A Multi-criteria Recommendation Algorithm Based On Probability Matrix Factorization

Collaborative filtering algorithm is a classical method in the application and study of recommendation system. The main idea of traditional collaborative filtering algorithm is mining user interest and making recommendation based on the user's single overall rating for item.However,some research suggests that those approaches based on overall rating have not characterize about users' key interests very well, and the recommendation technology based on Multi-criteria was proposed. The core idea of new technology is build user interest model and make recommendation for user more accurate item list by different dimensions of user's criteria rating for item. There are few researches on Multi-criteria recommendation algorithm, most algorithms have two main problems with scalability and sparsity. Related researches about Multi-criteria recommendation technology can be divided into three categories: 1) Decomposing Multi-criteria rating recommendation problem into single criteria rating problem, then for each dimensional criteria using any existing collaborative recommendation algorithm to predict, and last utilize predict result of each criteria to predict final overall rate.The disadvantage of this approach is that it presuppose users have a same degree preference for each criteria, the reality is that users may exist different degree preference for different criteria. 2) Using aggregate function represented overall rating as linear relation of Multi-criteria rating,utilizing statistical or machine learning method to obtain aggregate function and make predict recommend, the disadvantage of this method is susceptible to data noise or sparse train data. 3) Simple clustering method, using latent semantic analysis method analysis users, which considered only the impact of Multi-criteria to users, while ignoring Multi-criteria also have an impact on the item.Aim at shortcoming the current work problems about Multi-criteria recommendation. Multi-Criteria collaborative filtering algorithm based on Probabilistic Matrix Factorization(MCPMF) to solve the scalability and sparsity problems is proposed in this paper. This research considers traditional user-item single rate relationship as three relationships, respectively are user-(multi-criteria),item-(multi-criteria),user-item. With the help of probability matrix factorization, MCPMF can reduce the impact of the noise data and large-scale train data. We assume that the data distribution of each relation follows the Gauss Distribution, then consider the impact of Multi-criteria to all user and all item as a weight matrix. Two methods to compute the weight matrix are proposed in this paper. The first method is based on covariance matrix. The other method is based on a assume that the data distribution of the impact of Multi-criteria to user and item is Gauss Distribution, and the twoimpacts mutual independent, and expression the joint probability distribution of the two impact as weight matrix. The MCMF feature matrix of user and item are learn by Gradient descent. Experimental results on two real datasets(Dazong food comment dataset and Xiecheng scenic spots comment) show that the proposed method is more accurate in forecasting the user's overall rating compared with methods which only considered single overall rating and several commonly Multi-criteria recommendation methods. The experimental results also show that the proposed algorithm could reduce the impact of data sparsity to recommendation algorithms with Multi-criteria recommendation algorithms, such as FGPLSA.The main contribution of this paper are: 1) the processing of Multi-criteria weight matrix, consider Multi-criteria by two weight matrix compute methods.2) The fusion of weight matrix with the user(item) feature vectors, assuming potential distribution of user and item will be affected by the Multi-criteria,using the idea of Probability Matrix Factorization to handle the fusion. 3) The adapt of algorithm to the sparse data, using the idea of Probability Matrix Factorization Algorithm avoid over-fitting at some extent.