Keras是一种搭建神经网络的框架，它封装得很好，简便易用，对于新手来讲还是十分友好的。它主要包括两种模型，其一为序列式模型，即一步步往后走，一条路走到黑；另一种为函数式模型，适合多输入；我们的输入包括User和Item，因此，使用的是函数式模型。

核心算法

  本文最初的实现参照了这篇文章，但文中方法有人提出未加正则，且分解出来是负数。针对这两个问题，进行改进从而得到如下代码：

def Recmand_model(num_user,num_item,d):K.clear_session()input_uer = Input(shape=[None,],dtype="int32")model_uer = Embedding(num_user,d,input_length = 1,embeddings_constraint=non_neg() #非负，下同)(input_uer)Dropout(0.2)model_uer = BatchNormalization()(model_uer)model_uer = Reshape((d,))(model_uer)input_item = Input(shape=[None,],dtype="int32")model_item  = Embedding(num_item,d,input_length = 1,embeddings_constraint=non_neg())(input_item)Dropout(0.2)model_item = BatchNormalization()(model_item)model_item = Reshape((d,))(model_item)out = Dot(1)([model_uer,model_item]) #点积运算model = Model(inputs=[input_uer,input_item], outputs=out)model.compile(loss= 'mse', optimizer='sgd')model.summary()return model

  关于非负，指的是分解后的两个矩阵每个值都要非负，实现起来比较简单，Embedding层刚好有进行约束的参数，但思想上还存在一定模糊，电影评分是处于[1-5]的，预测评分为什么一定要非负？负数是否可以代表该用户不喜欢该项目？由于推荐结果实际上只与分值的大小排序有关，非负还是否一定更好？
  除此以外，还尝试了神经网络的一些trick，加了dropout防止过拟合，加了BatchNormalization更易靠近最优解。下面是Keras的结构图，一目了然。

有效性验证

  同样我们先看核心算法是不是真的能完成矩阵分解，结果如下，非零值与原矩阵接近，完成验证。下附验证代码。

'''
Created on Fri Oct 18 15:08:00 2019@author: YLC
'''
import os
import numpy as np
import pandas as pd
import time
import math
from keras import Model
import keras.backend as K
from keras.layers import Embedding,Reshape,Input,Dot,Dense,Dropout,concatenate
from keras.models import load_model
from keras.utils import to_categorical
from keras import regularizers
from keras.constraints import non_negdef Recmand_model(num_user,num_item,d):K.clear_session()input_uer = Input(shape=[None,],dtype="int32")model_uer = Embedding(num_user,d,input_length = 1,embeddings_constraint=non_neg() #非负，下同)(input_uer)Dropout(0.2)model_uer = BatchNormalization()(model_uer)model_uer = Reshape((d,))(model_uer)input_item = Input(shape=[None,],dtype="int32")model_item  = Embedding(num_item,d,input_length = 1,embeddings_constraint=non_neg())(input_item)Dropout(0.2)model_item = BatchNormalization()(model_item)model_item = Reshape((d,))(model_item)out = Dot(1)([model_uer,model_item]) #点积运算model = Model(inputs=[input_uer,input_item], outputs=out)model.compile(loss= 'mse', optimizer='sgd')model.summary()return modeldef train(num_user,num_item,train_data,d,step):model = Recmand_model(num_user,num_item,d)train_user = train_data[:,0]train_item = train_data[:,1]train_x = [train_user,train_item]train_y = train_data[:,2]model.fit(train_x,train_y,batch_size = 4,epochs = step)model.save("./MFmodel.h5")def test(num_user,num_item,R):model = load_model('./MFmodel.h5')nR = np.zeros([num_user,num_item])for i in range(num_user):for j in range(num_item):nR[i][j] = model.predict([[i],[j]])return nRdef cal_e(R,nR):e = 0cnt = 0for i in range(len(R)):for j in range(len(R[0])):if(R[i][j]!=0):cnt = cnt + 1e = e + math.pow(R[i][j]-nR[i][j],2)e = 1.0 * e/cntreturn edef RtransT(R):user = [u for u in range(len(R))]item = [i for i in range(len(R[0]))]Table = []for i in user:for j in item:if R[i][j]!= 0:Table.append([i,j,R[i][j]])Table = np.array(Table)return Tabledef NMF(R,d,step):T = RtransT(R)M=len(R)N=len(R[0])train(M,N,T,d,step)nR = test(M,N,R)e = cal_e(R,nR)return e,nRif __name__ == '__main__':R=[[5,2,0,3,1],[0,2,1,4,5],[1,1,0,2,4],[2,2,0,5,0]]R=np.array(R)dimension = 3step = 2000e,nR = NMF(R,dimension,step)print('-----原矩阵R：------')print(R)print('-----近似矩阵nR：------')print(nR)print('e is:',e)

训练

   模型的构建有三个参数，用户数、项目数和嵌入向量的维度，而模型的输入为训练集的用户记录数据、项目记录数据和真实评分。batch_size是批处理参数，epochs是模型的迭代次数，h5为HDF5文件格式。

def train(all_user,all_item,train_data,d):num_user = max(all_user) + 1num_item = max(all_item) + 1model = Recmand_model(num_user,num_item,d)train_user = train_data['user'].valuestrain_item = train_data['item'].valuestrain_x = [train_user,train_item]
#    train_data['rating'] = 1 #不用评分train_y = train_data['rating'].valuesmodel.fit(train_x,train_y,batch_size = 128,epochs = 8)plot_model(model, to_file='./NN MF/NNMF.png',show_shapes=True) #输出框架图model.save("./NN MF/MFmodel.h5")

测试

   同(三)一样，加入推荐新项目的限制。

def test(train_data,test_data,all_item,k):model = load_model('./NN MF/MFmodel.h5')PRE = 0REC = 0MAP = 0MRR = 0AP = 0HITS = 0sum_R = 0sum_T = 0valid_cnt = 0stime = time.time()test_user = np.unique(test_data['user'])for user in test_user:
#        user = 0visited_item = list(train_data[train_data['user']==user]['item'])
#        print('访问过的item:',visited_item)if len(visited_item)==0: #没有训练数据，跳过continueper_st = time.time()testlist = list(test_data[test_data['user']==user]['item'].drop_duplicates()) #去重保留第一个testlist = list(set(testlist)-set(testlist).intersection(set(visited_item))) #去掉访问过的itemif len(testlist)==0: #过滤后为空，跳过continuevalid_cnt = valid_cnt + 1 #有效测试数poss = {}        for item in all_item:if item in visited_item:continueelse:poss[item] = float(model.predict([[user],[item]]))
#        print(poss)
#        print("对用户",user)rankedlist,test_score = topk(poss,k) 
#        print("Topk推荐:",rankedlist)
#        print("实际访问:",testlist)
#        print("单条推荐耗时:",time.time() - per_st)AP_i,len_R,len_T,MRR_i,HITS_i= cal_indicators(rankedlist, testlist)AP += AP_isum_R += len_Rsum_T += len_TMRR += MRR_iHITS += HITS_i
#        print(test_score)
#        print('--------')
#        breaketime = time.time()PRE = HITS/(sum_R*1.0)REC = HITS/(sum_T*1.0)MAP = AP/(valid_cnt*1.0)MRR = MRR/(valid_cnt*1.0)p_time = (etime-stime)/valid_cntprint('评价指标如下:')print('PRE@',k,':',PRE)print('REC@',k,':',REC)print('MAP@',k,':',MAP)print('MRR@',k,':',MRR)print('平均每条推荐耗时:',p_time)with open('./Basic MF/result_'+dsname+'.txt','w') as f:f.write('评价指标如下:\n')f.write('PRE@'+str(k)+':'+str(PRE)+'\n')f.write('REC@'+str(k)+':'+str(REC)+'\n')f.write('MAP@'+str(k)+':'+str(MAP)+'\n')f.write('MRR@'+str(k)+':'+str(MRR)+'\n') f.write('平均每条推荐耗时@:'+str(k)+':'+str(p_time)+'\n')

Main函数

   与(三）不同，这里取$d=60$。

if __name__ == '__main__':dsname = 'ML100K'dformat = ['user','item','rating','time']all_user,all_item,train_data,test_data = getUI(dsname,dformat) #第一次使用需取消注释d = 60 #隐因子维度steps = 10k = 10train(all_user,all_item,train_data,d)test(train_data,test_data,all_item,k)

实验结果

   先看ML100K的结果。

  再看ML1M的结果。

进阶！灵魂拷问

  拷问1. 利用神经网络做矩阵分解(下称NNMF(Neural Network Matrix Factorization))与传统矩阵分解相比，哪种更好？
  从实验结果上来看，Basic MF会更好。以下为传统矩阵分解的实验结果。但从个人观点，NNMF的潜力更大。相比于传统矩阵分解的过程，利用神经网络做矩阵分解有以下好处：
  1).NNMF训练的时耗远低于Basic MF。因为NNMF是直接嵌入，不需要构建矩阵，且神经网络的优化器什么的都是现成的。
  2).NNMF吃神经网络的红利。理论上任何有利于神经网络的技术都可以用过来，比如本文用到的Dropout、BN等。
  那为什么效果会差呢？个人认为一方面是参数没有调到最优，另一方面是数据量不够，众所周知，神经网络是数据驱动的。不过在本次试验中，两者的差距并非很大。

  拷问2. 评分矩阵和0-1矩阵在此实验中效果如何？
  以下为0-1矩阵的。明显基本没有效果，不过如果数据量够大的话还是有机会。

完整代码

# -*- coding: utf-8 -*-
"""
Created on Fri Oct 18 15:08:00 2019@author: YLC
"""import os
import numpy as np
import pandas as pd
import time
import math
from keras import Model
import keras.backend as K
from keras.layers import Embedding,Reshape,Input,Dot,Dense,Dropout,concatenate,BatchNormalization
from keras.models import load_model
from keras.utils import plot_model,to_categorical
from keras import regularizers
from keras.constraints import non_neg
from keras import optimizersdef getUI(dsname,dformat): #获取全部用户和项目st = time.time()train = pd.read_csv(dsname+'_train.txt',header = None,names = dformat)test = pd.read_csv(dsname+'_test.txt',header = None,names = dformat)data = pd.concat([train,test])all_user = np.unique(data['user'])all_item = np.unique(data['item'])train.sort_values(by=['user','item'],axis=0,inplace=True) #先按时间、再按用户排序if os.path.exists('./NN MF'):passelse:os.mkdir('./NN MF')train.to_csv('./NN MF/train.txt',index = False,header=0)test.to_csv('./NN MF/test.txt',index = False,header=0)et = time.time()print("get UI complete! cost time:",et-st)return all_user,all_item,train,testdef topk(dic,k):keys = []values = []for i in range(0,k):key,value = max(dic.items(),key=lambda x: x[1])keys.append(key)values.append(value)dic.pop(key)return keys,valuesdef cal_indicators(rankedlist, testlist):HITS_i = 0sum_precs = 0AP_i = 0 len_R = 0 len_T = 0MRR_i = 0 ranked_score = []for n in range(len(rankedlist)):if rankedlist[n] in testlist:HITS_i += 1sum_precs += HITS_i / (n + 1.0)if MRR_i == 0:MRR_i = 1.0/(rankedlist.index(rankedlist[n])+1)else:ranked_score.append(0)if HITS_i > 0:AP_i = sum_precs/len(testlist)len_R = len(rankedlist)len_T = len(testlist)return AP_i,len_R,len_T,MRR_i,HITS_idef Recmand_model(num_user,num_item,d):K.clear_session()input_uer = Input(shape=[None,],dtype="int32")model_uer = Embedding(num_user,d,input_length = 1,embeddings_constraint=non_neg() #非负，下同)(input_uer)Dropout(0.2)model_uer = BatchNormalization()(model_uer)model_uer = Reshape((d,))(model_uer)input_item = Input(shape=[None,],dtype="int32")model_item  = Embedding(num_item,d,input_length = 1,embeddings_constraint=non_neg())(input_item)Dropout(0.2)model_item = BatchNormalization()(model_item)model_item = Reshape((d,))(model_item)out = Dot(1)([model_uer,model_item]) #点积运算model = Model(inputs=[input_uer,input_item], outputs=out)model.compile(loss= 'mse', optimizer='sgd')model.summary()return modeldef train(all_user,all_item,train_data,d):num_user = max(all_user) + 1num_item = max(all_item) + 1model = Recmand_model(num_user,num_item,d)train_user = train_data['user'].valuestrain_item = train_data['item'].valuestrain_x = [train_user,train_item]
#    train_data['rating'] = 1 #不用评分train_y = train_data['rating'].valuesmodel.fit(train_x,train_y,batch_size = 128,epochs = 8)plot_model(model, to_file='./NN MF/NNMF.png',show_shapes=True) #输出框架图model.save("./NN MF/MFmodel.h5")def test(train_data,test_data,all_item,k):model = load_model('./NN MF/MFmodel.h5')PRE = 0REC = 0MAP = 0MRR = 0AP = 0HITS = 0sum_R = 0sum_T = 0valid_cnt = 0stime = time.time()test_user = np.unique(test_data['user'])for user in test_user:
#        user = 0visited_item = list(train_data[train_data['user']==user]['item'])
#        print('访问过的item:',visited_item)if len(visited_item)==0: #没有训练数据，跳过continueper_st = time.time()testlist = list(test_data[test_data['user']==user]['item'].drop_duplicates()) #去重保留第一个testlist = list(set(testlist)-set(testlist).intersection(set(visited_item))) #去掉访问过的itemif len(testlist)==0: #过滤后为空，跳过continuevalid_cnt = valid_cnt + 1 #有效测试数poss = {}        for item in all_item:if item in visited_item:continueelse:poss[item] = float(model.predict([[user],[item]]))
#        print(poss)
#        print("对用户",user)rankedlist,test_score = topk(poss,k) 
#        print("Topk推荐:",rankedlist)
#        print("实际访问:",testlist)
#        print("单条推荐耗时:",time.time() - per_st)AP_i,len_R,len_T,MRR_i,HITS_i= cal_indicators(rankedlist, testlist)AP += AP_isum_R += len_Rsum_T += len_TMRR += MRR_iHITS += HITS_i
#        print(test_score)
#        print('--------')
#        breaketime = time.time()PRE = HITS/(sum_R*1.0)REC = HITS/(sum_T*1.0)MAP = AP/(valid_cnt*1.0)MRR = MRR/(valid_cnt*1.0)p_time = (etime-stime)/valid_cntprint('评价指标如下:')print('PRE@',k,':',PRE)print('REC@',k,':',REC)print('MAP@',k,':',MAP)print('MRR@',k,':',MRR)print('平均每条推荐耗时:',p_time)with open('./Basic MF/result_'+dsname+'.txt','w') as f:f.write('评价指标如下:\n')f.write('PRE@'+str(k)+':'+str(PRE)+'\n')f.write('REC@'+str(k)+':'+str(REC)+'\n')f.write('MAP@'+str(k)+':'+str(MAP)+'\n')f.write('MRR@'+str(k)+':'+str(MRR)+'\n') f.write('平均每条推荐耗时@:'+str(k)+':'+str(p_time)+'\n')if __name__ == '__main__':dsname = 'ML100K'dformat = ['user','item','rating','time']all_user,all_item,train_data,test_data = getUI(dsname,dformat) #第一次使用需取消注释d = 60 #隐因子维度steps = 10k = 10train(all_user,all_item,train_data,d)test(train_data,test_data,all_item,k)