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Nonnegative Tensor Factorization, Completely Positive Tensors, and a Hierarchical Elimination Algorithm [PDF]

SIAM Journal on Matrix Analysis and Applications, 2014
Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has a symmetric nonnegative factorization, is called a completely positive (CP) tensor. The H-eigenvalues of a CP tensor are always nonnegative.
Liqun Qi, Changqing Xu
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Constrained Nonnegative Tensor Factorization for Clustering

2010 Ninth International Conference on Machine Learning and Applications, 2010
Constrained clustering through matrix factorization has been shown to largely improve clustering accuracy by incorporating prior knowledge into the factorization process. Although it has been well studied, none of them deal with constrained multi-way data factorization. Multi-way data or Tensors are encoded as high-order data structures.
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Nonnegative Tensor Decomposition

2013
It is more and more common to encounter applications where the collected data is most naturally stored or represented in a multi-dimensional array, known as a tensor. The goal is often to approximate this tensor as a sum of some type of combination of basic elements, where the notation of what is a basic element is specific to the type of factorization
N. Hao, L. Horesh, M. E. Kilmer
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Nonnegative tensors revisited: plane stochastic tensors

Linear and Multilinear Algebra, 2018
In this paper, we develop and enrich the theory of nonnegative tensors. We define the sign nonsingular tensors and establish the relationship between the combinatorial determinant and the permanent...
Maolin Che, Changjiang Bu, Liqun Qi, Yimin Wei   +3 more
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Nonnegative Tensor Factorization with Smoothness Constraints

2008
Nonnegative Tensor Factorization (NTF) is an emerging technique in multidimensional signal analysis and it can be used to find parts-based representations of high-dimensional data. In many applications such as multichannel spectrogram processing or multiarray spectra analysis, the unknown features have locally smooth temporal or spatial structure.
Rafal Zdunek, Tomasz M. Rutkowski
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Nonnegative Tensor Cofactorization and Its Unified Solution

IEEE Transactions on Image Processing, 2014
In this paper, we present a new joint factorization algorithm, called Nonnegative Tensor Co-Factorization (NTCoF). The key idea is to simultaneously factorize multiple visual features of the same data into nonnegative dimensionality-reduced representations, and meanwhile, to maximize the correlations of the low-dimensional representations.
Xiaobai Liu, Qian Xu, Shuicheng Yan, Gang Wang 0012, Hai Jin 0001, Seong-Whan Lee   +5 more
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Some bounds for the spectral radius of nonnegative tensors

Numerische Mathematik, 2014
This paper extends well-known spectral results from matrices to tensors \(\mathcal A\). It uses the Perron like theory of nonnegative tensors to find upper and lower spectral radius bounds from the entries of first index in \(\mathcal A\) and also from the symmetric tensor \(\mathcal S\) that is associated with \(\mathcal A\).
Wen Li 0006, Michael K. Ng 0001
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Variable Selection for Efficient Nonnegative Tensor Factorization

2015 IEEE International Conference on Data Mining, 2015
Nonnegative Tensor Factorization (NTF) has become a popular tool for extracting informative patterns from tensor data. However, NTF has high computational cost both in space and in time, mostly in iterative calculation of the gradient. In this paper, we consider variable selection to reduce the cost, assuming sparsity of the factor matrices.
Keigo Kimura, Mineichi Kudo
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Algorithms for Nonnegative Tensor Factorization

2009
Nonnegative Matrix Factorization (NMF) is a decomposition which incorporates nonnegativity constraints in both the weights and the bases of the representation. The nonnegativity constraints in NMF correspond better to the intuitive notion of combining parts in order to create a complete object, since the object is represented using only additions of ...
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Strictly Nonnegative Tensors and Nonnegative Tensor Partition

Science China Mathematics, 2014
Liqun Qi, Shenglong Hu, Zheng-Hai Huang
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