Deep Matrix Factorization Models for Recommender Systems

1 Deep Matrix Factorization Models for Recommender Systems Hong-Jian Xue, Xin-Yu Dai, Jianbing Zhang, Shujian Huang, Jiajun ChenNational Key Laboratory for Novel Software Technology; Nanjing University, Nanjing 210023, ChinaCollaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing 210023, Systems usually make personalizedrecommendation with user-item interaction ratings,implicit feedback and auxiliary information. Ma-trix Factorization is the basic idea to predict a per-sonalized ranking over a set of items for an indi-vidual user with the similarities among users anditems.

2 In this paper, we propose a novel matrixfactorization model with neural network architec-ture. Firstly, we construct a user-item Matrix withexplicit ratings and non-preference implicit feed-back. With this Matrix as the input, we present adeep structure learning architecture to learn a com-mon low dimensional space for the representationsof users and items. Secondly, we design a new lossfunction based on binary cross entropy, in whichwe consider both explicit ratings and implicit feed-back for a better optimization. The experimentalresults show the effectiveness of both our proposedmodel and the loss function.

3 On several bench-mark datasets, our model outperformed other state-of-the-art methods. We also conduct extensive ex-periments to evaluate the performance within dif-ferent experimental IntroductionIn the era of information explosion, information overload isone of the dilemmas we are confronted with. Recommendersystems (RSs) are instrumental to address this problem asthey help determine which information to offer to individualconsumers and allow online users to quickly find the person-alized information that fits their needs[Sarwaret al.]

4 , 2001;Lindenet al., 2003]. RSs are nowadays ubiquitous in e-commerce platforms, such as recommendation of books atAmazon, music at , movie at Netflix and referenceat filtering(CF) Recommender approaches areextensively investigated in research community and widelyused in industry. They are based on the simple intuition that Xin-Yu Dai is the corresponding work wassupported by the 863 program(2015AA015406) and the NSFC(61472183,61672277).if users rate items similarly in the past, they are likely to rateother items similarly in the future[Sarwaret al.

5 , 2001; Lindenet al., 2003]. As the most popular approach among variouscollaborative filtering techniques, Matrix Factorization (MF)which learns a latent space to represent a user or an item be-comes a standard model for recommendation due to its scal-ability, simplicity, and flexibility[Billsus and Pazzani, 1998;Korenet al., 2009]. In the latent space, the recommendersystem predicts a personalized ranking over a set of items foreach individual user with the similarities among the users in the user-item interaction Matrix are explicitknowledge which have been deeply exploited in early rec-ommendation methods.

6 Because of the variation in ratingvalues associated with users on items, biased Matrix factor-ization[Korenet al., 2009]are used to enhance the rat-ing prediction. To overcome the sparseness of the ratings,additional extra data are integrated into MF, such as socialmatrix Factorization with social relations[Maet al., 2008;Tanget al., 2013], topic Matrix Factorization with itemcontents or reviews text[McAuley and Leskovec, 2013;Baoet al., 2014], and so , modeling only observed ratings is insufficient tomake good top-Nrecommendations[Huet al.]

7 , 2008]. Im-plicit feedback, such as purchase history and unobserved rat-ings, is applied in Recommender Systems [Oardet al., 1998].The SVD++[Koren, 2008]model firstly factorizes the ratingmatrix with the implicit feedback, and is followed by manytechniques for Recommender Systems [Rendleet al., 2009;Mnih and Teh, 2012; He and McAuley, 2015].Recently, due to the powerful representation learning abil-ities, deep learning methods have been successfully appliedincluding various areas of Computer Vision, Audio Recogni-tion and Natural Language Processing. A few efforts havealso been made to apply deep learning Models in recom-mender Systems .

8 Restricted Boltzmann Machines[Salakhut-dinovet al., 2007]was firstly proposed to model users ex-plicit ratings on items. Autoencoders and the denoising au-toencoders have also been applied for recommendation[Lietal., 2015; Sedhainet al., 2015; Strub and Mary, 2015]. Thekey idea of these methods is to reconstruct the users ratingsthrough learning hidden structures with the explicit historicalratings. Implicit feedback is also applied in this research lineof deep learning for recommendation. An extended work pre-Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (IJCAI-17)3203sented a collaborative denoising autoencoder (CDAE)[Wuetal.]

9 , 2016]to model user s preference with implicit work of neural collaborative filtering (NCF)[Heetal., 2017]was proposed to model the user-item interactionswith a multi-layer feedforward neural network. Two recentworks above exploit only implicit feedback for item recom-mendations instead of explicit rating this paper, to make use of both explicit ratings andimplicit feedback, we propose a new neural Matrix factor-ization model for top-Nrecommendation. We firstly con-struct a user-item Matrix with both explicit ratings and non-preference implicit feedback, which is different from otherrelated methods using either only explicit ratings or only im-plicit ratings.

10 With this full Matrix (explicit ratings and zeroof implicit feedback) as input, a neural network architecture isproposed to learn a common latent low dimensional space torepresent the users and items. This architecture is inspired bythe deep structured semantic Models which have been provedto be useful for web search[Huanget al., 2013], where it canmap the query and document in a latent space through multi-ple layers of non-linear projections. In addition, we design anew loss function based on cross entropy, which includes theconsiderations of both explicit ratings and implicit sum, our main contributions are outlined as follows.