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evaluation.py
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#!/usr/bin/env python2
# -*- coding: utf-8 -*-
"""
Created on Mon May 8 20:50:36 2017
@author: zhouyi
"""
import numpy as np
'''
Calculate the normalized discounting gain for matrix factorization
Refer to:
https://en.wikipedia.org/wiki/Discounted_cumulative_gain#Normalized_DCG
Args:
train_data: Matrix,shape(n_users,n_items). The data you use to train
held_out_data: Matrix,shape(n_users,n_items). The data you use to calculate NDCG scores
theta: Matrix,shape(n_users,n_components), user factors
beta: Matrix,shape(n_items,n_components), user factors
mu: Matrix,shape(n_users,n_items), weight vectors for Rating ,if necessary
k: Number of results to consider
(R[u,i]=theta[u]*beta[i]*mu[u,i] or R[u,i]=theta[u]*beta[i])
Return:
average NDCG across users
'''
def NDCG_at_k(train_data,held_out_data,theta,beta,k,mu=None):
assert train_data.shape == held_out_data.shape
assert theta.shape[1] == beta.shape[1]
assert theta.shape[0] == train_data.shape[0]
assert beta.shape[0] == train_data.shape[1]
n_users,n_items=train_data.shape
user_NDCG_table=np.zeros(n_users)
for u in range(n_users):
DCG_at_k=0
IDCG_at_k=0
Rank_list=[]
for i in range(n_items):
'''To use the np.sort, preference should be negative'''
Rank_list.append((i,0-theta[u].dot(beta[i])))
table_dtype = [('item_index', int), ('preference', float)]
Rank_Table=np.array(Rank_list,dtype=table_dtype)
Rank_Table=np.sort(Rank_Table, order=['preference'])
#print Rank_Table
for top_k in range(k):
item_index=Rank_Table[top_k][0]
#print (u,item_index)
''''held_out_data[u,item_index]!=0'''
if held_out_data[u,item_index]> 0.1 :
DCG_at_k+=1.0/np.log2(top_k+1+1)
IDCG_at_k+=1.0/np.log2(top_k+1+1)
user_NDCG_table[u]=DCG_at_k/IDCG_at_k
#print user_NDCG_table
return sum(user_NDCG_table)/n_users
def weighted_NDCG_at_k(train_data,held_out_data,theta,beta,k,mu):
assert train_data.shape == held_out_data.shape
assert train_data.shape == mu.shape
assert theta.shape[1] == beta.shape[1]
assert theta.shape[0] == train_data.shape[0]
assert beta.shape[0] == train_data.shape[1]
n_users,n_items=train_data.shape
user_NDCG_table=np.zeros(n_users)
for u in range(n_users):
DCG_at_k=0
IDCG_at_k=0
Rank_list=[]
for i in range(n_items):
'''To use the np.sort, preference should be negative'''
Rank_list.append((i,0-theta[u].dot(beta[i])*mu[u,i]))
table_dtype = [('item_index', int), ('preference', float)]
Rank_Table=np.array(Rank_list,dtype=table_dtype)
Rank_Table=np.sort(Rank_Table, order=['preference'])
#print Rank_Table
for top_k in range(k):
item_index=Rank_Table[top_k][0]
#print (u,item_index)
''''held_out_data[u,item_index]!=0'''
if held_out_data[u,item_index]> 0.1 :
DCG_at_k+=1.0/np.log2(top_k+1+1)
IDCG_at_k+=1.0/np.log2(top_k+1+1)
user_NDCG_table[u]=DCG_at_k/IDCG_at_k
#print user_NDCG_table
return sum(user_NDCG_table)/n_users
'''
Calculate the Mean Average Precision for matrix factorization
Refer to:
https://www.kaggle.com/wiki/MeanAveragePrecision
assuming: k << m
ap@k=∑Precision(n)/k , n=1...k
map@k=Average(ap@k)
Args:
train_data: Matrix,shape(n_users,n_items). The data you use to train
held_out_data: Matrix,shape(n_users,n_items). The data you use to calculate MAP scores
theta: Matrix,shape(n_users,n_components), user factors
beta: Matrix,shape(n_items,n_components), user factors
mu: Matrix,shape(n_users,n_items), weight vectors for Rating ,if necessary
k: Number of results to consider
(R[u,i]=theta[u]*beta[i]*mu[u,i] or R[u,i]=theta[u]*beta[i])
Return:
average ap@k across users
'''
def MAP_at_k(train_data,held_out_data,theta,beta,k,mu=None):
assert train_data.shape == held_out_data.shape
assert theta.shape[1] == beta.shape[1]
assert theta.shape[0] == train_data.shape[0]
assert beta.shape[0] == train_data.shape[1]
n_users,n_items=train_data.shape
user_AP_table=np.zeros(n_users)
for u in range(n_users):
Rank_list=[]
for i in range(n_items):
'''To use the np.sort, preference should be negative'''
Rank_list.append((i,0-theta[u].dot(beta[i])))
table_dtype = [('item_index', int), ('preference', float)]
Rank_Table=np.array(Rank_list,dtype=table_dtype)
Rank_Table=np.sort(Rank_Table, order=['preference'])
#print Rank_Table
count=0.0
AP_k=0.0
for top_k in range(k):
item_index=Rank_Table[top_k][0]
#print (u,item_index)
''''held_out_data[u,item_index]!=0'''
if held_out_data[u,item_index]> 0.1 :
count+=1.0
Precesion_top_k=count/(top_k+1)
AP_k+=Precesion_top_k/k
user_AP_table[u]=AP_k
#print user_AP_table
return sum(user_AP_table)/n_users
def weighted_MAP_at_k(train_data,held_out_data,theta,beta,k,mu):
assert train_data.shape == held_out_data.shape
assert theta.shape[1] == beta.shape[1]
assert theta.shape[0] == train_data.shape[0]
assert beta.shape[0] == train_data.shape[1]
n_users,n_items=train_data.shape
user_AP_table=np.zeros(n_users)
for u in range(n_users):
Rank_list=[]
for i in range(n_items):
'''To use the np.sort, preference should be negative'''
Rank_list.append((i,0-theta[u].dot(beta[i])*mu[u,i]))
table_dtype = [('item_index', int), ('preference', float)]
Rank_Table=np.array(Rank_list,dtype=table_dtype)
Rank_Table=np.sort(Rank_Table, order=['preference'])
#print Rank_Table
count=0.0
AP_k=0.0
for top_k in range(k):
item_index=Rank_Table[top_k][0]
#print (u,item_index)
''''held_out_data[u,item_index]!=0'''
if held_out_data[u,item_index]> 0.1 :
count+=1.0
Precesion_top_k=count/(top_k+1)
AP_k+=Precesion_top_k/k
user_AP_table[u]=AP_k
#print user_AP_table
return sum(user_AP_table)/n_users
'''
Calculate the Mean Recall for matrix factorization
Refer to:
https://en.wikipedia.org/wiki/Precision_and_recall#Recall
Recall in information retrieval is the fraction of the documents that are
relevant to the query that are successfully retrieved.
Args:
train_data: Matrix,shape(n_users,n_items). The data you use to train
held_out_data: Matrix,shape(n_users,n_items). The data you use to calculate RECALL scores
theta: Matrix,shape(n_users,n_components), user factors
beta: Matrix,shape(n_items,n_components), user factors
mu: Matrix,shape(n_users,n_items), weight vectors for Rating ,if necessary
k: Number of results to consider
(R[u,i]=theta[u]*beta[i]*mu[u,i] or R[u,i]=theta[u]*beta[i])
Return:
average Recall@k across users
'''
def Recall_at_k(train_data,held_out_data,theta,beta,k,mu=None):
assert train_data.shape == held_out_data.shape
assert theta.shape[1] == beta.shape[1]
assert theta.shape[0] == train_data.shape[0]
assert beta.shape[0] == train_data.shape[1]
n_users,n_items=train_data.shape
user_Recall_table=np.zeros(n_users)
for u in range(n_users):
#print "user:",u
Rank_list=[]
for i in range(n_items):
'''To use the np.sort, preference should be negative'''
Rank_list.append((i,0-theta[u].dot(beta[i])))
table_dtype = [('item_index', int), ('preference', float)]
Rank_Table=np.array(Rank_list,dtype=table_dtype)
Rank_Table=np.sort(Rank_Table, order=['preference'])
#print Rank_Table
rank_k_set=set()
for top_k in range(k):
item_index=Rank_Table[top_k][0]
rank_k_set.add(item_index)
#print rank_k_set
count_in_rank_k_set=0.0
count_in_held_out_data=0.0
for i in range(n_items):
if held_out_data[u,i]> 0.1 :
count_in_held_out_data+=1
if i in rank_k_set:
count_in_rank_k_set+=1
size=min(k,count_in_held_out_data)
if size > 0.1:
user_Recall_table[u]=count_in_rank_k_set/size
else:
user_Recall_table[u]=0
#print user_Recall_table
return sum(user_Recall_table)/n_users
def weighted_Recall_at_k(train_data,held_out_data,theta,beta,k,mu):
assert train_data.shape == held_out_data.shape
assert theta.shape[1] == beta.shape[1]
assert theta.shape[0] == train_data.shape[0]
assert beta.shape[0] == train_data.shape[1]
n_users,n_items=train_data.shape
user_Recall_table=np.zeros(n_users)
for u in range(n_users):
#print "user:",u
Rank_list=[]
for i in range(n_items):
'''To use the np.sort, preference should be negative'''
Rank_list.append((i,0-theta[u].dot(beta[i])*mu[u,i]))
table_dtype = [('item_index', int), ('preference', float)]
Rank_Table=np.array(Rank_list,dtype=table_dtype)
Rank_Table=np.sort(Rank_Table, order=['preference'])
#print Rank_Table
rank_k_set=set()
for top_k in range(k):
item_index=Rank_Table[top_k][0]
rank_k_set.add(item_index)
#print rank_k_set
count_in_rank_k_set=0.0
count_in_held_out_data=0.0
for i in range(n_items):
if held_out_data[u,i]> 0.1 :
count_in_held_out_data+=1
if i in rank_k_set:
count_in_rank_k_set+=1
size=min(k,count_in_held_out_data)
if size > 0.1:
user_Recall_table[u]=count_in_rank_k_set/size
else:
user_Recall_table[u]=0
#print user_Recall_table
return sum(user_Recall_table)/n_users
'''
#Test Script
#3 user, 4 items, 5 components
train_data=np.random.rand(3,4)
mu=np.random.rand(3,4)
held_out_data=np.array([[1,1,1,0],[0,0,1,0],[1,0,1,0]])
theta=np.random.rand(3,5)
beta=np.random.rand(4,5)
print weighted_Recall_at_k(train_data,held_out_data,theta,beta,2,mu)
'''