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Nonsmooth nonnegative matrix factorization (nsNMF)

A. Pascual-Montano, J.M. Carazo, K. Kochi, D. Lehmann, R.D. Pascual-Marqui
2006 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Unlike the classical nonnegative matrix factorization (NMF) technique, this new model, denoted "nonsmooth nonnegative matrix factorization" (nsNMF), corresponds to the optimization of an unambiguous cost  ...  We propose a novel nonnegative matrix factorization model that aims at finding localized, part-based, representations of nonnegative multivariate data items.  ...  OUR PROPOSAL: NONSMOOTH NONNEGATIVE MATRIX FACTORIZATION (nsNMF) All the methods described in the previous section try to achieve further sparseness in the nonnegative matrix factorization model by means  ... 
doi:10.1109/tpami.2006.60 pmid:16526426 fatcat:gd4qa3g7srdt5pbxbouig7j6se

Learning the Hierarchical Parts of Objects by Deep Non-Smooth Nonnegative Matrix Factorization [article]

Jinshi Yu, Guoxu Zhou, Andrzej Cichocki, Shengli Xie
2018 arXiv   pre-print
Nonsmooth Nonnegative Matrix Factorization (nsNMF) is capable of producing more localized, less overlapped feature representations than other variants of NMF while keeping satisfactory fit to data.  ...  The deep nsNMF not only gives parts-based features due to the nonnegativity constraints, but also creates higher-level, more abstract features by combing lower-level ones.  ...  INTRODUCTION N ONNEGATIVE matrix factorization (NMF) is a technique that represents a nonnegative data matrix X as the product of two nonnegative matrices Z and H, i.e., X = ZH, where Z and H are often  ... 
arXiv:1803.07226v1 fatcat:pczy3ilavbe7fmvg6ossfxvtvu

Topic Diffusion Discovery based on Sparseness-constrained Non-negative Matrix Factorization [article]

Yihuang Kang, Keng-Pei Lin, I-Ling Cheng
2018 arXiv   pre-print
In this paper, we consider a novel topic diffusion discovery technique that incorporates sparseness-constrained Non-negative Matrix Factorization with generalized Jensen-Shannon divergence to help understand  ...  In this paper, we propose using a normalized Nonsmooth Nonnegative Matrix Factorization (nsNMF) [20] , which is originally defined as: X ≈WSH where S∈ℝ k ×k is a positive symmetric smoothing matrix defined  ...  In this paper, we consider using Nonsmooth Nonnegative Matrix Factorization (nsNMF) [20] that puts sparseness constraints on both basis and coefficient matrices so as to extract highly localized patterns  ... 
arXiv:1807.04386v1 fatcat:gj4ynkg4tncopcyl54t7rzoznm

Cancer classification and pathway discovery using non-negative matrix factorization [article]

Zexian Zeng, Andy Vo, Chengsheng Mao, Susan E Clare, Seema A Khan, Yuan Luo
2018 arXiv   pre-print
We used multinomial logistic regression, nonsmooth non-negative matrix factorization (nsNMF), and support vector machine (SVM) to utilize the full range of sequencing data, aiming at better aggregating  ...  Using the factor matrices derived from the nsNMF, we identified multiple genes and pathways that are significantly associated with each cancer type.  ...  Specifically, for the purpose of sparseness, we used non-smooth Nonnegative Matrix Factorization (nsNMF) for feature selection [41] .  ... 
arXiv:1809.10681v2 fatcat:ftx3mj2oifbkxmvsrsmjsl45my

Biclustering of gene expression data by Non-smooth Non-negative Matrix Factorization

Pedro Carmona-Saez, Roberto D Pascual-Marqui, F Tirado, Jose M Carazo, Alberto Pascual-Montano
2006 BMC Bioinformatics  
Our approach is based on a new data mining technique, Non-smooth Non-Negative Matrix Factorization (nsNMF), able to identify localized patterns in large datasets.  ...  the factors and encoding vectors by making use of nonsmoothness constraints.  ...  The new method, here referred to as Non-smooth Non-Negative Matrix Factorization (nsNMF) [23] , differs from the original in the use of an extra smoothness matrix to impose sparseness.  ... 
doi:10.1186/1471-2105-7-78 pmid:16503973 pmcid:PMC1434777 fatcat:whgqxq4nzrexxpsu6s5hbbn54m

From student research to intrusion detection

N. Paul Schembari
2015 Proceedings of the 2015 Information Security Curriculum Development Conference on - InfoSec '15  
The IDS uses data mining with the Bag of Words methodology, creates a matrix model, and clusters the records using k-means and sparse nonnegative matrix factorization.  ...  The IDS data is represented by vectors, and the vectors are clustered using Sparse Nonnegative Matrix Factorization.  ...  Hence, they give an algorithm to force sparseness on W called Nonsmooth NMF (nsNMF). We have implemented nsNMF in BoWIDS.  ... 
doi:10.1145/2885990.2885995 dblp:conf/infoseccd/Schembari15 fatcat:bprmjsyc45eyvfi23qscljkaba

Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing

Sen Jia, Yuntao Qian
2009 IEEE Transactions on Geoscience and Remote Sensing  
Index Terms-Discontinuity adaptive model, hyperspectral unmixing, nonnegative matrix factorization (NMF), sparse coding.  ...  During the last few years, nonnegative matrix factorization (NMF), as a suitable candidate for the linear spectral mixture model, has been applied to unmix hyperspectral data.  ...  On the other hand, due to the nonnegativity of both spectra and abundances, a new BSS method, nonnegative matrix factorization (NMF) [17] , which decomposes the data into two nonnegative matrices (i.e  ... 
doi:10.1109/tgrs.2008.2002882 fatcat:r4jfrtr6anbffcctzef44kkeza

Simplicial nonnegative matrix factorization

Duy Khuong Nguyen, Khoat Than, Tu Bao Ho
2013 The 2013 RIVF International Conference on Computing & Communication Technologies - Research, Innovation, and Vision for Future (RIVF)  
Nonnegative matrix factorization (NMF) plays a crucial role in machine learning and data mining, especially for dimension reduction and component analysis.  ...  factorization (locNMF) [5] , convolutional NMF(conNMF) [19] , and Nonsmooth Nonnegative Matrix Factorization (nsNMF) [7] .  ...  Algorithm 1 Nonnegative Matrix Factorization Input: Data matrix X = {x m } M m=1 2 R M ⇥N + and K.  ... 
doi:10.1109/rivf.2013.6719865 dblp:conf/rivf/NguyenTH13 fatcat:5mmg3vrxz5fbxgkwc66wso6erm

Smooth nonnegative matrix and tensor factorizations for robust multi-way data analysis

Tatsuya Yokota, Rafal Zdunek, Andrzej Cichocki, Yukihiko Yamashita
2015 Signal Processing  
In this paper, we discuss new efficient algorithms for nonnegative matrix factorization (NMF) with smoothness constraints imposed on nonnegative components or factors.  ...  Moreover, we extend the proposed approach to the smooth nonnegative Tucker decomposition and smooth nonnegative canonical polyadic decomposition (also called smooth nonnegative tensor factorization).  ...  Next, we applied the nonnegative matrix and tensor factorization techniques to the analysis of a color image.  ... 
doi:10.1016/j.sigpro.2015.02.003 fatcat:mhmmoff3tzgbraff2lrcydo4uq

bioNMF: a web-based tool for nonnegative matrix factorization in biology

E. Mejia-Roa, P. Carmona-Saez, R. Nogales, C. Vicente, M. Vazquez, X. Y. Yang, C. Garcia, F. Tirado, A. Pascual-Montano
2008 Nucleic Acids Research  
Nonnegative matrix factorization (NMF) has been established as a very effective method to reveal information about the complex latent relationships in experimental data sets.  ...  This variant, denoted as Nonsmooth Nonnegative Matrix Factorization (nsNMF) (14) , produces a sparse representation of the gene-expression data matrix, making possible the simultaneous clustering of genes  ...  Nonnegative matrix factorization (NMF) (1) is one of such techniques that, although relatively new, is increasingly used in biomedical sciences.  ... 
doi:10.1093/nar/gkn335 pmid:18515346 pmcid:PMC2447803 fatcat:rg5zeastkvaxto3qbqws24iefy

Extracting non-negative basis images using pixel dispersion penalty

Wei-Shi Zheng, JianHuang Lai, Shengcai Liao, Ran He
2012 Pattern Recognition  
Non-negativity matrix factorization (NMF) and its variants have been explored in the last decade and are still attractive due to its ability of extracting non-negative basis images.  ...  Furthermore, by incorporating the proposed PDP, we develop a spatial non-negative matrix factorization (Spatial NMF) and a spatial non-negative component analysis (Spatial NCA).  ...  Hence, we mainly compare our proposed two methods Spatial NMF and Spatial NCA with NMF [6] , localized non-negative matrix factorization (LNMF) [8] , nonsmooth non-negative matrix factorization and (  ... 
doi:10.1016/j.patcog.2012.01.022 fatcat:bnu3msmomnal5jkqfcrq53mbqy

Nonnegative Matrix Factorization: Models, Algorithms and Applications [chapter]

Zhong-Yuan Zhang
2012 Intelligent Systems Reference Library  
In recent years, Nonnegative Matrix Factorization (NMF) has become a popular model in data mining society.  ...  In summary, we draw the following conclusions: 1) NMF has a good interpretability due to its nonnegative constraints; 2) NMF is very flexible regarding the choices of its objective functions and the algorithms  ...  Nonsmooth Nonnegative Matrix Factorization, nsNMF ([15]) nsNMF is also motivated by sparseness requirement of many applications and can be formulated as: = , where = (1 − ) + is a "smoothing" matrix, is  ... 
doi:10.1007/978-3-642-23241-1_6 fatcat:ohxfkn7wojhcrnkrshz2s7zxpu

Robust Feature Extraction for Speaker Recognition Based on Constrained Nonnegative Tensor Factorization

Qiang Wu, Li-Qing Zhang, Guang-Chuan Shi
2010 Journal of Computer Science and Technology  
In this paper, we investigate robust feature extraction for speech signal based on tensor structure and develop a new method called constrained Nonnegative Tensor Factorization (cNTF).  ...  The nonsmooth NMF (nsNMF) model [33] proposed a factorization model V = W SH, providing a smoothing matrix S ∈ R k×k given by S = (1 − θ)I + θ k 11 T , (13) where · T is the transpose operater, I is  ...  Constrained Nonnegative Tensor Factorization Given a nonnegative M -way tensor X ∈ R N1×N2×···×N M , nonnegative tensor factorization (NTF) seeks a factorization of X in the form: X ≈X = R r=1 A (1) :,  ... 
doi:10.1007/s11390-010-9365-6 fatcat:6h4wzfjq7ng6no3477k6e7yac4

On Constrained Sparse Matrix Factorization

Wei-Shi Zheng, Stan Z. Li, J. H. Lai, Shengcai Liao
2007 2007 IEEE 11th International Conference on Computer Vision  
In this paper, we analyze the problem in a more general framework called Constrained Sparse Matrix Factorization (CSMF).  ...  Various linear subspace methods can be formulated in the notion of matrix factorization in which a cost function is minimized subject to some constraints.  ...  It can be formulated in the notion of matrix factorization (MF) that training data matrix X is approximately factorized into a component matrix W and a coefficient matrix H.  ... 
doi:10.1109/iccv.2007.4408911 dblp:conf/iccv/ZhengLLL07 fatcat:y3g34g73ereezpt3ch5cxhc3aa

Nonnegative Matrix Factorization: A Comprehensive Review

Yu-Xiong Wang, Yu-Jin Zhang
2013 IEEE Transactions on Knowledge and Data Engineering  
Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception.  ...  It incorporates the nonnegativity constraint and thus obtains the parts-based representation as well as enhancing the interpretability of the issue correspondingly.  ...  In fact this is identical to the previous work of Nonsmooth NMF (NSNMF) [115] , where the incorporation of a very smooth factor S S makes U U and V V quite sparse, and thus reconciles the contradiction  ... 
doi:10.1109/tkde.2012.51 fatcat:ocxepl7gdrhszawqhsj36qhpme
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