Related papers: Efficient Nonnegative Tensor Factorization via Sat…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the…
The time-frequency map (TFM) is frequently used in condition monitoring, necessitating further processing to select an informative frequency band (IFB) or directly detect damage. However, selecting an IFB is challenging due to the…
Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a…
How can we capture the hidden properties from a tensor and a matrix data simultaneously in a fast, accurate, and scalable way? Coupled matrix-tensor factorization (CMTF) is a major tool to extract latent factors from a tensor and matrices…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
Let $F$ be a set-valued mapping from an $N$-element metric space $({\mathcal M},\rho)$ into the family of all closed half-planes in ${\bf R}^2$. In this paper, we provide an efficient algorithm for a Lipschitz selection of $F$, i.e., a…
Nonnegative matrix factorization (NMF) was popularized as a tool for data mining by Lee and Seung in 1999. NMF attempts to approximate a matrix with nonnegative entries by a product of two low-rank matrices, also with nonnegative entries.…
Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy data sets with applications in data mining, text recognition, dimension reduction, face…
Tensor factorizations (TF) are powerful tools for the efficient representation and analysis of multidimensional data. However, classic TF methods based on maximum likelihood estimation underperform when applied to zero-inflated count data,…
Though there have been hundreds of methods on solving rational spectral factorization, most of them are based on a positive definite density matrix assumption. In this work, we propose a novel approach on the spectral factorization of a…
This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
In recent years, Deep Neural Networks (DNN) based methods have achieved remarkable performance in a wide range of tasks and have been among the most powerful and widely used techniques in computer vision. However, DNN-based methods are both…
Feature selection is an important process in machine learning and knowledge discovery. By selecting the most informative features and eliminating irrelevant ones, the performance of learning algorithms can be improved and the extraction of…
Despite the ubiquity of multiway data across scientific domains, there are few user-friendly tools that fit tailored nonnegative tensor factorizations. Researchers may use gradient-based automatic differentiation (which often struggles in…
In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are…
Large-scale Dynamic Networks (LDNs) are becoming increasingly important in the Internet age, yet the dynamic nature of these networks captures the evolution of the network structure and how edge weights change over time, posing unique…
Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usually with much fewer columns than $A$, such that $A \approx HH^T$. SymNMF can be used for…