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Manifold regularization methods for matrix factorization rely on the cluster assumption, whereby the neighborhood structure of data in the input space is preserved in the factorization space. We argue that using the k-neighborhoods of all…

Recommender system has attracted lots of attentions since it helps users alleviate the information overload problem. Matrix factorization technique is one of the most widely employed collaborative filtering techniques in the research of…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

Factorization Machines (FM) are only used in a narrow range of applications and are not part of the standard toolbox of machine learning models. This is a pity, because even though FMs are recognized as being very successful for recommender…

Multivector retrieval models achieve state-of-the-art effectiveness through fine-grained token-level representations, but their deployment incurs substantial computational and memory costs. Current solutions, based on the well-known k-means…

Recent demands on data privacy have called for federated learning (FL) as a new distributed learning paradigm in massive and heterogeneous networks. Although many FL algorithms have been proposed, few of them have considered the matrix…

We propose the convex factorization machine (CFM), which is a convex variant of the widely used Factorization Machines (FMs). Specifically, we employ a linear+quadratic model and regularize the linear term with the $\ell_2$-regularizer and…

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices and has been widely used for unsupervised learning tasks such as product recommendation based on a rating matrix. However, although…

Factorization machines (FM) are a popular model class to learn pairwise interactions by a low-rank approximation. Different from existing FM-based approaches which use a fixed rank for all features, this paper proposes a Rank-Aware FM…

Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation and wavelet regularization. These priors specify that a convolutional structured matrix,…

Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…

We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…

BioFabrics were introduced by Longabaugh in 2012 as a way to draw large graphs in a clear and uncluttered manner. The visual quality of BioFabrics crucially depends on the order of vertices and edges, which can be chosen independently.…

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…

Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF…

For applied intelligence, utility-driven pattern discovery algorithms can identify insightful and useful patterns in databases. However, in these techniques for pattern discovery, the number of patterns can be huge, and the user is often…

The overfitting is one of the cursing subjects in the deep learning field. To solve this challenge, many approaches were proposed to regularize the learning models. They add some hyper-parameters to the model to extend the generalization;…

Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix…

This paper proposes a new detection algorithm for MIMO communication systems employing high order QAM constellations. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, a straightforward…