Related papers: Efficient Matrix Factorization Via Householder Ref…
Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…
The unpivoted and pivoted Householder QR factorizations are ubiquitous in numerical linear algebra. A difficulty with pivoted Householder QR is the communication bottleneck introduced by pivoting. In this paper we propose using random…
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…
A convergent algorithm for nonnegative matrix factorization with orthogonality constraints imposed on both factors is proposed in this paper. This factorization concept was first introduced by Ding et al. with intent to further improve…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
We propose a method for computing binary orthogonal non-negative matrix factorization (BONMF) for clustering and classification. The method is tested on several representative real-world data sets. The numerical results confirm that the…
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…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…
Traditional NMF-based signal decomposition relies on the factorization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn…
This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a $m\times n$ matrix with $m\approx n$ provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The…
Identifying informative components in binary data is an essential task in many research areas, including life sciences, social sciences, and recommendation systems. Boolean matrix factorization (BMF) is a family of methods that performs…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
We give an algorithm for computing approximate PSD factorizations of nonnegative matrices. The running time of the algorithm is polynomial in the dimensions of the input matrix, but exponential in the PSD rank and the approximation error.…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
This paper proposes uni-orthogonal and bi-orthogonal nonnegative matrix factorization algorithms with robust convergence proofs. We design the algorithms based on the work of Lee and Seung [1], and derive the converged versions by utilizing…
We propose a unified and systematic framework for performing online nonnegative matrix factorization in the presence of outliers. Our framework is particularly suited to large-scale data. We propose two solvers based on projected gradient…
We develop a unified and systematic framework for performing online nonnegative matrix factorization under a wide variety of important divergences. The online nature of our algorithm makes it particularly amenable to large-scale data. We…