One-Class Matrix Completion with Low-Density Factorizations

Abstract

Abstract-Consider a typical recommendation problem. A company has historical records of products sold to a large customer base. These records may be compactly represented as a sparse customer-times-product "who-bought-what" binary matrix. Given this matrix, the goal is to build a model that provides recommendations for which products should be sold next to the existing customer base. Such problems may naturally be formulated as collaborative filtering tasks. However, this is a one-class setting, that is, the only known entries in the matrix are one-valued. If a customer has not bought a product yet, it does not imply that the customer has a low propensity to potentially be interested in that product. In the absence of entries explicitly labeled as negative examples, one may resort to considering unobserved customer-product pairs as either missing data or as surrogate negative instances. In this paper, we propose an approach to explicitly deal with this kind of ambiguity by instead treating the unobserved entries as optimization variables. These variables are optimized in conjunction with learning a weighted, low-rank nonnegative matrix factorization (NMF) of the customer-product matrix, similar to how Transductive SVMs implement the low-density separation principle for semi-supervised learning. Experimental results show that our approach gives significantly better recommendations in comparison to various competing alternatives on one-class collaborative filtering tasks.

Selection of Negative Samples for One-class Matrix Factorization

“…We will include one rankingloss approach in our empirical comparison. In [27], a variable is simultaneously optimized to decide if a missing entry is negative or not. To be focused, in the current work we do not discuss this approach.…”

Dual-Regularized One-Class Collaborative Filtering

“…In this paper, we focus on the uniform strategy, and will refer to this approach as iZAN in the following. Note that the similar idea was also implicitly explored in [31].…”

“…Paquet and Koenigstein [25] propose a sampling-based method where the degree distributions of users/items are preserved. Sindhwani et al [31] propose to treat the unobserved data as optimization variables, which is essentially the imputation-based method.…”

Effective Matrix Factorization for Online Rating Prediction

“…Hanhuai and Arindam used a Gaussian prior with an arbitrary mean over u and v, and combined the correlated topic model and latent Dirichlet allocation work with their matrix model [6]. Vikas, Serhat, Jianying and Aleksandra introduced a new binary matrix, in which 0 means 'not purchased' and 1 means 'purchased', into the factor-learning process in non-negative Matrix Factorization (NMF) approach [7]. Compared to the above algorithms, the proposed new MF approach in this paper concentrates on transforming the original rating matrix and modifying already-predicted ratings using item attributes.…”

“…Most MF researches improve the accuracy by taking the data (e.g. movie ratings) as the point of penetration without considering the impact of item attributes [5], [6], [7]. Although these new MF approaches can provide more accurate ratings, an improvement from different perspective will be necessary when they reach a bottleneck.…”