Recommender systems (RS) help users to find their appropriate items among large volumes of information. Among the different types of RS, context-aware recommender systems aim at personalizing as much as possible the recommendations based on the context situation in which the user is. In this paper we present an approach integrating contextual information into the recommendation process by modeling either item-based or user-based influence of the context on ratings, using the Pearson Correlation Coefficient. The proposed solution aims at taking advantage of content and contextual information in the recommendation process. We evaluate and show effectiveness of our approach on three different contextual datasets and analyze the performances of the variants of our approach based on the characteristics of these datasets, especially the sparsity level of the input data and amount of available information.
CAMF @cite_22 is an extension of matrix factorization @cite_18 , that tries to take into account the context situation of users by integrating additional model parameters in the matrix factorization equation. @cite_11 proposed a similarity-based version of this approach.
@cite_18 @cite_22 @cite_11
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This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm identifies a matrix C such that X approximately equals CX and some linear constraints. The constraints are chosen to ensure that the matrix C selects features; these features can then be used to find a low-rank NMF of X. A theoretical analysis demonstrates that this approach has guarantees similar to those of the recent NMF algorithm of (2012). In contrast with this earlier work, the proposed method extends to more general noise models and leads to efficient, scalable algorithms. Experiments with synthetic and real datasets provide evidence that the new approach is also superior in practice. An optimized C++ implementation can factor a multigigabyte matrix in a matter of minutes. We propose a new matrix completion algorithm— Kernelized Probabilistic Matrix Factorization (KPMF), which effectively incorporates external side information into the matrix factorization process. Unlike Probabilistic Matrix Factorization (PMF) [14], which assumes an independent latent vector for each row (and each column) with Gaussian priors, KMPF works with latent vectors spanning all rows (and columns) with Gaussian Process (GP) priors. Hence, KPMF explicitly captures the underlying (nonlinear) covariance structures across rows and columns. This crucial difference greatly boosts the performance of KPMF when appropriate side information, e.g., users’ social network in recommender systems, is incorporated. Furthermore, GP priors allow the KPMF model to fill in a row that is entirely missing in the original matrix based on the side information alone, which is not feasible for standard PMF formulation. In our paper, we mainly work on the matrix completion problem with a graph among the rows and or columns as side information, but the proposed framework can be easily used with other types of side information as well. Finally, we demonstrate the efficacy of KPMF through two different applications: 1) recommender systems and 2) image restoration. CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender system. The key idea in CMF is that the embeddings are shared across the matrices, which enables transferring information between them. The existing solutions, however, break down when the individual matrices have low-rank structure not shared with others. In this work we present a novel CMF solution that allows each of the matrices to have a separate low-rank structure that is independent of the other matrices, as well as structures that are shared only by a subset of them. We compare MAP and variational Bayesian solutions based on alternating optimization algorithms and show that the model automatically infers the nature of each factor using group-wise sparsity. Our approach supports in a principled way continuous, binary and count observations and is efficient for sparse matrices involving missing data. We illustrate the solution on a number of examples, focusing in particular on an interesting use-case of augmented multi-view learning.