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On Rationality of Nonnegative Matrix Factorization [PDF]
Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. NMF has a wide variety of applications, including bioinformatics, chemometrics, communication complexity, machine learning, polyhedral combinatorics, among many others ...
Dmitry Chistikov 0001 +4 more
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Coseparable Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under separability assumption, which requires the columns of factor matrix
Junjun Pan, Michael Ng 0001
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A Survey of Community Detection in Complex Networks Using Nonnegative Matrix Factorization
Community detection is one of the popular research topics in the field of complex networks analysis. It aims to identify communities, represented as cohesive subgroups or clusters, where nodes in the same community link to each other more densely than ...
Chaobo He +5 more
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Self-Supervised Symmetric Nonnegative Matrix Factorization [PDF]
Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of variables ...
Yuheng Jia +4 more
semanticscholar +1 more source
Nonnegative matrix factorizationalgorithms and applications
Data-mining has become a hot topic in recent years. It consists of extracting relevant information or structures from data such as: pictures, textual material, networks, etc.
Ngoc-Diep, Ho
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Tracking Time Evolution of Collective Attention Clusters in Twitter: Time Evolving Nonnegative Matrix Factorisation. [PDF]
Micro-blogging services, such as Twitter, offer opportunities to analyse user behaviour. Discovering and distinguishing behavioural patterns in micro-blogging services is valuable.
Shota Saito +3 more
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Co-sparse Non-negative Matrix Factorization
Non-negative matrix factorization, which decomposes the input non-negative matrix into product of two non-negative matrices, has been widely used in the neuroimaging field due to its flexible interpretability with non-negativity property.
Fan Wu +3 more
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Transductive Nonnegative Matrix Tri-Factorization
Nonnegative matrix factorization (NMF) decomposes a nonnegative matrix into the product of two lower-rank nonnegative matrices. Since NMF learns parts-based representation, it has been widely used as a feature learning component in many fields.
Xiao Teng +4 more
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The Growth of Powers of a Nonnegative Matrix [PDF]
Let A be a nonnegative $n \times n$ matrix. In this paper we study the growth of the powers $A^m, m = 1,2,3, \cdots $ when $\rho ( A ) = 1$. These powers occur naturally in the iteration process \[x^{( m + 1 )} = Ax^{( m )} ,\quad x^{( 0 )} \geqq 0,\] which is important in applications and numerical techniques.
Shmuel Friedland, Hans Schneider
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A Note on NIEP for Leslie and Doubly Leslie Matrices
The nonnegative inverse eigenvalue problem (NIEP) consists of finding necessary and sufficient conditions for the existence of a nonnegative matrix with a given list of complex numbers as its spectrum.
Luis Medina, Hans Nina, Elvis Valero
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