Related papers: BMF: Block matrix approach to factorization of lar…
This article proposes new multiplicative updates for nonnegative matrix factorization (NMF) with the $\beta$-divergence objective function. Our new updates are derived from a joint majorization-minimization (MM) scheme, in which an…
Matrix factorization (MF), a cornerstone of recommender systems, decomposes user-item interaction matrices into latent representations. Traditional MF approaches, however, employ a two-stage, non-end-to-end paradigm, sequentially performing…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
Field-aware Factorization Machines (FFMs) have emerged as a powerful model for click-through rate prediction, particularly excelling in capturing complex feature interactions. In this work, we present an in-depth analysis of our in-house,…
Large Language Models (LLMs) are powerful but incur high memory and computation costs. Quantization is an effective solution, with INT weights and FP activations being widely adopted to preserve accuracy. Prior works further reduce FP…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
The BFS algorithm is a basic graph data processing algorithm and many other graph data processing algorithms have similar architectural features with BFS algorithm and can be built on the basis of BFS algorithm model. We analyze the…
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
Non-negative Matrix Factorization (NMF) is a useful method to extract features from multivariate data, but an important and sometimes neglected concern is that NMF can result in non-unique solutions. Often, there exist a Set of Feasible…
Kernel methods are extensively employed for nonlinear data clustering, yet their effectiveness heavily relies on selecting suitable kernels and associated parameters, posing challenges in advance determination. In response, Multiple Kernel…
As users and developers, we are witnessing the opening of a new computing scenario: the introduction of hybrid processors into a single die, such as an accelerated processing unit (APU) processor, and the plug-and-play of additional…
Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear…
Data movement is the dominating factor affecting performance and energy in modern computing systems. Consequently, many algorithms have been developed to minimize the number of I/O operations for common computing patterns. Matrix…
Symmetric nonnegative matrix factorization (SNMF) is equivalent to computing a symmetric nonnegative low rank approximation of a data similarity matrix. It inherits the good data interpretability of the well-known nonnegative matrix…
Simplex-structured matrix factorization (SSMF) is a generalization of nonnegative matrix factorization, a fundamental interpretable data analysis model, and has applications in hyperspectral unmixing and topic modeling. To obtain…
Binary quantization approaches, which replace weight matrices with binary matrices and substitute costly multiplications with cheaper additions, offer a computationally efficient approach to address the increasing computational and storage…
Matrix factorization methods - including Factor analysis (FA), and Principal Components Analysis (PCA) - are widely used for inferring and summarizing structure in multivariate data. Many matrix factorization methods exist, corresponding to…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
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…
We explore the trade-offs of performing linear algebra using Apache Spark, compared to traditional C and MPI implementations on HPC platforms. Spark is designed for data analytics on cluster computing platforms with access to local disks…