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Nonnegative Matrix/Tensor factorization (NMF/NTF) have been used in the study of EEG, and the fit (explained variation) is often used to evaluate the performance of a nonnegative decomposition algorithm. However, this parameter only reveals the information derived from the mathematical model and just exhibits the reliability of the algorithms, and the property of EEG can not be reflected. If fits...
Parallel factor analysis (PARAFAC) is a multi-way decomposition method which allows to find hidden factors from the raw tensor data. Recently, the nonnegative tensor factorization (NTF), a variant of the model with nonnegativity constraints imposed on hidden factors has attracted interesting due to meaningful representation with many potential applications in neuroscience, bioinformatics, chemometrics...
Anomalous environmental electromagnetic (EM) radiation waves have been reported as the portents of earthquakes. We have been measuring the extremely low frequency (ELF) range all over Japan. Our goal is to predict earthquakes using EM radiation waves. Previously, we proposed a method of detecting anomalous signals by focusing on linear prediction errors. However, this method also sensitively responds...
In this paper we propose a family of new algorithms for non-negative matrix/tensor factorization (NMF/NTF) and sparse nonnegative coding and representation that has many potential applications in computational neuroscience, multi-sensory, multidimensional data analysis and text mining. We have developed a class of local algorithms which are extensions of hierarchical alternating least squares (HALS)...
Nonnegative tucker decomposition (NTD) is a recent multiway extension of nonnegative matrix factorization (NMF), where nonnega- tivity constraints are incorporated into Tucker model. In this paper we consider alpha-divergence as a discrepancy measure and derive multiplicative updating algorithms for NTD. The proposed multiplicative algorithm includes some existing NMF and NTD algorithms as its special...
In this paper, we discuss why non-negative matrix factorization (NMF) potentially works for zero-grounded non-negative components and why it fails when the components are not zero-grounded. We show the demixing process is not uniquely defined (up to the usual permutation/scaling ambiguity) when the original matrices are not zero-grounded. If fact, zero-groundedness alone is not enough. The key observation...
In these lecture notes, the authors have outlined several approaches to solve a NMF/NTF problem. The following main conclusions can be drawn: 1) Multiplicative algorithms are not necessary the best approaches for NMF, especially if data representations are not very redundant or sparse. 2) Much better performance can be achieved using the FP-ALS (especially for large-scale problems), IPC, and QN methods...
In this paper we develop several algorithms for non-negative matrix factorization (NMF) in applications to blind (or semi blind) source separation (BSS), when sources are generally statistically dependent under conditions that additional constraints are imposed such as nonnegativity, sparsity, smoothness, lower complexity or better predictability. We express the non-negativity constraints using a...
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