# -*- Encoding:UTF-8 -*-
'''
@author: Jason.F
@data: 2019.07.18
@function: Implementing PMF
Dataset: Movielen Dataset(ml-1m)
Evaluating: hitradio,ndcg
https://papers.nips.cc/paper/3208-probabilistic-matrix-factorization.pdf
Matlab: http://www.utstat.toronto.edu/~rsalakhu/BPMF.html
@reference: https://github.com/adamzjw/Probabilistic-matrix-factorization-in-Python
'''
import numpy as np
import pandas as pd
from numpy.random import RandomState
import copy
import heapq
import math
from numpy import linalg as LA
import random
#define class PMF
class PMF:
def __init__(self, num_feat=8, epsilon=1, _lambda=0.1, momentum=0.8, maxepoch=20, num_batches=10, batch_size=1000):
self.num_feat = num_feat
self.epsilon = epsilon
self._lambda = _lambda
self.momentum = momentum
self.maxepoch = maxepoch
self.num_batches = num_batches
self.batch_size = batch_size
self.w_C = None
self.w_I = None
self.err_train = []
self.err_val = []
def fit(self, train_vec, val_vec):
# mean subtraction
self.mean_inv = np.mean(train_vec[:,2])
pairs_tr = train_vec.shape[0]
pairs_va = val_vec.shape[0]
# 1-p-i, 2-m-c
num_inv = int(max(np.amax(train_vec[:,0]), np.amax(val_vec[:,0]))) + 1
num_com = int(max(np.amax(train_vec[:,1]), np.amax(val_vec[:,1]))) + 1
incremental = False
if ((not incremental) or (self.w_C is None)):
# initialize
self.epoch = 0
self.w_C = 0.1 * np.random.randn(num_com, self.num_feat)
self.w_I = 0.1 * np.random.randn(num_inv, self.num_feat)
self.w_C_inc = np.zeros((num_com, self.num_feat))
self.w_I_inc = np.zeros((num_inv, self.num_feat))
while self.epoch < self.maxepoch:
self.epoch += 1
# Shuffle training truples
shuffled_order = np.arange(train_vec.shape[0])
np.random.shuffle(shuffled_order)
# Batch update
for batch in range(self.num_batches):
# print "epoch %d batch %d" % (self.epoch, batch+1)
batch_idx = np.mod(np.arange(self.batch_size * batch,
self.batch_size * (batch+1)),
shuffled_order.shape[0])
batch_invID = np.array(train_vec[shuffled_order[batch_idx], 0], dtype='int32')
batch_comID = np.array(train_vec[shuffled_order[batch_idx], 1], dtype='int32')
# Compute Objective Function
pred_out = np.sum(np.multiply(self.w_I[batch_invID,:],
self.w_C[batch_comID,:]),
axis=1) # mean_inv subtracted
rawErr = pred_out - train_vec[shuffled_order[batch_idx], 2] + self.mean_inv
# Compute gradients
Ix_C = 2 * np.multiply(rawErr[:, np.newaxis], self.w_I[batch_invID,:]) \
+ self._lambda * self.w_C[batch_comID,:]
Ix_I = 2 * np.multiply(rawErr[:, np.newaxis], self.w_C[batch_comID,:]) \
+ self._lambda * self.w_I[batch_invID,:]
dw_C = np.zeros((num_com, self.num_feat))
dw_I = np.zeros((num_inv, self.num_feat))
# loop to aggreate the gradients of the same element
for i in range(self.batch_size):
dw_C[batch_comID[i],:] += Ix_C[i,:]
dw_I[batch_invID[i],:] += Ix_I[i,:]
# Update with momentum
self.w_C_inc = self.momentum * self.w_C_inc + self.epsilon * dw_C / self.batch_size
self.w_I_inc = self.momentum * self.w_I_inc + self.epsilon * dw_I / self.batch_size
self.w_C = self.w_C - self.w_C_inc
self.w_I = self.w_I - self.w_I_inc
# Compute Objective Function after
if batch == self.num_batches - 1:
pred_out = np.sum(np.multiply(self.w_I[np.array(train_vec[:,0], dtype='int32'),:],
self.w_C[np.array(train_vec[:,1], dtype='int32'),:]),
axis=1) # mean_inv subtracted
rawErr = pred_out - train_vec[:, 2] + self.mean_inv
obj = LA.norm(rawErr) ** 2 \
+ 0.5*self._lambda*(LA.norm(self.w_I) ** 2 + LA.norm(self.w_C) ** 2)
self.err_train.append(np.sqrt(obj/pairs_tr))
# Compute validation error
if batch == self.num_batches - 1:
pred_out = np.sum(np.multiply(self.w_I[np.array(val_vec[:,0], dtype='int32'),:],
self.w_C[np.array(val_vec[:,1], dtype='int32'),:]),
axis=1) # mean_inv subtracted
rawErr = pred_out - val_vec[:, 2] + self.mean_inv
self.err_val.append(LA.norm(rawErr)/np.sqrt(pairs_va))
# Print info
if batch == self.num_batches - 1:
print ('Training RMSE: %f, Val RMSE %f' % (self.err_train[-1], self.err_val[-1]))
def predict(self, invID, comID):
return np.dot(self.w_C[comID,:], self.w_I[invID,:]) + self.mean_inv
def evaluate(self, test_vec, k=10):
def getHitRatio(ranklist, gtItem):
for item in ranklist:
if item == gtItem:
return 1
return 0
def getNDCG(ranklist, gtItem):
for i in range(len(ranklist)):
item = ranklist[i]
if item == gtItem:
return math.log(2) / math.log(i+2)
return 0
testset = pd.DataFrame(test_vec, columns=['u','i'])
hits = []
ndcgs = []
list_csr = list(set(np.array(testset['u']).tolist()))
for u in list_csr:
csrset = np.array(testset[testset['u']==u]).tolist()
scorelist = []
positem = csrset[0][1]#first item is positive
for _, i in csrset:
scorelist.append([i, self.predict(u,i)])
#get topk
map_item_score = {}
for item, rate in scorelist: #turn dict
map_item_score[item] = rate
ranklist = heapq.nlargest(10, map_item_score, key=map_item_score.get)#default Topn=10
hr = getHitRatio(ranklist, positem)
hits.append(hr)
ndcg = getNDCG(ranklist, positem)
ndcgs.append(ndcg)
hitratio,ndcg = np.array(hits).mean(), np.array(ndcgs).mean()
return hitratio,ndcg
#loading dataset
def getTrainset(filePath):
trainset = []
maxu = 0
maxi = 0
maxr = 0.0
with open(filePath, 'r') as fd:
line = fd.readline()
while line != None and line != "":
arr = line.split("\t")
u, i, rating = int(arr[0]), int(arr[1]), float(arr[2])
trainset.append([int(arr[0]), int(arr[1]), float(arr[2])])
if rating > maxr: maxr = rating
if u > maxu: maxu = u
if i > maxi: maxi = i
line = fd.readline()
return trainset, maxr, maxu, maxi
def getTestset(filePath):
testset = []
with open(filePath, 'r') as fd:
line = fd.readline()
while line != None and line != '':
arr = line.split('\t')
u = eval(arr[0])[0]
testset.append([u, eval(arr[0])[1]])#one postive item
for i in arr[1:]:
testset.append([u, int(i)]) #99 negative items
line = fd.readline()
return testset
def getTrainDict(data):
dataDict = {}
for i in data:
dataDict[(i[0], i[1])] = i[2]
return dataDict
def getNegTrain(data, maxi, negNum=4):
datadict = getTrainDict(data)
trainneg = []
for i in data:
trainneg.append([i[0],i[1],i[2]])
for t in range(negNum):
j = np.random.randint(maxi)
while (i[0], j) in datadict:
j = np.random.randint(maxi)
trainneg.append([i[0], j, 0.0])
return trainneg
if __name__ == '__main__':
trainset, maxr, maxu, maxi = getTrainset("/data/fjsdata/ctKngBase/ml/ml-1m.train.rating")
trainneg = getNegTrain(trainset, maxi)
testset = getTestset("/data/fjsdata/ctKngBase/ml/ml-1m.test.negative")
print('Dataset Statistics: Interaction = %d, User = %d, Item = %d, Sparsity = %.4f' % (len(trainset), maxu+1, maxi+1, len(trainset)/(maxu*maxr)))
print ("%3s%20s%20s" % ('K','HR@10', 'NDCG@10'))
for K in [8, 16, 32, 64]:
pmf = PMF(num_feat=K)
valtest = random.sample(trainset,int(0.2*len(trainset)))
pmf.fit(np.array(trainneg), np.array(valtest))
hit, ndcg = pmf.evaluate(testset)
print ("%3d%20.6f%20.6f" % (K, hit, ndcg))
'''
nohup python -u PMF-ml.py > pmf-ml.log &
K HR@10 NDCG@10
8 0.101325 0.045585
16 0.099338 0.046128
32 0.094371 0.042417
64 0.105795 0.047519
'''
矩阵分解模型的概率角度解释。
