/
optimization.py
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/
optimization.py
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# Import the Required Libraries
import autograd.numpy as np
from autograd import grad
import random
lmd_BPR = 100
lmd_u = 1
lmd_v = 1
def lossfunction_all(rating_matrix, movie_vectors, user_vectors, flag):
if flag == 1: # used in user tree construction, user_vectors is a 1*K vector
user_vectors = np.array([user_vectors for i in range(len(rating_matrix))])
if flag == 0: # used in item tree construction, movie_vectors is a 1*K vector
movie_vectors = np.array([movie_vectors for i in range(rating_matrix.shape[1])])
value = 0
# Add regularization term
user_l = user_vectors[np.nonzero(user_vectors)]
value = value + lmd_u * np.dot(user_l, user_l)
mov_l = movie_vectors[np.nonzero(movie_vectors)]
value = value + lmd_v * np.dot(mov_l, mov_l)
if len(rating_matrix) == 0:
return value
predict = np.dot(user_vectors, movie_vectors.T)
P = predict[np.nonzero(rating_matrix)]
R = rating_matrix[np.nonzero(rating_matrix)]
Err = P - R
value = value + np.dot(Err, Err)
np.random.seed(0)
num_pair = 20
num_user, num_item = rating_matrix.shape
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if rating_matrix[u1][i1] > rating_matrix[u2][i2]:
diff = np.dot(user_vectors[u1, :].T, movie_vectors[i1, :]) - np.dot(user_vectors[u2, :].T,
movie_vectors[i2, :])
diff = -diff
value = value + lmd_BPR * np.log(1 + np.exp(diff))
return value
def selfgradu(rating_matrix, movie_vectors, current_vector, user_vector):
delta_u = np.zeros_like(user_vector)
num_point = 100
num_pair = 20
num_user, num_item = rating_matrix.shape
np.random.seed(0)
user_vector = user_vector + current_vector
if len(rating_matrix) == 0:
return delta_u
for i in range(num_point):
c1 = np.random.randint(0, num_item * num_user)
u1, i1 = c1 // num_item, c1 % num_item
if rating_matrix[u1][i1] != 0:
delta_u += -2 * (rating_matrix[u1][i1] - np.dot(user_vector, movie_vectors[i1])) * movie_vectors[i1] + 2 * lmd_u * user_vector
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if rating_matrix[u1][i1] > rating_matrix[u2][i2]:
diff = np.dot(user_vector.T, movie_vectors[i1, :]) - np.dot(user_vector.T, movie_vectors[i2, :])
diff = -diff
delta_u += lmd_BPR * (movie_vectors[i2, :] - movie_vectors[i1, :]) * np.exp(diff) / (1 + np.exp(diff))
return delta_u
def selfgradv(rating_matrix, movie_vector, current_vector, user_vectors):
delta_v = np.zeros_like(movie_vector)
num_point = 100
num_pair = 20
num_user, num_item = rating_matrix.shape
np.random.seed(0)
movie_vector = movie_vector + current_vector
if len(rating_matrix) == 0:
return delta_v
for i in range(num_point):
c1 = np.random.randint(0, num_item * num_user)
u1, i1 = c1 // num_item, c1 % num_item
if rating_matrix[u1][i1] != 0:
delta_v += -2 * (rating_matrix[u1][i1] - np.dot(user_vectors[u1], movie_vector)) * user_vectors[u1] + 2 * lmd_v * movie_vector
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if rating_matrix[u1][i1] > rating_matrix[u2][i2]:
diff = np.dot(user_vectors[u1].T, movie_vector) - np.dot(user_vectors[u2].T, movie_vector)
diff = -diff
delta_v += lmd_BPR * (user_vectors[u2, :] - user_vectors[u1, :]) * np.exp(diff) / (1 + np.exp(diff))
return delta_v
def cf_user(rating_matrix, item_vectors, current_vector, indices, K):
# user_vector is 1*K vector
np.random.seed(0)
user_vector = np.random.random(size = current_vector.shape)
index_matrix = rating_matrix[indices]
num_iter = 20
eps = 1e-8
lr = 0.1
# set the variable user_vector to be gradient
# mg = grad(lossfunction, argnum=2)
sum_square_u = eps + np.zeros_like(user_vector)
# SGD procedure:
for i in range(num_iter):
# print(i)
delta_u = selfgradu(index_matrix, item_vectors, current_vector, user_vector)
# print("self",delta_u)
# delta_u = mg(index_matrix, movie_vectors, user_vector)
# print("mg",delta_u)
sum_square_u += np.square(delta_u)
lr_u = np.divide(lr, np.sqrt(sum_square_u))
# print(np.dot(lr_u * delta_u,lr_u * delta_u))
user_vector -= lr_u * delta_u
user_vector = user_vector + current_vector
return user_vector
def cf_item(rating_matrix, user_vectors, current_vector, indices, K):
np.random.seed(0)
movie_vector = np.random.random(size = current_vector.shape)
rating_matrix = rating_matrix[:, indices]
num_iter = 1000
eps = 1e-8
lr = 0.1
sum_square_v = eps + np.zeros_like(movie_vector)
# SGD procedure:
for i in range(num_iter):
delta_v = selfgradv(rating_matrix, movie_vector, current_vector, user_vectors)
sum_square_v += np.square(delta_v)
lr_v = np.divide(lr, np.sqrt(sum_square_v))
movie_vector -= lr_v * delta_v
movie_vector = movie_vector + current_vector
return movie_vector
def cal_splitvalue(rating_matrix, movie_vectors, current_vector, indices_like, indices_dislike, indices_unknown, K):
like = rating_matrix[indices_like]
dislike = rating_matrix[indices_dislike]
unknown = rating_matrix[indices_unknown]
like_vector = np.zeros(K)
dislike_vector = np.zeros(K)
unknown_vector = np.zeros(K)
value = 0.0
if len(indices_like) > 0:
# print(indices_like)
like_vector = cf_user(rating_matrix, movie_vectors, current_vector, indices_like, K)
like_vector = np.array([like_vector for i in range(len(indices_like))])
pre_like = np.dot(like_vector, movie_vectors.T)
Err_like = pre_like[np.nonzero(like)] - like[np.nonzero(like)]
value = value + np.dot(Err_like, Err_like)
if len(indices_dislike) > 0:
# print(indices_dislike)
dislike_vector = cf_user(rating_matrix, movie_vectors, current_vector, indices_dislike, K)
dislike_vector = np.array([dislike_vector for i in range(len(indices_dislike))])
pre_dislike = np.dot(dislike_vector, movie_vectors.T)
Err_dislike = pre_dislike[np.nonzero(dislike)] - dislike[np.nonzero(dislike)]
value = value + np.dot(Err_dislike, Err_dislike)
if len(indices_unknown) > 0:
# print(indices_unknown)
unknown_vector = cf_user(rating_matrix, movie_vectors, current_vector, indices_unknown, K)
unknown_vector = np.array([unknown_vector for i in range(len(indices_unknown))])
pre_unknown = np.dot(unknown_vector, movie_vectors.T)
Err_unknown = pre_unknown[np.nonzero(unknown)] - unknown[np.nonzero(unknown)]
value = value + np.dot(Err_unknown, Err_unknown)
lkv_l = like_vector[np.nonzero(like_vector)]
dlkv_l = dislike_vector[np.nonzero(dislike_vector)]
unkv_l = unknown_vector[np.nonzero(unknown_vector)]
value = value + lmd_u * (np.dot(lkv_l, lkv_l) + np.dot(dlkv_l, dlkv_l) + np.dot(unkv_l, unkv_l))
mov_l = movie_vectors[np.nonzero(movie_vectors)]
value = value + lmd_v * np.dot(mov_l, mov_l)
np.random.seed(0)
num_pair = 20
num_user, num_item = like.shape
if num_user * num_item != 0:
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if like[u1][i1] > like[u2][i2]:
diff = np.dot(like_vector[u1, :].T, movie_vectors[i1, :]) - np.dot(like_vector[u2, :].T,
movie_vectors[i2, :])
diff = -diff
value = value + lmd_BPR * np.log(1 + np.exp(diff))
num_user, num_item = dislike.shape
if num_user * num_item != 0:
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if dislike[u1][i1] > dislike[u2][i2]:
diff = np.dot(dislike_vector[u1, :].T, movie_vectors[i1, :]) - np.dot(dislike_vector[u2, :].T,
movie_vectors[i2, :])
diff = -diff
value = value + lmd_BPR * np.log(1 + np.exp(diff))
num_user, num_item = unknown.shape
if num_user * num_item != 0:
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if unknown[u1][i1] > unknown[u2][i2]:
diff = np.dot(unknown_vector[u1, :].T, movie_vectors[i1, :]) - np.dot(unknown_vector[u2, :].T,
movie_vectors[i2, :])
diff = -diff
value = value + lmd_BPR * np.log(1 + np.exp(diff))
print(value)
return value
def cal_splitvalueI(rating_matrix, user_vectors, current_vector, indices_like, indices_dislike, indices_unknown, K):
like = rating_matrix[:, indices_like]
dislike = rating_matrix[:, indices_dislike]
unknown = rating_matrix[:, indices_unknown]
like_vector = np.zeros(K)
dislike_vector = np.zeros(K)
unknown_vector = np.zeros(K)
value = 0
if len(indices_like) > 0:
# print(indices_like)
like_vector = cf_item(rating_matrix, user_vectors, current_vector, indices_like, K)
like_vector = np.array([like_vector for i in range(len(indices_like))])
pre_like = np.dot(user_vectors, like_vector.T)
Err_like = pre_like[np.nonzero(like)] - like[np.nonzero(like)]
value = value + np.dot(Err_like, Err_like)
# print(value)
if len(indices_dislike) > 0:
# print(indices_dislike)
dislike_vector = cf_item(rating_matrix, user_vectors, current_vector, indices_dislike, K)
dislike_vector = np.array([dislike_vector for i in range(len(indices_dislike))])
pre_dislike = np.dot(user_vectors, dislike_vector.T)
Err_dislike = pre_dislike[np.nonzero(dislike)] - dislike[np.nonzero(dislike)]
value = value + np.dot(Err_dislike, Err_dislike)
# print(value)
if len(indices_unknown) > 0:
# print(indices_unknown)
unknown_vector = cf_item(rating_matrix, user_vectors, current_vector, indices_unknown, K)
unknown_vector = np.array([unknown_vector for i in range(len(indices_unknown))])
pre_unknown = np.dot(user_vectors, unknown_vector.T)
Err_unknown = pre_unknown[np.nonzero(unknown)] - unknown[np.nonzero(unknown)]
value = value + np.dot(Err_unknown, Err_unknown)
# print(value)
lkv_l = like_vector[np.nonzero(like_vector)]
dlkv_l = dislike_vector[np.nonzero(dislike_vector)]
unkv_l = unknown_vector[np.nonzero(unknown_vector)]
value = value + lmd_v * (np.dot(lkv_l, lkv_l) + np.dot(dlkv_l, dlkv_l) + np.dot(unkv_l, unkv_l))
user_l = user_vectors[np.nonzero(user_vectors)]
value = value + lmd_u * np.dot(user_l, user_l)
np.random.seed(0)
num_pair = 20
num_user, num_item = like.shape
if num_user * num_item != 0:
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if like[u1][i1] > like[u2][i2]:
diff = np.dot(user_vectors[u1, :].T, like_vector[i1, :]) - np.dot(user_vectors[u2, :].T,
like_vector[i2, :])
diff = -diff
value = value + lmd_BPR * np.log(1 + np.exp(diff))
num_user, num_item = dislike.shape
if num_user * num_item != 0:
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if dislike[u1][i1] > dislike[u2][i2]:
diff = np.dot(user_vectors[u1, :].T, dislike_vector[i1, :]) - np.dot(user_vectors[u2, :].T,
dislike_vector[i2, :])
diff = -diff
value = value + lmd_BPR * np.log(1 + np.exp(diff))
num_user, num_item = unknown.shape
if num_user * num_item != 0:
for i in range(num_pair):
c1, c2 = np.random.randint(0, num_item * num_user, 2)
u1, i1 = c1 // num_item, c1 % num_item
u2, i2 = c2 // num_item, c2 % num_item
if unknown[u1][i1] > unknown[u2][i2]:
diff = np.dot(user_vectors[u1, :].T, unknown_vector[i1, :]) - np.dot(user_vectors[u2, :].T,
unknown_vector[i2, :])
diff = -diff
value = value + lmd_BPR * np.log(1 + np.exp(diff))
print(value)
return value