Related papers: Improved SVD-based Initialization for Nonnegative …
We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion},…
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…
Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and…
Non-negative Matrix Factorization (NMF) is one of the most popular techniques for data representation and clustering, and has been widely used in machine learning and data analysis. NMF concentrates the features of each sample into a…
Non-negative matrix factorization (NMF) is a fundamental matrix decomposition technique that is used primarily for dimensionality reduction and is increasing in popularity in the biological domain. Although finding a unique NMF is generally…
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…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…
With the abundance of data in recent years, interesting challenges are posed in the area of recommender systems. Producing high quality recommendations with scalability and performance is the need of the hour. Singular Value…
Nonnegative Matrix Factorization (NMF) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first, it was shown that…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…
Low-latency gravitational wave search pipelines such as GstLAL take advantage of low-rank factorization of the template matrix via singular value decomposition (SVD). With unprecedented improvements in detector bandwidth and sensitivity in…
Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…
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…
Unsupervised integrative analysis of multiple data sources has become common place and scalable algorithms are necessary to accommodate ever increasing availability of data. Only few currently methods have estimation speed as their focus,…
We introduce a fast low-rank factorization-based framework for compressing large language models that enables rapid compression of billion-parameter models without retraining. Unlike existing factorization-based approaches that optimize…
The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its…
Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, $X$, by the product of two nonnegative factors, $WH$, where $W$ has $r$ columns and $H$ has $r$ rows. In this paper, we consider NMF using the component-wise L1 norm…
This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…