Nonnegative Tensor Factorization, Completely Positive Tensors, and a Hierarchical Elimination Algorithm
نویسندگان
چکیده
منابع مشابه
Nonnegative Tensor Factorization, Completely Positive Tensors, and a Hierarchical Elimination Algorithm
Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has an exact symmetric nonnegative factorization, is called a completely positive tensor. This concept extends the concept of completely positive matrices. A classical result in the theory of completely positive m...
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In the paper we present new Alternating Least Squares (ALS) algorithms for Nonnegative Matrix Factorization (NMF) and their extensions to 3D Nonnegative Tensor Factorization (NTF) that are robust in the presence of noise and have many potential applications, including multi-way Blind Source Separation (BSS), multi-sensory or multi-dimensional data analysis, and nonnegative neural sparse coding....
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T here has been a recent surge of interest in matrix and tensor factorization (decomposition), which provides meaningful latent (hidden) components or features with physical or physiological meaning and interpretation. Nonnegative matrix factorization (NMF) and its extension to three-dimensional (3-D) nonnegative tensor factorization (NTF) attempt to recover hidden nonnegative common structures...
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Nonnegative Matrix Factorization (NMF) is an efficient technique to approximate a large matrix containing only nonnegative elements as a product of two nonnegative matrices of significantly smaller size. The guaranteed nonnegativity of the factors is a distinctive property that other widely used matrix factorization methods do not have. Matrices can also be seen as second-order tensors. For som...
متن کاملBuilding a completely positive factorization
Using a bordering approach, and building upon an already known factorization of a principal block, we establish sufficient conditions under which we can extend this factorization to the full matrix. Simulations show that the approach is promising also in higher dimensions.
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2014
ISSN: 0895-4798,1095-7162
DOI: 10.1137/13092232x