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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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On the Complexity of Nonnegative Matrix Factorization [PDF]
SIAM Journal on Optimization, 2009 Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases, and other information retrieval and clustering applications. The problem is most naturally posed as continuous optimization. In this report, we define an exact version of NMF. Then we establish several results about exact NMF: (i)
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Nonnegative Matrix Factorizations Performing Object Detection and Localization
Applied Computational Intelligence and Soft Computing, 2012 We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by nonnegative matrix factorizations.
G. Casalino, N. Del Buono, M. Minervini
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Novel Algorithms Based on Majorization Minimization for Nonnegative Matrix Factorization
IEEE Access, 2019 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 nonnegative matrix into ...
R. Jyothi, Prabhu Babu, Rajendar Bahl
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Weighted Nonnegative Matrix Factorization for Image Inpainting and Clustering
International Journal of Computational Intelligence Systems, 2020 Conventional nonnegative matrix factorization and its variants cannot separate the noise data space into a clean space and learn an effective low-dimensional subspace from Salt and Pepper noise or Contiguous Occlusion.
Xiangguang Dai +3 more
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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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Theorems on positive data: on the uniqueness of NMF. [PDF]
, 2008 We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not.
Plumbley, MD +9 more
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The Sinkhorn-Knopp algorithm : convergence and applications [PDF]
, 2008 As long as a square nonnegative matrix A contains sufficient nonzero elements, then the Sinkhorn-Knopp algorithm can be used to balance the matrix, that is, to find a diagonal scaling of A that is doubly stochastic.
Knight, P.A.
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Directional clustering through matrix factorization [PDF]
, 2016 This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction.
Blumensath, Thomas
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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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