-
Notifications
You must be signed in to change notification settings - Fork 0
/
CUR.py
282 lines (242 loc) · 9.93 KB
/
CUR.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
import pickle
import math
import numpy as np
import os
import time
import cur
np.set_printoptions(threshold=np.inf)
np.random.seed(30)
def CUR(A,num_dimensions,recomputeMatrix=False,energy_needed=1.0):
'''
Takes the user rating matrix and returns the computed C, U and R matrices.
If it finds that the file CUR_Matrices.txt already exists, it unpickles it and returns them,
else it computes them, pickles them and then returns them, You can recompute these matrices
using the boolean flag recomputeMatrix .
@type A: Numpy array
@param A : matrix that has to be decomposed
@type recomputeMatrix: boolean
@param recomputeMatrix : as name suggests, recompute the decomposition matrices, pickle them and return the matrices
@type: energy_needed: float in range [0,1]
@param energy_needed: float, the energy that has to be retained during the decomposition
@rtype (C,U,R) tuple of Numpy arrays
@return (C,U,R): tuple of decomposed matrices
'''
if energy_needed > 1 or energy_needed < 0:
raise Exception('energy_needed should not exceed 1. The value of energy_needed was: {}'.format(energy_needed))
file = 'CUR_Matrices.txt'
if recomputeMatrix or not os.path.exists(file):
num_rows = num_columns = num_dimensions
# Computing C matrix
temp = np.power(A,2)
p_column = np.sum(temp,axis=0)/np.sum(temp)
selected_columns = np.random.choice(A.shape[1],size=num_columns,p=p_column)
# selected_columns = np.random.choice(A.shape[1],replace=False,size=num_columns,p=p_column)
temp_C = A[:,selected_columns]
column_scaling_factor = np.sqrt(p_column[selected_columns] * num_columns)
# print(temp_C.shape,len(column_scaling_factor))
C = temp_C/column_scaling_factor
print('C computed')
# Computing R matrix
temp = np.power(A,2)
p_rows = np.sum(temp,axis=1)/np.sum(temp)
# selected_rows = np.random.choice(A.shape[0],replace=False,size=num_rows,p=p_rows)
selected_rows = np.random.choice(A.shape[0],size=num_rows,p=p_rows)
temp_R = A[selected_rows,:].T
rows_scaling_factor = np.sqrt(p_rows[selected_rows] * num_rows)
R = temp_R/rows_scaling_factor
R = R.T
print('R computed')
# compute U
W = A[selected_rows,:][:,selected_columns]
# SVD for W
W_WT = np.dot(W,W.T)
WT_W = np.dot(W.T,W)
# eigenvalue decomposition of W WT
eigenvalues_W_WT, X = np.linalg.eig(W_WT)
idx = np.argsort(eigenvalues_W_WT)
idx = idx[::-1]
eigenvalues_W_WT = eigenvalues_W_WT[idx]
eigenvalues_W_WT[np.abs(eigenvalues_W_WT) <= 1e-10] = 0
X = X[:,idx]
X = X.real
# eigenvalue decomposition of WT W
eigenvalues_WT_W, Y = np.linalg.eig(WT_W)
idx = np.argsort(eigenvalues_WT_W)
idx = idx[::-1]
eigenvalues_WT_W = eigenvalues_WT_W[idx]
eigenvalues_WT_W[np.abs(eigenvalues_WT_W) <= 1e-10] = 1e200
Y = Y[:,idx]
Y = Y.real
# energy based selection, if necessary that is...
if energy_needed != 1:
variances = np.power(eigenvalues_W_WT,2)
variances = variances.real
total_energy = np.sum(variances)
total_energy = total_energy.real
index_to_slice = 0
for i in range(0,variances.shape[0],-1):
current_energy = np.sum(variances[:i])
if current_energy >= energy_needed*total_energy:
index_to_slice = i
else:
break
eigenvalues_WT_W = eigenvalues_WT_W[:index_to_slice + 1]
X = X[:,:index_to_slice + 1]
Y = Y[:,:index_to_slice + 1]
Z_plus = np.eye(eigenvalues_WT_W.shape[0])
Z_plus = Z_plus*1/eigenvalues_WT_W
Z_plus[Z_plus == 1e-200] = 0
U = np.dot(Y,Z_plus)
U = np.dot(U,X.T)
U = U.real
eigenvalues_WT_W[np.abs(eigenvalues_WT_W) == 1e200] = 0
# save file
with open(file,'wb') as f:
data = {}
data['C'] = C
data['R'] = R
data['U'] = U
data['eigenvalues'] = eigenvalues_WT_W
# save pickled data
pickle.dump(data,f)
else:
with open(file,'rb') as f:
data = pickle.load(f)
print('done')
C = data['C']
R = data['R']
U = data['U']
eigenvalues_WT_W = data['eigenvalues']
return C,U,R,eigenvalues_WT_W
def rmse(originalMatrix,C,U,R):
'''
Calculates the Root mean Squared Error(RMSE) incurred after CUR decomposition
@param A: original matrix
@param C: Vector numpy
@param U: Vector numpy
@param R:Vector numpy
@return error: reconstruction error incurred while decomposing
'''
reconstructedMatrix = np.dot(C,U)
reconstructedMatrix = np.dot(reconstructedMatrix,R)
error = np.sum(np.power((originalMatrix-reconstructedMatrix),2))/(reconstructedMatrix.shape[0] * reconstructedMatrix.shape[1])
error = np.power(error,0.5)
return error
def query(q,R):
'''
This function queries the CUR matrix given a query vector
@type q: Square matrix (1D) (numpy Array)
@param q: Query vector
@type R: Square matrix (numpy Array)
@param R: The V obtained from the SVD
@rtype: Square matrix (1D) (numpy Array)
@return: The result vector obtained
'''
start_time = time.clock()
# print('query R',R.shape)
temp = np.dot(R.T,R)
final = np.dot(temp,q)
# print(final)
duration = time.clock() - start_time
return final,duration
def precisionTopK(k,q,R):
'''
This function calculates the Precision Top K
@type k : number
@param k : The k in Precision Top k
@type q: Square matrix (1D) (numpy Array)
@parma q: Query Vector
@type R: Square matrix (numpy Array)
@param R: The V obtained from the SVD
@rtype: number
@return: Precision Top K value obtained
'''
query_result,duration = query(q,R)
# print(query_result)
query_result[query_result < 3.5] = 0
query_result[query_result > 3.5] = 1
q[q < 3.5] = 0
q[q > 3.5] = 1
idx = query_result.argsort()[::-1]
query_result = query_result[idx]
q = q[:,idx]
prec_val = 0
for i in range(0,k-1):
if(query_result[i,0] == 1 and q[i,0] == 1) or (query_result[i,0] == 0 and q[i,0] == 0):
prec_val +=1
prec_val = prec_val / k
return prec_val
def spearmanCoefficient(predicted_rating,test_rating):
'''
This function calculates the spearman coefficient of two vectors
@type predicted_rank: Numpy array
@param: predicted_rating: predicted rating by the decomposition
@type test_rating: Numpy array
@param: test_rating: actual rating
@rtype: float
@return rho: the spearman coefficient
'''
predicted_rank = np.argsort(predicted_rating)
test_rank = np.argsort(test_rating)
d = test_rank - predicted_rank
d_squared = np.power(d,2)
sum_d_squared = np.sum(d_squared)
n = d.shape[0]
rho = 1 - (6*sum_d_squared)/(n*(n**2 - 1))
return rho
def Energy(A):
A = A*A
return A.sum()
if __name__=='__main__':
movie_size = 2000 #INCLUSIVE OF 2000th movie
user_size = 610 #INCLUSIVE OF 1500th movie
test_shift = 10
movie_pickle = open("movie_file.txt", 'rb')
rating_pickle = open("rating_file.txt", 'rb')
movie_dict = pickle.load(movie_pickle)
rating_dict = pickle.load(rating_pickle)
movieIds = movie_dict.keys()
userIds = rating_dict.keys()
user_rating_matrix = [0] * (len(userIds) + 1)
for i in range(0, len(user_rating_matrix)):
user_rating_matrix[i] = [0] * (movie_size+1) #Possible Change
for user in userIds:
user_movies = rating_dict[user].keys()
for movie in user_movies:
user_rating_matrix[int(user)][int(movie)] = float(rating_dict[user][movie])
user_rating_matrix = np.array(user_rating_matrix)
# calculating best size (number of columns for fitting the data)
# min_error = 1e50
# min_error_index = 0
# for i in range(1,user_rating_matrix.shape[0]):
# C,U,R,eigenvalues = CUR(user_rating_matrix,605,recomputeMatrix=True) # found experimentally.. assuming equal to the rank of the matrix
# error = rmse(user_rating_matrix,C,U,R)
# if error < min_error:
# min_error = error
# min_error_index = i
# print(min_error,i)
# print('min error at ',min_error,min_error_index)
C,U,R,eigenvalues = CUR(user_rating_matrix,605,recomputeMatrix=True)
error = rmse(user_rating_matrix,C,U,R)
print('rmse: ',error)
C_reduced,U_reduced,R_reduced,eigenvalues_reduced = CUR(user_rating_matrix,605,recomputeMatrix=True,energy_needed=.9)
error = rmse(user_rating_matrix,C_reduced,U_reduced,R_reduced)
print('rmse 90% energy: ',error)
test_array = user_rating_matrix[user_size-test_shift:,:]
user_array = user_rating_matrix[1:(user_size-test_shift),:]
precision = 0
precision_reduced = 0
print('computing average precision')
for i in range(test_array.shape[0]):
q = test_array[1,:]
q = np.reshape(q,(q.shape[0],1))
precision += precisionTopK(10,q,R)
precision_reduced += precisionTopK(10,q,R_reduced)
print('CUR: ',precision/test_array.shape[0])
print('CUR: 90% energy: ',precision_reduced/test_array.shape[0])
predicted_rating,duration_query = query(q,R)
predicted_rating_reduced,duration_query_reduced = query(q,R_reduced)
print("Spearman Coeff:",spearmanCoefficient(predicted_rating,q))
print("Spearman Coeff (90% reduced):",spearmanCoefficient(predicted_rating_reduced,q))
print('duration ',duration_query*1000,' milli-seconds')
print('duration reduced query',duration_query_reduced*1000,' milli-seconds')