Related papers: Matrix Factorization in Tropical and Mixed Tropica…

Over the past few years, deep learning has firmly established its prowess across various domains, including computer vision, speech recognition, and natural language processing. Motivated by its outstanding success, researchers have been…

Decentralized recommender system does not rely on the central service provider, and the users can keep the ownership of their ratings. This article brings the theoretically well-studied matrix factorization method into the decentralized…

Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…

Federated Learning (FL) has been becoming a popular interdisciplinary research area in both applied mathematics and information sciences. Mathematically, FL aims to collaboratively optimize aggregate objective functions over distributed…

Recommender systems are considered one of the most rapidly growing branches of Artificial Intelligence. The demand for finding more efficient techniques to generate recommendations becomes urgent. However, many recommendations become…

Recommending items to potentially interested users has been an important commercial task that faces two main challenges: accuracy and explainability. While most collaborative filtering models rely on statistical computations on a large…

Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…

In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…

Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…

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…

Recently, malevolent user hacking has become a huge problem for real-world companies. In order to learn predictive models for recommender systems, factorization techniques have been developed to deal with user-item ratings. In this paper,…

With the rapid development of large language models (LLMs) and the growing demand for personalized content, recommendation systems have become critical in enhancing user experience and driving engagement. Collaborative filtering algorithms,…

Recently, matrix factorization-based recommendation methods have been criticized for the problem raised by the triangle inequality violation. Although several metric learning-based approaches have been proposed to overcome this issue,…

We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in…

We propose a general technique for improving alternating optimization (AO) of nonconvex functions. Starting from the solution given by AO, we conduct another sequence of searches over subspaces that are both meaningful to the optimization…

This paper contributes improvements on both the effectiveness and efficiency of Matrix Factorization (MF) methods for implicit feedback. We highlight two critical issues of existing works. First, due to the large space of unobserved…

We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…

Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…

Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…