Novel Algorithm for Non-Negative Matrix Factorization

Hien, Tran Dang; Tuan, Do Van; At, Pham Van; Son, Le Hung

doi:10.1142/s1793005715400013

Cited by 12 publications

(11 citation statements)

References 5 publications

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“…Since the above theorem corresponds to [14] (Theorem 3.2.2) and the proof is the same as that in [14] (Theorem 3.2.2), we will not prove it here.…”

Section: Theorem 6 Suppose ( ) Is a Limit Point Of ( ) Andmentioning

confidence: 99%

“…In this section, we will discuss the procedure to update an element of the matrices and . In [14], is adjusted by adding a parameter :̃=…”

Section: Algorithm For Updating An Element Of Matrixmentioning

confidence: 99%

“…In this section, we give some numerical experiments of Algorithm 3 and compare its behavior with the method of [14] In experiments, we will compare the following statistics: the number of iterations (Iter), the CPU time in second (time), the speed of convergence to stationary point, and the minimum value of objective function value (fun). Same as [14], the speed of convergence is measured by using the following formula:…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…For the sake of solving the minimum problem (2), Hien et al [14] have proposed a novel algorithm, in which the update rule contains only a parameter and the parameter selection is considered exact in some cases. Compared with multiplicative update algorithm, the novel algorithm [14] has fast convergence speed and small decomposition error.…”

Section: Introductionmentioning

confidence: 99%

“…Some inexact technique is widely applied to large scale optimization problems. Based on this idea, we employ an inexact parameter instead of the exact parameter [14]. In the meantime, we add another parameter to accelerate the speed decrease of objective function.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Inexact Update Method with Double Parameters for Nonnegative Matrix Factorization

Zhang

Xiang

et al. 2016

Mathematical Problems in Engineering

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Nonnegative matrix factorization (NMF) has been used as a powerful date representation tool in real world, because the nonnegativity of matrices is usually required. In recent years, many new methods are available to solve NMF in addition to multiplicative update algorithm, such as gradient descent algorithms, the active set method, and alternating nonnegative least squares (ANLS). In this paper, we propose an inexact update method, with two parameters, which can ensure that the objective function is always descent before the optimal solution is found. Experiment results show that the proposed method is effective.

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“…Since the above theorem corresponds to [14] (Theorem 3.2.2) and the proof is the same as that in [14] (Theorem 3.2.2), we will not prove it here.…”

Section: Theorem 6 Suppose ( ) Is a Limit Point Of ( ) Andmentioning

confidence: 99%

“…In this section, we will discuss the procedure to update an element of the matrices and . In [14], is adjusted by adding a parameter :̃=…”

Section: Algorithm For Updating An Element Of Matrixmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Inexact Update Method with Double Parameters for Nonnegative Matrix Factorization

Zhang

Xiang

et al. 2016

Mathematical Problems in Engineering

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Deep neural network techniques for monaural speech enhancement and separation: state of the art analysis

Ochieng

2023

Artif Intell Rev

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Deep neural networks (DNN) techniques have become pervasive in domains such as natural language processing and computer vision. They have achieved great success in tasks such as machine translation and image generation. Due to their success, these data driven techniques have been applied in audio domain. More specifically, DNN models have been applied in speech enhancement and separation to perform speech denoising, dereverberation, speaker extraction and speaker separation. In this paper, we review the current DNN techniques being employed to achieve speech enhancement and separation. The review looks at the whole pipeline of speech enhancement and separation techniques from feature extraction, how DNN-based tools models both global and local features of speech, model training (supervised and unsupervised) to how they address label ambiguity problem. The review also covers the use of domain adaptation techniques and pre-trained models to boost speech enhancement process. By this, we hope to provide an all inclusive reference of all the state of art DNN based techniques being applied in the domain of speech separation and enhancement. We further discuss future research directions. This survey can be used by both academic researchers and industry practitioners working in speech separation and enhancement domain.

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Versatile domain mapping of scanning electron nanobeam diffraction datasets utilising variational autoencoders

et al. 2023

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Characterisation of structure across the nanometre scale is key to bridging the gap between the local atomic environment and macro-scale and can be achieved by means of scanning electron nanobeam diffraction (SEND). As a technique, SEND allows for a broad range of samples, due to being relatively tolerant of specimen thickness with low electron dosage. This, coupled with the capacity for automation of data collection over wide areas, allows for statistically representative probing of the microstructure. This paper outlines a versatile, data-driven approach for producing domain maps, and a statistical approach for assessing their applicability. The workflow utilises a Variational AutoEncoder to identify the sources of variance in the diffraction signal, and this, in combination with clustering techniques, is used to produce domain maps. This approach is agnostic to domain crystallinity, requires no prior knowledge of crystal structure, and does not require simulation of a library of expected diffraction patterns.

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Novel Algorithm for Non-Negative Matrix Factorization

Cited by 12 publications

References 5 publications

An Inexact Update Method with Double Parameters for Nonnegative Matrix Factorization

An Inexact Update Method with Double Parameters for Nonnegative Matrix Factorization

Deep neural network techniques for monaural speech enhancement and separation: state of the art analysis

Versatile domain mapping of scanning electron nanobeam diffraction datasets utilising variational autoencoders

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