Multiple kernel nonnegative matrix factorization

An, Shounan; Yun, Jeong-Min; Choi, Seungjin

doi:10.1109/icassp.2011.5946897

Cited by 26 publications

(17 citation statements)

References 9 publications

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“…The term r is usually chosen such that r mn m+n . The usual method of solving this is to reformulate (1) where W, H ≥ 0 means that all elements of W and H are non-negative and · F is the Frobenius norm. Since NMF was proposed by Lee and Seung [18] in 1999, it has been investigated by many researchers, such as Paatero and Tapper [23].…”

Section: Introductionmentioning

confidence: 99%

Non-monotone projection gradient method for non-negative matrix factorization

Liu

Zheng

2010

Comput Optim Appl

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Since Non-negative Matrix Factorization (NMF) was first proposed over a decade ago, it has attracted much attention, particularly when applied to numerous data analysis problems. Most of the existing algorithms for NMF are based on multiplicative iterative and alternating least squares algorithms. However, algorithms based on the optimization method are few, especially in the case where two variables are derived at the same time. In this paper, we propose a non-monotone projection gradient method for NMF and establish the convergence results of our algorithm. Experimental results show that our algorithm converges to better solutions than popular multiplicative update-based algorithms.

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Section: Introductionmentioning

confidence: 99%

Non-monotone projection gradient method for non-negative matrix factorization

Liu

Zheng

2010

Comput Optim Appl

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“…Through this work, the authors introduced the notion of 'biologically plausible' feature extraction algorithm, and interesting property of extending NMF into several layers by demonstrating hierarchical facial feature development process along the layers. In their later work in [7], they applied their algorithm, to PET image data, and showed that multi-layer NMF not only demonstrates interesting property of intuitive hierarchical feature extraction, but also does its job as a feature extraction algorithm successfully by demonstrating activation of feature coefficients.…”

Section: Related Workmentioning

confidence: 96%

“…In [6], the authors focused on introducing a novel notion of multi-layer NMF algorithm that demonstrates an interesting property of intuitive hierarchical feature learning process, and proving its successful job as a feature extraction algorithm [7]. In [8,9], the research focus was on separating mixed signals.…”

Section: Related Workmentioning

confidence: 99%

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Hierarchical feature extraction by multi-layer non-negative matrix factorization network for classification task

et al. 2015

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“…Multi-kernel learning (Chen, Li, Wei, Xu, & Shi, 2011;Yeh, Huang, & Lee, 2011), which seeks the optimal kernel by a weighted, linear combination of predefined candidate kernels, has been introduced to handle the problem of kernel selection. An, Yun, and Choi (2011), presented the Multi-Kernel NMF (NMF MK ), which learns the best convex combination of multiple kernel matrices and NMF parameters jointly. However, graph regularization was not taken into consideration in their framework.…”

Section: Introductionmentioning

confidence: 99%

Feature selection and multi-kernel learning for adaptive graph regularized nonnegative matrix factorization

Wang

Huang

Sun

et al. 2015

Expert Systems with Applications

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a b s t r a c tNonnegative matrix factorization (NMF), a popular part-based representation technique, does not capture the intrinsic local geometric structure of the data space. Graph regularized NMF (GNMF) was recently proposed to avoid this limitation by regularizing NMF with a nearest neighbor graph constructed from the input data set. However, GNMF has two main bottlenecks. First, using the original feature space directly to construct the graph is not necessarily optimal because of the noisy and irrelevant features and nonlinear distributions of data samples. Second, one possible way to handle the nonlinear distribution of data samples is by kernel embedding. However, it is often difficult to choose the most suitable kernel. To solve these bottlenecks, we propose two novel graph-regularized NMF methods, AGNMF FS and AGNMF MK , by introducing feature selection and multiple-kernel learning to the graph regularized NMF, respectively. Instead of using a fixed graph as in GNMF, the two proposed methods learn the nearest neighbor graph that is adaptive to the selected features and learned multiple kernels, respectively. For each method, we propose a unified objective function to conduct feature selection/multi-kernel learning, NMF and adaptive graph regularization simultaneously. We further develop two iterative algorithms to solve the two optimization problems. Experimental results on two challenging pattern classification tasks demonstrate that the proposed methods significantly outperform state-of-the-art data representation methods.

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Multiple kernel nonnegative matrix factorization

Cited by 26 publications

References 9 publications

Non-monotone projection gradient method for non-negative matrix factorization

Non-monotone projection gradient method for non-negative matrix factorization

Hierarchical feature extraction by multi-layer non-negative matrix factorization network for classification task

Feature selection and multi-kernel learning for adaptive graph regularized nonnegative matrix factorization

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