Alternating Least Squares(ASL) for Implicit Feedback Datasets的数学推导以及用Python实现

numpy as np import scipy.sparse as sparse from scipy.sparse.linalg import spsolve import time def load_matrix(filename, num_users, num_items): t0 = time.time() counts = np.zeros((num_users, num_items)) total = 0.0 num_zeros = num_users * num_items ‘‘‘假设要对一个列表或者数组既要遍历索引又要遍历元素时。能够用enumerate，当传入參数为文件时，索引为 行号，元素相应的一行内容‘‘‘ for i, line in enumerate(open(filename, ‘r‘)): #strip()去除最前面和最后面的空格 user, item, count = line.strip().split(‘\t‘) user = int(user) item = int(item) count = float(count) if user >= num_users: continue if item >= num_items: continue if count != 0: counts[user, item] = count total += count num_zeros -= 1 if i % 100000 == 0: print ‘loaded %i counts...‘ % i #数据导入完成后计算稀疏矩阵中零元素个数和非零元素个数的比例，记为alpha alpha = num_zeros / total print ‘alpha %.2f‘ % alpha counts *= alpha #用CompressedSparse Row Format将稀疏矩阵压缩 counts = sparse.csr_matrix(counts) t1 = time.time() print ‘Finished loading matrix in %f seconds‘ % (t1 - t0) return counts class ImplicitMF(): def __init__(self, counts, num_factors=40, num_iterations=30, reg_param=0.8): self.counts = counts self.num_users = counts.shape[0] self.num_items = counts.shape[1] self.num_factors = num_factors self.num_iterations = num_iterations self.reg_param = reg_param def train_model(self): #创建user_vectors和item_vectors，他们的元素~N(0,1)的正态分布 self.user_vectors = np.random.normal(size=(self.num_users, self.num_factors)) self.item_vectors = np.random.normal(size=(self.num_items, self.num_factors)) ‘‘‘要生成非常大的数字序列的时候，用xrange会比range性能优非常多， 因为不须要一上来就开辟一块非常大的内存空间，这两个基本上都是在循环的时候用‘‘‘ for i in xrange(self.num_iterations): t0 = time.time() print ‘Solving for user vectors...‘ self.user_vectors = self.iteration(True, sparse.csr_matrix(self.item_vectors)) print ‘Solving for item vectors...‘ self.item_vectors = self.iteration(False, sparse.csr_matrix(self.user_vectors)) t1 = time.time() print ‘iteration %i finished in %f seconds‘ % (i + 1, t1 - t0) def iteration(self, user, fixed_vecs): #相当于C的三木运算符。if user=True num_solve = num_users,反之为num_items num_solve = self.num_users if user else self.num_items num_fixed = fixed_vecs.shape[0] YTY = fixed_vecs.T.dot(fixed_vecs) eye = sparse.eye(num_fixed) lambda_eye = self.reg_param * sparse.eye(self.num_factors) solve_vecs = np.zeros((num_solve, self.num_factors)) t = time.time() for i in xrange(num_solve): if user: counts_i = self.counts[i].toarray() else: #假设要求item_vec,counts_i为counts中的第i列的转置 counts_i = self.counts[:, i].T.toarray() ‘‘‘ 原论文中c_ui=1+alpha*r_ui,可是在计算Y’CuY时为了减少时间复杂度,利用了 Y‘CuY=Y‘Y+Y‘(Cu-I)Y,因为Cu是对角矩阵,其元素为c_ui，即1+alpha*r_ui。 所以Cu-I也就是对角元素为alpha*r_ui的对角矩阵‘‘‘ CuI = sparse.diags(counts_i, [0]) pu = counts_i.copy() #np.where(pu != 0)返回pu中元素不为0的索引，然后将这些元素赋值为1,不知道这里为什么要赋值为1? pu[np.where(pu != 0)] = 1.0 YTCuIY = fixed_vecs.T.dot(CuI).dot(fixed_vecs) YTCupu = fixed_vecs.T.dot(CuI + eye).dot(sparse.csr_matrix(pu).T) xu = spsolve(YTY + YTCuIY + lambda_eye, YTCupu) solve_vecs[i] = xu if i % 1000 == 0: print ‘Solved %i vecs in %d seconds‘ % (i, time.time() - t) t = time.time() return solve_vecs

Alternating Least Squares(ASL) for Implicit Feedback Datasets的数学推导以及用Python实现

标签：序列   continue   csdn   运算   运算符   利用   imp   它的   i++