item] = 0
+                item_popularity[item] += 1
+    ret = 0
+    n=0
+    for user in train.keys():
+        rank = GetRecommendation(user, N)
+        for item, pui in rank:
+            ret += math.log(1 + item_popularity[item])
+            n += 1
+    ret /= n * 1.0
+    return ret
+

src/python/16.RecommendedSystem/graph-based.py

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+
+def PersonalRank(G, alpha, root):
+    rank = dict()
+    rank = {x:0 for x in G.keys()}
+    rank[root] = 1
+    for k in range(20):
+        tmp = {x:0 for x in G.keys()}
+        for i, ri in G.items():
+            for j, wij in ri.items():
+                if j not in tmp:
+                    tmp[j] = 0
+                tmp[j] += 0.6 * rank[i] / (1.0 * len(ri))
+                if j == root:
+                    tmp[j] += 1 - alpha
+        rank = tmp
+    return rank
+

src/python/16.RecommendedSystem/itemcf.py

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+#-*- coding: utf-8 -*-
+'''
+Created on 2015-06-22
+
+@author: Lockvictor
+'''
+import sys, random, math
+from operator import itemgetter
+
+
+random.seed(0)
+
+
+class ItemBasedCF():
+    ''' TopN recommendation - ItemBasedCF '''
+    def __init__(self):
+        self.trainset = {}
+        self.testset = {}
+
+        self.n_sim_movie = 20
+        self.n_rec_movie = 10
+
+        self.movie_sim_mat = {}
+        self.movie_popular = {}
+        self.movie_count = 0
+
+        print >> sys.stderr, 'Similar movie number = %d' % self.n_sim_movie
+        print >> sys.stderr, 'Recommended movie number = %d' % self.n_rec_movie
+
+
+    @staticmethod
+    def loadfile(filename):
+        ''' load a file, return a generator. '''
+        fp = open(filename, 'r')
+        for i, line in enumerate(fp):
+            yield line.strip('\r\n')
+            if i % 100000 == 0:
+                print >> sys.stderr, 'loading %s(%s)' % (filename, i)
+        fp.close()
+        print >> sys.stderr, 'load %s succ' % filename
+
+
+    def generate_dataset(self, filename, pivot=0.7):
+        ''' load rating data and split it to training set and test set '''
+        trainset_len = 0
+        testset_len = 0
+
+        for line in self.loadfile(filename):
+            user, movie, rating, _ = line.split('::')
+            # split the data by pivot
+            if (random.random() < pivot):
+                self.trainset.setdefault(user, {})
+                self.trainset[user][movie] = int(rating)
+                trainset_len += 1
+            else:
+                self.testset.setdefault(user, {})
+                self.testset[user][movie] = int(rating)
+                testset_len += 1
+
+        print >> sys.stderr, 'split training set and test set succ'
+        print >> sys.stderr, 'train set = %s' % trainset_len
+        print >> sys.stderr, 'test set = %s' % testset_len
+
+
+    def calc_movie_sim(self):
+        ''' calculate movie similarity matrix '''
+        print >> sys.stderr, 'counting movies number and popularity...'
+
+        for user, movies in self.trainset.iteritems():
+            for movie in movies:
+                # count item popularity 
+                if movie not in self.movie_popular:
+                    self.movie_popular[movie] = 0
+                self.movie_popular[movie] += 1
+
+        print >> sys.stderr, 'count movies number and popularity succ'
+
+        # save the total number of movies
+        self.movie_count = len(self.movie_popular)
+        print >> sys.stderr, 'total movie number = %d' % self.movie_count
+
+        # count co-rated users between items
+        itemsim_mat = self.movie_sim_mat
+        print >> sys.stderr, 'building co-rated users matrix...'
+
+        for user, movies in self.trainset.iteritems():
+            for m1 in movies:
+                for m2 in movies:
+                    if m1 == m2: continue
+                    itemsim_mat.setdefault(m1,{})
+                    itemsim_mat[m1].setdefault(m2,0)
+                    itemsim_mat[m1][m2] += 1
+
+        print >> sys.stderr, 'build co-rated users matrix succ'
+
+        # calculate similarity matrix 
+        print >> sys.stderr, 'calculating movie similarity matrix...'
+        simfactor_count = 0
+        PRINT_STEP = 2000000
+
+        for m1, related_movies in itemsim_mat.iteritems():
+            for m2, count in related_movies.iteritems():
+                itemsim_mat[m1][m2] = count / math.sqrt(
+                        self.movie_popular[m1] * self.movie_popular[m2])
+                simfactor_count += 1
+                if simfactor_count % PRINT_STEP == 0:
+                    print >> sys.stderr, 'calculating movie similarity factor(%d)' % simfactor_count
+
+        print >> sys.stderr, 'calculate movie similarity matrix(similarity factor) succ'
+        print >> sys.stderr, 'Total similarity factor number = %d' %simfactor_count
+
+
+    def recommend(self, user):
+        ''' Find K similar movies and recommend N movies. '''
+        K = self.n_sim_movie
+        N = self.n_rec_movie
+        rank = {}
+        watched_movies = self.trainset[user]
+
+        for movie, rating in watched_movies.iteritems():
+            for related_movie, w in sorted(self.movie_sim_mat[movie].items(),
+                    key=itemgetter(1), reverse=True)[:K]:
+                if related_movie in watched_movies:
+                    continue
+                rank.setdefault(related_movie, 0)
+                rank[related_movie] += w * rating
+        # return the N best movies
+        return sorted(rank.items(), key=itemgetter(1), reverse=True)[:N]
+
+
+    def evaluate(self):
+        ''' return precision, recall, coverage and popularity '''
+        print >> sys.stderr, 'Evaluation start...'
+
+        N = self.n_rec_movie
+        #  varables for precision and recall 
+        hit = 0
+        rec_count = 0
+        test_count = 0
+        # varables for coverage
+        all_rec_movies = set()
+        # varables for popularity
+        popular_sum = 0
+
+        for i, user in enumerate(self.trainset):
+            if i % 500 == 0:
+                print >> sys.stderr, 'recommended for %d users' % i
+            test_movies = self.testset.get(user, {})
+            rec_movies = self.recommend(user)
+            for movie, w in rec_movies:
+                if movie in test_movies:
+                    hit += 1
+                all_rec_movies.add(movie)
+                popular_sum += math.log(1 + self.movie_popular[movie])
+            rec_count += N
+            test_count += len(test_movies)
+
+        precision = hit / (1.0 * rec_count)
+        recall = hit / (1.0 * test_count)
+        coverage = len(all_rec_movies) / (1.0 * self.movie_count)
+        popularity = popular_sum / (1.0 * rec_count)
+
+        print >> sys.stderr, 'precision=%.4f\trecall=%.4f\tcoverage=%.4f\tpopularity=%.4f' \
+                % (precision, recall, coverage, popularity)
+
+
+if __name__ == '__main__':
+    ratingfile = 'input/16.RecommendedSystem/ml-1m/ratings.dat'
+    itemcf = ItemBasedCF()
+    itemcf.generate_dataset(ratingfile)
+    itemcf.calc_movie_sim()
+    itemcf.evaluate()

src/python/16.RecommendedSystem/lfm.py

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+
+# 负样本采样过程
+def RandomSelectNegativeSample(self, items):
+    ret = dict()
+    for i in items.keys():
+        ret[i] = 1
+    
+    n = 0
+    for i in range(0, len(items) * 3):
+        item = items_pool[random.randint(0, len(items_pool) - 1)]
+        if item in ret:
+            continue
+        ret[item] = 0
+        n + = 1
+        if n > len(items):
+            break
+    return ret
+
+
+def LatentFactorModel(user_items, F, N, alpha, lambda):
+    [P, Q] = InitModel(user_items, F)
+    for step in range(0,N):
+        for user, items in user_items.items():
+            samples = RandSelectNegativeSamples(items)
+            for item, rui in samples.items():
+                eui = rui - Predict(user, item)
+                for f in range(0, F):
+                    P[user][f] += alpha * (eui * Q[item][f] - lambda * P[user][f])
+                    Q[item][f] += alpha * (eui * P[user][f] - lambda * Q[item][f])
+        alpha *= 0.9
+
+
+def Recommend(user, P, Q):
+    rank = dict()
+    for f, puf in P[user].items():
+        for i, qfi in Q[f].items():
+            if i not in rank:
+                rank[i] += puf * qfi
+    return rank
+
+

src/python/16.RecommendedSystem/usercf.py

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+#-*- coding: utf-8 -*-
+'''
+Created on 2015-06-22
+
+@author: Lockvictor
+'''
+import sys, random, math
+from operator import itemgetter
+
+
+random.seed(0)
+
+
+class UserBasedCF():
+    ''' TopN recommendation - UserBasedCF '''
+    def __init__(self):
+        self.trainset = {}
+        self.testset = {}
+
+        self.n_sim_user = 20
+        self.n_rec_movie = 10
+
+        self.user_sim_mat = {}
+        self.movie_popular = {}
+        self.movie_count = 0
+
+        print >> sys.stderr, 'Similar user number = %d' % self.n_sim_user
+        print >> sys.stderr, 'recommended movie number = %d' % self.n_rec_movie
+
+
+    @staticmethod
+    def loadfile(filename):
+        ''' load a file, return a generator. '''
+        fp = open(filename, 'r')
+        for i,line in enumerate(fp):
+            yield line.strip('\r\n')
+            if i%100000 == 0:
+                print >> sys.stderr, 'loading %s(%s)' % (filename, i)
+        fp.close()
+        print >> sys.stderr, 'load %s succ' % filename
+
+
+    def generate_dataset(self, filename, pivot=0.7):
+        ''' load rating data and split it to training set and test set '''
+        trainset_len = 0
+        testset_len = 0
+
+        for line in self.loadfile(filename):
+            user, movie, rating, timestamp = line.split('::')
+            # split the data by pivot
+            if (random.random() < pivot):
+                self.trainset.setdefault(user,{})
+                self.trainset[user][movie] = int(rating)
+                trainset_len += 1
+            else:
+                self.testset.setdefault(user,{})
+                self.testset[user][movie] = int(rating)
+                testset_len += 1
+
+        print >> sys.stderr, 'split training set and test set succ'
+        print >> sys.stderr, 'train set = %s' % trainset_len
+        print >> sys.stderr, 'test set = %s' % testset_len
+
+
+    def calc_user_sim(self):
+        ''' calculate user similarity matrix '''
+        # build inverse table for item-users
+        # key=movieID, value=list of userIDs who have seen this movie
+        print >> sys.stderr, 'building movie-users inverse table...'
+        movie2users = dict()
+
+        for user,movies in self.trainset.iteritems():
+            for movie in movies:
+                # inverse table for item-users
+                if movie not in movie2users:
+                    movie2users[movie] = set()
+                movie2users[movie].add(user)
+                # count item popularity at the same time
+                if movie not in self.movie_popular:
+                    self.movie_popular[movie] = 0
+                self.movie_popular[movie] += 1
+        print >> sys.stderr, 'build movie-users inverse table succ'
+
+        # save the total movie number, which will be used in evaluation
+        self.movie_count = len(movie2users)
+        print >> sys.stderr, 'total movie number = %d' % self.movie_count
+
+        # count co-rated items between users
+        usersim_mat = self.user_sim_mat
+        print >> sys.stderr, 'building user co-rated movies matrix...'
+
+        for movie,users in movie2users.iteritems():
+            for u in users:
+                for v in users:
+                    if u == v: continue
+                    usersim_mat.setdefault(u,{})
+                    usersim_mat[u].setdefault(v,0)
+                    usersim_mat[u][v] += 1
+        print >> sys.stderr, 'build user co-rated movies matrix succ'
+
+        # calculate similarity matrix 
+        print >> sys.stderr, 'calculating user similarity matrix...'
+        simfactor_count = 0
+        PRINT_STEP = 2000000
+        for u,related_users in usersim_mat.iteritems():
+            for v,count in related_users.iteritems():
+                usersim_mat[u][v] = count / math.sqrt(
+                        len(self.trainset[u]) * len(self.trainset[v]))
+                simfactor_count += 1
+                if simfactor_count % PRINT_STEP == 0:
+                    print >> sys.stderr, 'calculating user similarity factor(%d)' % simfactor_count
+
+        print >> sys.stderr, 'calculate user similarity matrix(similarity factor) succ'
+        print >> sys.stderr, 'Total similarity factor number = %d' %simfactor_count
+
+
+    def recommend(self, user):
+        ''' Find K similar users and recommend N movies. '''
+        K = self.n_sim_user
+        N = self.n_rec_movie
+        rank = dict()
+        watched_movies = self.trainset[user]
+
+        # v=similar user, wuv=similarity factor
+        for v, wuv in sorted(self.user_sim_mat[user].items(),
+                key=itemgetter(1), reverse=True)[0:K]:
+            for movie in self.trainset[v]:
+                if movie in watched_movies:
+                    continue
+                # predict the user's "interest" for each movie
+                rank.setdefault(movie,0)
+                rank[movie] += wuv
+        # return the N best movies
+        return sorted(rank.items(), key=itemgetter(1), reverse=True)[0:N]
+
+
+    def evaluate(self):
+        ''' return precision, recall, coverage and popularity '''
+        print >> sys.stderr, 'Evaluation start...'
+
+        N = self.n_rec_movie
+        #  varables for precision and recall 
+        hit = 0
+        rec_count = 0
+        test_count = 0
+        # varables for coverage
+        all_rec_movies = set()
+        # varables for popularity
+        popular_sum = 0
+
+        for i, user in enumerate(self.trainset):
+            if i % 500 == 0:
+                print >> sys.stderr, 'recommended for %d users' % i
+            test_movies = self.testset.get(user, {})
+            rec_movies = self.recommend(user)
+            for movie, w in rec_movies:
+                if movie in test_movies:
+                    hit += 1
+                all_rec_movies.add(movie)
+                popular_sum += math.log(1 + self.movie_popular[movie])
+            rec_count += N
+            test_count += len(test_movies)
+
+        precision = hit / (1.0*rec_count)
+        recall = hit / (1.0*test_count)
+        coverage = len(all_rec_movies) / (1.0*self.movie_count)
+        popularity = popular_sum / (1.0*rec_count)
+
+        print >> sys.stderr, 'precision=%.4f\trecall=%.4f\tcoverage=%.4f\tpopularity=%.4f' % \
+                (precision, recall, coverage, popularity)
+
+
+if __name__ == '__main__':
+    ratingfile = 'input/16.RecommendedSystem/ml-1m/ratings.dat'
+    usercf = UserBasedCF()
+    usercf.generate_dataset(ratingfile)
+    usercf.calc_user_sim()
+    usercf.evaluate()

src/python/16.RecommendedSystem/基于物品.py

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+
+def ItemSimilarity1(train):
+    #calculate co-rated users between items
+    C = dict()
+    N = dict()
+    for u, items in train.items():
+        for i in users:
+            N[i] += 1
+            for j in users:
+                if i == j:
+                    continue
+                C[i][j] += 1
+
+    #calculate finial similarity matrix W
+    W = dict()
+    for i,related_items in C.items():
+        for j, cij in related_items.items():
+            W[u][v] = cij / math.sqrt(N[i] * N[j])
+    return W
+
+
+def ItemSimilarity2(train):
+    #calculate co-rated users between items
+    C = dict()
+    N = dict()
+    for u, items in train.items():
+        for i in users:
+            N[i] += 1
+            for j in users:
+                if i == j:
+                continue
+            C[i][j] += 1 / math.log(1 + len(items) * 1.0)
+
+    #calculate finial similarity matrix W
+    W = dict()
+    for i,related_items in C.items():
+        for j, cij in related_items.items():
+            W[u][v] = cij / math.sqrt(N[i] * N[j])
+    return W
+
+
+def Recommendation1(train, user_id, W, K):
+    rank = dict()
+    ru = train[user_id]
+    for i,pi in ru.items():
+        for j, wj in sorted(W[i].items(), key=itemgetter(1), reverse=True)[0:K]:
+            if j in ru:
+                continue
+            rank[j] += pi * wj
+    return rank
+
+
+def Recommendation2(train, user_id, W, K):
+    rank = dict()
+    ru = train[user_id]
+    for i,pi in ru.items():
+        for j, wj in sorted(W[i].items(), key=itemgetter(1), reverse=True)[0:K]:
+            if j in ru:
+                continue
+            rank[j].weight += pi * wj
+            rank[j].reason[i] = pi * wj
+    return rank
+
+

src/python/16.RecommendedSystem/基于用户.py

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+
+def UserSimilarity1(train):
+    W = dict()
+    for u in train.keys():
+        for v in train.keys():
+            if u == v:
+                continue
+            W[u][v] = len(train[u] & train[v])
+            W[u][v] /= math.sqrt(len(train[u]) * len(train[v]) * 1.0)
+    return W
+
+def UserSimilarity2(train):
+    # build inverse table for item_users
+    item_users = dict()
+    for u, items in train.items():
+        for i in items.keys():
+            if i not in item_users:
+                item_users[i] = set()
+            item_users[i].add(u)
+
+    #calculate co-rated items between users
+    C = dict()
+    N = dict()
+    for i, users in item_users.items():
+        for u in users:
+            N[u] += 1
+            for v in users:
+                if u == v:
+                    continue
+                C[u][v] += 1
+
+    #calculate finial similarity matrix W
+    W = dict()
+    for u, related_users in C.items():
+        for v, cuv in related_users.items():
+            W[u][v] = cuv / math.sqrt(N[u] * N[v])
+    return W
+
+
+def UserSimilarity3(train):
+    # build inverse table for item_users
+    item_users = dict()
+    for u, items in train.items():
+        for i in items.keys():
+            if i not in item_users:
+                item_users[i] = set()
+            item_users[i].add(u)
+
+    #calculate co-rated items between users
+    C = dict()
+    N = dict()
+    for i, users in item_users.items():
+        for u in users:
+            N[u] += 1
+            for v in users:
+                if u == v:
+                    continue
+                C[u][v] += 1 / math.log(1 + len(users))
+
+    #calculate finial similarity matrix W
+    W = dict()
+    for u, related_users in C.items():
+        for v, cuv in related_users.items():
+            W[u][v] = cuv / math.sqrt(N[u] * N[v])
+    return W
+
+
+def Recommend(user, train, W):
+    rank = dict()
+    interacted_items = train[user]
+    for v, wuv in sorted(W[u].items, key=itemgetter(1), reverse=True)[0:K]:
+        for i, rvi in train[v].items:
+            if i in interacted_items:
+                #we should filter items user interacted before
+                continue
+            rank[i] += wuv * rvi
+    return rank
+