Spectral clustering of high-dimensional data via Nonnegative Matrix Factorization

2015 ◽  
Author(s):  
Shulin Wang ◽  
Fang Chen ◽  
Jianwen Fang
Keyword(s):  
Matrix Factorization ◽  
Spectral Clustering ◽  
Nonnegative Matrix Factorization ◽  
High Dimensional Data ◽  
Nonnegative Matrix ◽  
High Dimensional

Improved Nonnegative Matrix Factorization Based Feature Selection for High Dimensional Data Analysis

2013 ◽  
Vol 347-350 ◽  
pp. 2344-2348
Author(s):  
Lin Cheng Jiang ◽  
Wen Tang Tan ◽  
Zhen Wen Wang ◽  
Feng Jing Yin ◽  
Bin Ge ◽  
...  
Keyword(s):  
Feature Selection ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
High Dimensional Data ◽  
Nonnegative Matrix ◽  
High Dimensional ◽  
Feature Subset ◽  
Feature Extraction Method ◽  
Optimal Feature Subset ◽  
Optimal Feature

Feature selection has become the focus of research areas of applications with high dimensional data. Nonnegative matrix factorization (NMF) is a good method for dimensionality reduction but it cant select the optimal feature subset for its a feature extraction method. In this paper, a two-step strategy method based on improved NMF is proposed.The first step is to get the basis of each catagory in the dataset by NMF. Added constrains can guarantee these basises are sparse and mostly distinguish from each other which can contribute to classfication. An auxiliary function is used to prove the algorithm convergent.The classic ReliefF algorithm is used to weight each feature by all the basis vectors and choose the optimal feature subset in the second step.The experimental results revealed that the proposed method can select a representive and relevant feature subset which is effective in improving the performance of the classifier.

scholarly journals Image Retrieval Based on Multiview Constrained Nonnegative Matrix Factorization and Gaussian Mixture Model Spectral Clustering Method

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Qunyi Xie ◽  
Hongqing Zhu
Keyword(s):  
Image Retrieval ◽  
Objective Function ◽  
Matrix Factorization ◽  
Spectral Clustering ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Gaussian Mixture ◽  
Sparse Representations ◽  
Clustering Method ◽  
Spectral Clustering Method

Content-based image retrieval has recently become an important research topic and has been widely used for managing images from repertories. In this article, we address an efficient technique, called MNGS, which integrates multiview constrained nonnegative matrix factorization (NMF) and Gaussian mixture model- (GMM-) based spectral clustering for image retrieval. In the proposed methodology, the multiview NMF scheme provides competitive sparse representations of underlying images through decomposition of a similarity-preserving matrix that is formed by fusing multiple features from different visual aspects. In particular, the proposed method merges manifold constraints into the standard NMF objective function to impose an orthogonality constraint on the basis matrix and satisfy the structure preservation requirement of the coefficient matrix. To manipulate the clustering method on sparse representations, this paper has developed a GMM-based spectral clustering method in which the Gaussian components are regrouped in spectral space, which significantly improves the retrieval effectiveness. In this way, image retrieval of the whole database translates to a nearest-neighbour search in the cluster containing the query image. Simultaneously, this study investigates the proof of convergence of the objective function and the analysis of the computational complexity. Experimental results on three standard image datasets reveal the advantages that can be achieved with the proposed retrieval scheme.

LOCALITY PRESERVING NONNEGATIVE MATRIX FACTORIZATION WITH APPLICATION TO FACE RECOGNITION

2010 ◽  
Vol 08 (05) ◽  
pp. 835-846 ◽  
Author(s):  
TAIPING ZHANG ◽  
BIN FANG ◽  
YUAN Y. TANG ◽  
ZHAOWEI SHANG
Keyword(s):  
Face Recognition ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
High Dimensional ◽  
Face Space ◽  
Manifold Structure ◽  
Locality Preserving ◽  
The Cost ◽  
Dimensional Face

In this paper, we propose a Locality Preserving Nonnegative Matrix Factorization (LPNMF) method to discover the manifold structure embedded in high-dimensional face space that is applied for face recognition. It is done by incorporating locality preserving constraints inside the cost function of NMF, then a new decomposition of a face with locality preserving can be obtained. As a result, the proposed LPNMF method shares some properties with the Locality Preserving Projection (LPP) such that it can effectively discover the manifold structure embedded in a high-dimensional face space. Experimental results show that LPNMF provides a better representation and achieves higher recognition rates in face recognition.

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