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

numpy as npimport scipy。sparse as sparsefrom scipy。sparse。linalg import spsolveimport timedef 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 countsclass 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_vecsAlternating Least Squares(ASL) for Implicit Feedback Datasets的数学推导以及用Python实现。