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Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics
Mathematics, 2023 Compressed sensing is an alternative to Shannon/Nyquist sampling for acquiring sparse or compressible signals. Sparse coding represents a signal as a sparse linear combination of atoms, which are elementary signals derived from a predefined dictionary ...
Ke-Lin Du +3 more
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Monotonous (semi-)nonnegative matrix factorization [PDF]
Proceedings of the Second ACM IKDD Conference on Data Sciences, 2015 Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals can be monotonous in nature.
Bhatt, Nirav, Ayyar, Arun
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Toeplitz nonnegative realization of spectra via companion matrices
Special Matrices, 2019 The nonnegative inverse eigenvalue problem (NIEP) is the problem of finding conditions for the existence of an n × n entrywise nonnegative matrix A with prescribed spectrum Λ = {λ1, . . ., λn}.
Collao Macarena +2 more
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More on proper nonnegative splittings of rectangular matrices
AIMS Mathematics, 2021 In this paper, we further investigate the single proper nonnegative splittings and double proper nonnegative splittings of rectangular matrices. Two convergence theorems for the single proper nonnegative splitting of a semimonotone matrix are derived ...
Ting Huang, Shu-Xin Miao
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A Symmetric Rank-one Quasi Newton Method for Non-negative Matrix Factorization [PDF]
, 2013 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.
Lai, Shu-Zhen +2 more
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Online kernel nonnegative matrix factorization [PDF]
Signal Processing, 2017 Nonnegative matrix factorization (NMF) has become a prominent signal processing and data analysis technique. To address streaming data, online methods for NMF have been introduced recently, mainly restricted to the linear model. In this paper, we propose a framework for online nonlinear NMF, where the factorization is conducted in a kernel-induced ...
Zhu, Fei, Honeine, Paul
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Smoothed separable nonnegative matrix factorization
Linear Algebra and its Applications, 2023 31 pages + 10 pages of supplementary. Many clarifications have been brought to the paper, and we have added numerical experiments on facial ...
Nicolas Nadisic +2 more
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Sufficient conditions to be exceptional
Special Matrices, 2016 A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A
Johnson Charles R., Reams Robert B.
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Robust Graph Regularized Nonnegative Matrix Factorization
IEEE Access, 2022 Nonnegative Matrix Factorization (NMF) has become a popular technique for dimensionality reduction, and been widely used in machine learning, computer vision, and data mining. Existing unsupervised NMF methods impose the intrinsic geometric constraint on
Qi Huang +3 more
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Nonnegative Matrix Factorization [PDF]
, 2013 Matrix factorization or factor analysis is an important task that is helpful in the analysis of high-dimensional real-world data. SVD is a classical method for matrix factorization, which gives the optimal low-rank approximation to a real-valued matrix in terms of the squared error.
Ke-Lin Du, M. N. S. Swamy
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