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Factorization Machines (FM), a general predictor that can efficiently model feature interactions in linear time, was primarily proposed for collaborative recommendation and have been broadly used for regression, classification and ranking…

Machine Learning · Computer Science 2021-08-18 Yu Geng , Liang Lan

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…

Optimization and Control · Mathematics 2012-08-13 Nicolas Gillis , François Glineur

Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…

Numerical Analysis · Computer Science 2017-12-07 Gabriele Torre , Michael Graber

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Machine Learning · Statistics 2014-01-10 Jason Gejie Liu , Shuchin Aeron

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…

Methodology · Statistics 2022-12-14 Lorenzo Schiavon , Bernardo Nipoti , Antonio Canale

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-01 Ramakrishnan Kannan , Grey Ballard , Haesun Park

Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification,…

Machine Learning · Computer Science 2021-06-01 Jicong Fan , Chengrun Yang , Madeleine Udell

We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification,…

Machine Learning · Computer Science 2023-03-02 Tyler Will , Runyu Zhang , Eli Sadovnik , Mengdi Gao , Joshua Vendrow , Jamie Haddock , Denali Molitor , Deanna Needell

Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called…

Numerical Analysis · Mathematics 2014-04-29 Joel A. Tropp

CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender…

Machine Learning · Statistics 2014-11-19 Arto Klami , Guillaume Bouchard , Abhishek Tripathi

Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…

Machine Learning · Computer Science 2023-09-26 Ioannis Kordonis , Emmanouil Theodosis , George Retsinas , Petros Maragos

This paper explores the use of Column Generation (CG) techniques in constructing univariate binary decision trees for classification tasks. We propose a novel Integer Linear Programming (ILP) formulation, based on root-to-leaf paths in…

Machine Learning · Computer Science 2019-07-12 Murat Firat , Guillaume Crognier , Adriana F. Gabor , C. A. J. Hurkens , Yingqian Zhang

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…

Machine Learning · Computer Science 2026-03-03 Vladimír Boža , Vladimír Macko

In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…

Machine Learning · Statistics 2014-02-06 Jiaming Xu , Rui Wu , Kai Zhu , Bruce Hajek , R. Srikant , Lei Ying

The multi-scale factor models are particularly appealing for analyzing matrix- or tensor-valued data, due to their adaptiveness to local geometry and intuitive interpretation. However, the reliance on the binary tree for recursive…

Methodology · Statistics 2020-02-26 Maoran Xu , Leo L. Duan

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

Machine Learning · Statistics 2018-06-18 Pratik Jawanpuria , Bamdev Mishra

This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…

Data Structures and Algorithms · Computer Science 2019-08-01 Richard Kueng , Joel A. Tropp

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a…

Machine Learning · Statistics 2015-01-26 Paul Honeine , Fei Zhu

Matrix Factorization has many applications such as clustering. When the matrix is Boolean it is favorable to have Boolean factors too. This will save the efforts of quantizing the reconstructed data back, which usually is done using…

Data Structures and Algorithms · Computer Science 2019-03-26 Abdelmoneim Amer Desouki , Michael Röder , Axel-Cyrille Ngonga Ngomo

Non-negative matrix factorization (NMF) is a common method for generating topic models from text data. NMF is widely accepted for producing good results despite its relative simplicity of implementation and ease of computation. One…

Machine Learning · Computer Science 2016-08-09 Brendan Gavin , Vijay Gadepally , Jeremy Kepner