Matrix Factorization For Recommender Systems Research Articles

Incremental trust-aware matrix factorization for recommender systems: towards Green AI

Incremental trust-aware matrix factorization for recommender systems: towards Green AI

A novel constrained non-negative matrix factorization method based on users and items pairwise relationship for recommender systems

Non-negative matrix factorization (NMF) is a famous method to learn parts-based representations of non-negative data. It has been used successfully in various applications such as information retrieval and recommender systems. Most of the current NMF methods only focus on how each decomposed matrices vector should be modeled and disregard the relation among pairwise feature vectors of users and items. In recommender systems, the relationship between users’ factors or items’ features provides better factorization. This paper proposes a constrained non-negative matrix factorization for recommender systems (CNMF-RS), which puts constraints on pairwise vectors of users and items by applying penalties using similarity. Two cost functions are proposed to generate the corresponding updating rules for finding unknown ratings. The computational complexity analysis confirmed that CNMF-RS does not raise time complexity using constraints compared with the basic NMF. Experiments on benchmark datasets indicate that the suggested update rules converge quickly and obtain outstanding results compared to other methods.

User-controlled federated matrix factorization for recommender systems

User-controlled federated matrix factorization for recommender systems

Analyzing and improving stability of matrix factorization for recommender systems

Analyzing and improving stability of matrix factorization for recommender systems

BaPa: A Novel Approach of Improving Load Balance in Parallel Matrix Factorization for Recommender Systems

A simplified approach to accelerate matrix factorization of big data is to parallelize it. A commonly used method is to divide the matrix into multiple non-intersecting blocks and concurrently calculate them. This operation causes the Load balance problem, which significantly impacts parallel performance and is a big concern. A general belief is that the load balance across blocks is impossible by balancing rows and columns separately. We challenge the belief by proposing an approach of “Balanced Partitioning (BaPa)”. We demonstrate under what circumstance independently balancing rows and columns can lead to the balanced intersection of rows and columns, why, and how. We formally prove the feasibility of BaPa by observing the variance of rating numbers across blocks, and empirically validate its soundness by applying it to two standard parallel matrix factorization algorithms, DSGD and CCD++. Besides, we establish a mathematical model of “Imbalance Degree” to explain further why BaPa works well. BaPa is applied to synchronous parallel matrix factorization, but as a general load balance solution, it has significant application potential.

Addressing Interpretability and Cold-Start in Matrix Factorization for Recommender Systems

We consider the problem of generating interpretable recommendations by identifying overlapping co-clusters of clients and products, based only on positive or implicit feedback. Our approach is applicable on very large datasets because it exhibits almost linear complexity in the input examples and the number of co-clusters. We show, both on real industrial data and on publicly available datasets, that the recommendation accuracy of our algorithm is competitive to that of state-of-the-art matrix factorization techniques. In addition, our technique has the advantage of offering recommendations that are textually and visually interpretable. Our formulation can also address cold-start problems by gracefully meshing collaborative and content-based reasoning. Finally, we present efficient Graphical Processing Unit (GPU) implementations and demonstrate a speedup of more than 270 times over our baseline CPU implementation on a cluster of 16 GPUs.

HHMF: hidden hierarchical matrix factorization for recommender systems

Matrix factorization (MF) is one of the most powerful techniques used in recommender systems. MF models the (user, item) interactions behind historical explicit or implicit ratings. Standard MF does not capture the hierarchical structural correlations, such as publisher and advertiser in advertisement recommender systems, or the taxonomy (e.g., tracks, albums, artists, genres) in music recommender systems. There are a few hierarchical MF approaches, but they require the hierarchical structures to be known beforehand. In this paper, we propose a Hidden Hierarchical Matrix Factorization (HHMF) technique, which learns the hidden hierarchical structure from the user-item rating records. HHMF does not require the prior knowledge of hierarchical structure; hence, as opposed to existing hierarchical MF methods, HHMF can be applied when this information is either explicit or implicit. According to our extensive experiments, HHMF outperforms existing methods, demonstrating that the discovery of latent hierarchical structures indeed improves the quality of recommendation. [ABSTRACT FROM AUTHOR]

Deep Matrix Factorization for Recommender Systems with Missing Data not at Random

Matrix Factorization is a widely used collaborative filtering method in recommender systems. However, most of them are under the assumption that the rating data is missing at random (MAR), which may not be very common. For some users, they may only rate those movies they like, so the inferences will be biased in previous models. In this paper, we proposed a deep matrix factorization method based on missing not at random (MNAR) assumption. As far as we know, this model firstly uses deep learning method to address MNAR issue. The model consists of a complete data model (CDM) and a missing data model (MDM), which are both learned by neural networks. The CDM is nonlinearly determined by two factors, the user latent features and item latent features like other matrix factorization methods. And the MDM also use these two factors but taking the rating value as extra information while training. We used variational Bayesian inference to generate the posterior distribution of our proposed model. Through extensive experiments on different kind of datasets, our proposed model produce gains in some widely used metrics, comparing with several state-of-the-art models. We also explore the performance of our model within different experimental settings.

ClMF: A fine-grained and portable alternating least squares algorithm for parallel matrix factorization

Alternating least squares (ALS) has been proved to be an effective solver for matrix factorization in recommender systems. To speed up factorizing performance, various parallel ALS solvers have been proposed to leverage modern multi-cores and many-cores. Existing implementations are limited in either speed or portability. In this paper, we present an efficient and portable ALS solver (clMF) for recommender systems. On one hand, we diagnose the baseline implementation and observe that it lacks of the awareness of the hierarchical thread organization on modern hardware. To achieve high performance, we apply the thread batching technique, the fine-grained tiling technique and three architecture-specific optimizations. On the other hand, we implement the ALS solver in OpenCL so that it can run on various platforms (CPUs, GPUs and MICs). Based on the architectural specifics, we select a suitable code variant for each platform to efficiently map it to the underlying hardware. The experimental results show that our implementation performs 2.8×–15.7× faster on an Intel 16-core CPU, 23.9×–87.9× faster on an NVIDIA K20C GPU and 34.6×–97.1× faster on an AMD Fury X GPU than the baseline implementation. On the K20C GPU, our implementation also outperforms cuMF over different latent features ranging from 10 to 100 with various real-world recommendation datasets.

Joint user knowledge and matrix factorization for recommender systems

Currently, most of the existing recommendation methods treat social network users equally, which assume that the effect of recommendation on a user is decided by the user’s own preferences and social influence. However, a user’s own knowledge in a field has not been considered. In other words, to what extent does a user accept recommendations in social networks need to consider the user’s own knowledge or expertise in the field. In this paper, we propose a novel matrix factorization recommendation algorithm based on integrating social network information such as trust relationships, rating information of users and users’ own knowledge. Specifically, since we cannot directly measure a user’s knowledge in the field, we first use a user’s status in a social network to indicate a user’s knowledge in a field, and users’ status is inferred from the distributions of users’ ratings and followers across fields or the structure of domain-specific social network. Then, we model the final rating of decision-making as a linear combination of the user’s own preferences, social influence and user’s own knowledge. Experimental results on real world data sets show that our proposed approach generally outperforms the state-of-the-art recommendation algorithms that do not consider the knowledge level difference between the users.

Forgetting techniques for stream-based matrix factorization in recommender systems

Forgetting is often considered a malfunction of intelligent agents; however, in a changing world forgetting has an essential advantage. It provides means of adaptation to changes by removing effects of obsolete (not necessarily old) information from models. This also applies to intelligent systems, such as recommender systems, which learn users’ preferences and predict future items of interest. In this work, we present unsupervised forgetting techniques that make recommender systems adapt to changes of users’ preferences over time. We propose eleven techniques that select obsolete information and three algorithms that enforce the forgetting in different ways. In our evaluation on real-world datasets, we show that forgetting obsolete information significantly improves predictive power of recommender systems.

CMPTF: Contextual Modeling Probabilistic Tensor Factorization for recommender systems

Contextual information has been proven to be valuable factor for building personalized Recommender Systems. However, most existing solutions based on probabilistic matrix factorization in recommender systems do not provide a straightforward way of integrating information such as ratings, social relationships, item contents and contexts into one model simultaneously. In this paper, we deem the given data as an User-Item-Context-Rating tensor and introduce a high dimensional method of Collaborative Filtering named probabilistic tensor factorization (PTF) which is a generalization of probabilistic matrix factorization. Then, we further extend PTF to a new model named Contextual Modeling Probabilistic Tensor Factorization (CMPTF) which systematically integrates topic modeling, social relationships and contexts in contextual modeling manner to further improve the quality of recommendation. Comprehensive comparative experiments conducted using real-world datasets demonstrate the superiority of our approach.

FALCON: A matrix factorization framework for recommender systems using constrained optimization

Methods from the field of optimization theory have played an important role in developing training algorithms for matrix factorization in recommender systems. Indeed, the realization that simple stochastic unconstrained gradient descent can be applied with success to the factorization of the user-i tem matrix is responsible, to a great extent, for the recent research interest in this area, and the introduction of a plethora of matrix factorization methods. In this paper, motivated by earlier approaches in training neural networks, we introduce a constrained optimization framework for incorporating additional knowledge into the matrix factorization formalism, which can overcome certain drawbacks of the unconstrained minimization approach. We examine two types of such additional knowledge, and consequently derive two algorithms, as a result of incorporating the different knowledge types in the context of the constrained optimization framework. Both algorithms are designed to improve convergence and accuracy in the broader class of matrix factorization methods in recommender systems.

Two-level matrix factorization for recommender systems

Many existing recommendation methods such as matrix factorization (MF) mainly rely on user---item rating matrix, which sometimes is not informative enough, often suffering from the cold-start problem. To solve this challenge, complementary textual relations between items are incorporated into recommender systems (RS) in this paper. Specifically, we first apply a novel weighted textual matrix factorization (WTMF) approach to compute the semantic similarities between items, then integrate the inferred item semantic relations into MF and propose a two-level matrix factorization (TLMF) model for RS. Experimental results on two open data sets not only demonstrate the superiority of TLMF model over benchmark methods, but also show the effectiveness of TLMF for solving the cold-start problem.

Comparative analysis of neighborhood-based approache and matrix factorization in recommender systems

Unlike other works, this paper aims at searching a connection between two most popular approaches in recommender systems domain: Neighborhood-based (NB) and Matrix Factorization-based (MF). Provided analysis helps better understand advantages and disadvantages of each approach as well as their compatibility. While NB relies on the ratings of similar users to estimate the rating of a user on an item, MF relies on the identification of latent features that represent the underlying relation between users and items. However, as it was shown in this paper, if latent features of Non-negative Matrix Factorization are interpreted as users, the processes of rating estimation by two methods become similar. In addition, it was shown through experiments that in this case elements of NB and MF are highly correlated. Still there is a major difference between Matrix Factorization-based and Neighborhood-based approaches: the first one exploits the same set of base elements to estimate unknown ratings (the set of latent features), while the second forms different sets of base elements (in this case neighbors) for each user-item pair.

Parallel matrix factorization for recommender systems

Matrix factorization, when the matrix has missing values, has become one of the leading techniques for recommender systems. To handle web-scale datasets with millions of users and billions of ratings, scalability becomes an important issue. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two popular approaches to compute matrix factorization, and there has been a recent flurry of activity to parallelize these algorithms. However, due to the cubic time complexity in the target rank, ALS is not scalable to large-scale datasets. On the other hand, SGD conducts efficient updates but usually suffers from slow convergence that is sensitive to the parameters. Coordinate descent, a classical optimization approach, has been used for many other large-scale problems, but its application to matrix factorization for recommender systems has not been thoroughly explored. In this paper, we show that coordinate descent-based methods have a more efficient update rule compared to ALS and have faster and more stable convergence than SGD. We study different update sequences and propose the CCD++ algorithm, which updates rank-one factors one by one. In addition, CCD++ can be easily parallelized on both multi-core and distributed systems. We empirically show that CCD++ is much faster than ALS and SGD in both settings. As an example, with a synthetic dataset containing 14.6 billion ratings, on a distributed memory cluster with 64 processors, to deliver the desired test RMSE, CCD++ is 49 times faster than SGD and 20 times faster than ALS. When the number of processors is increased to 256, CCD++ takes only 16 s and is still 40 times faster than SGD and 20 times faster than ALS.