关键词: 矩阵近似, 梯度提升, 自适应秩, 样本权重, 推荐系统, 权重矩阵分解

Abstract: With the development of recommendation system, matrix approximation algorithm has become a research hotspot, and low-rank matrix approximation model represented by probability matrix decomposition has attracted wide attention because of its high recommendation accuracy. However, with the arrival of the era of large data, scoring matrices become more and more complex. Simple single matrix approximation model will make some hidden information in data ignored. To solve this problem, a hybrid rank matrix factorization (MRMF) algorithm based on boosting framework is proposed. The algorithm combines multiple different rank matrices to obtain rich scoring information. The specific method is to obtain the overall information of the matrix from the overall structure, and then obtain the residual matrix based on boosting deviation to capture the local phase. At the same time, in order to learn local features better, sample weights obeying Laplacian prior distribution are introduced to construct an adaptive weight matrix factorization (AWMF). After obtaining the residual matrix, the weight of the residual matrix is learnt by EM algorithm to avoid over-fitting of the model and reduce the complexity of manual adjustment. The proposed method has good recommendation accuracy on four real data sets (Ciao, Epinions, Douban, Movielens (10M)).

Key words: matrix approximation, gradient boosting, adaptive rank, weighted sample, recommendation systems, weight matrix factorization