Related papers: Asymmetric Multiresolution Matrix Factorization
Nonnegative Matrix Factorization (NMF) is a data analysis technique which allows compression and interpretation of nonnegative data. NMF became widely studied after the publication of the seminal paper by Lee and Seung (Learning the Parts…
Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
While building machine learning models, Feature selection (FS) stands out as an essential preprocessing step used to handle the uncertainty and vagueness in the data. Recently, the minimum Redundancy and Maximum Relevance (mRMR) approach…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
Pansharpening aims to combine a high-resolution panchromatic (PAN) image with a low-resolution multispectral (LRMS) image to produce a high-resolution multispectral (HRMS) image. Although pansharpening in the frequency domain offers clear…
Non-Negative Matrix Factorization (NMF) is a widely used dimension reduction method that factorizes a non-negative data matrix into two lower dimensional non-negative matrices: One is the basis or feature matrix which consists of the…
We study the underlying structure of data (approximately) generated from a union of independent subspaces. Traditional methods learn only one subspace, failing to discover the multi-subspace structure, while state-of-the-art methods analyze…
Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular…
Cancer, with its inherent heterogeneity, is commonly categorized into distinct subtypes based on unique traits, cellular origins, and molecular markers specific to each type. However, current studies primarily rely on complete multi-omics…
Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to decompose a given binary matrix as the Boolean product of two smaller binary matrices, revealing underlying…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be…
Non-Negative Matrix Factorization (NMF) is an unsupervised learning method offering low-rank representations across various domains such as audio processing, biomedical signal analysis, and image recognition. The incorporation of…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
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…
The relationships between objects in a network are typically diverse and complex, leading to the heterogeneous edges with different semantic information. In this paper, we focus on exploring the heterogeneous edges for network…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…