• Proceedings of the Korea Contents Association Conference
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• 2008.05a
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• pp.92-95
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• 2008

NMF(Non-negative Matrix Factorization) has been proposed as an useful algorithm for feature extraction. Using NMF, we can extract low-dimensional feature vectors. Also, we can find clustering effects in the NMF algorithm. Also, it is reported that the sparse NMF algorithm shows better clustering effects. This paper compares the two approaches in the viewpoint of clustering effects.

• The Journal of the Korea Contents Association
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• v.9 no.4
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• pp.121-130
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• 2009

In this paper, feature extraction methods, which is one field of reducing dimensions of high-dimensional data, are empirically investigated. We selected the traditional PCA(Principal Component Analysis), ICA(Independent Component Analysis), NMF(Non-negative Matrix Factorization), and sNMF(Sparse NMF) for comparisons. ICA has a similar feature with the simple cell of V1. NMF implemented a "parts-based representation in the brain" and sNMF is a improved version of NMF. In order to visually investigate the extracted features, handwritten digits are handled. Also, the extracted features are used to train multi-layer perceptrons for recognition test. The characteristic of each feature extraction method will be useful when applying feature extraction methods to many real-world problems.

• Korean Chemical Engineering Research
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• v.43 no.2
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• pp.259-265
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• 2005

Binary isothermal vapor-liquid equilibrium(VLE) data were measured for water+n-methylformamide(NMF), benzene+NMF and toluene+NMF systems by using headspace gas chromatography(HSGC) at 353.15K. Additionally, the ternary liquid-liquid Equilibrium(LLE) data were determined by measuring of tie-line for the systems of NMF+benzene+n-heptane and NMF+toluene+n-heptane at 298.15 K. The measured isothermal binary VLE data have no azeotropes and were correlated well with $g^E$ model equations of Margules, van Laar, Wilson, NRTL and UNIQUAC. The experimental ternary tie line data were also correlated well with NRTL and UNIQUAC models. Besides their accuracy was analyzed by Hirata-Fujita and Maior-Swenson equations.

• Journal of Computing Science and Engineering
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• v.4 no.2
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• pp.97-109
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• 2010

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, which is to decompose a data matrix into a product of two factor matrices with all entries restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering), but in some cases NMF produces the results inappropriate to the clustering problems. In this paper, we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. The result of orthogonal NMF can be clearly interpreted for the clustering problems, and also the performance of clustering is usually better than that of the NMF. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.

• Proceedings of the Korean Society for Language and Information Conference
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• 2007.11a
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• pp.430-439
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• 2007

In this paper, we use non-negative matrix factorization (NMF) to refine the document clustering results. NMF is a dimensional reduction method and effective for document clustering, because a term-document matrix is high-dimensional and sparse. The initial matrix of the NMF algorithm is regarded as a clustering result, therefore we can use NMF as a refinement method. First we perform min-max cut (Mcut), which is a powerful spectral clustering method, and then refine the result via NMF. Finally we should obtain an accurate clustering result. However, NMF often fails to improve the given clustering result. To overcome this problem, we use the Mcut object function to stop the iteration of NMF.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.7C
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• pp.554-564
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• 2012

The vehicle recognition consists of two steps; the vehicle region detection step and the vehicle identification step based on the feature extracted from the detected region. Features using linear transformations have the effect of dimension reduction as well as represent statistical characteristics, and show the robustness in translation and rotation of objects. Among the linear transformations, the NMF(Non-negative Matrix Factorization) is one of part-based representation. Therefore, we can extract NMF features with sparsity and improve the vehicle recognition rate by the representation of local features of a car as a basis vector. In this paper, we propose a feature extraction using NMF suitable for the vehicle recognition, and verify the recognition rate with it. Also, we compared the vehicle recognition rate for the occluded area using the SNMF(sparse NMF) which has basis vectors with constraint and LVQ2 neural network. We showed that the feature through the proposed NMF is robust in the urban scene where occlusions are frequently occur.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.107-116
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• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.4-6
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• 2003

A holistic representation, such as sparse ceding or independent component analysis (ICA), was successfully applied to explain early auditory processing and sound classification. In contrast, Part-based representation is an alternative way of understanding object recognition in brain. In this paper. we employ the non-negative matrix factorization (NMF)［1］which learns parts-based representation for sound classification. Feature extraction methods from spectrogram using NMF are explained. Experimental results show that NMF-based features improve the performance of sound classification over ICA-based features.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.8
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• pp.851-858
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• 2016

This paper presents a new statistical voice activity detection (VAD) based on the probabilistic interpretation of nonnegative matrix factorization (NMF). The objective function of the NMF using Kullback-Leibler divergence coincides with the negative log likelihood function of the data if the distribution of the data given the basis and encoding matrices is modeled as Poisson distributions. Based on this probabilistic NMF, the VAD is constructed using the likelihood ratio test assuming that speech and noise follow Poisson distributions. Experimental results show that the proposed approach outperformed the conventional Gaussian model-based and NMF-based methods at 0-15 dB signal-to-noise ratio simulation conditions.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2014.06a
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• pp.9-11
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• 2014

본 논문에서는 오디오 신호의 특성 표현에 유용한 nonnegative matrix factorization(NMF)에 대해 설명하였으며, expectation maximization (EM)을 이용한 NMF 파라미터 추출 및 EM-NMF 기반한 오디오 소스 분리 기술에 대해서 설명했다. 또한, 다중 단계 NMF-EM 구조의 객체 분리를 통해서 객체 분리 성능을 향상시키기 위한 알고리즘을 제안하며, 제안된 알고리즘은 K-pop 음원과 SDR(source distortion ratio)를 통해서 객체 분리 성능을 평가한다. 성능 평가 결과 제안된 알고리즘은 다중 단계를 통해 약 3dB 의 보컬 분리 성능이 향상되며, 상업적 음원 제작에서 사용되는 가상 오디오 효과가 많이 적용된 음원에서 약 5dB 의 분리 성능을 향상시켰다. 그러므로 제안된 방식은 오디오 객체 분리에 유용한 방법이 될 것으로 생각된다.