scholarly journals Ranking Preserving Nonnegative Matrix Factorization

2018 ◽  
Author(s):  
Jing Wang ◽  
Feng Tian ◽  
Weiwei Liu ◽  
Xiao Wang ◽  
Wenjie Zhang ◽  
...  
Keyword(s):  
Data Structure ◽  
Objective Function ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Relative Order ◽  
Structure Preserving ◽  
The Arts ◽  
Structured Representations ◽  
Clustering And Classification

Nonnegative matrix factorization (NMF),  a well-known technique  to find  parts-based representations of nonnegative data, has been widely studied. In reality,  ordinal relations often exist among data,  such as data i is more related to j than to q.  Such relative order is naturally available, and more importantly, it truly reflects the latent data structure.  Preserving the ordinal relations enables us to find structured representations of data that are faithful to the relative order, so that the learned representations become  more discriminative. However, current NMFs pay no attention to this. In this paper, we make the first attempt towards incorporating the ordinal relations and  propose a novel ranking preserving nonnegative matrix factorization (RPNMF) approach, which enforces the learned representations to be ranked according to the relations. We derive  iterative updating rules to solve RPNMF's objective function with  convergence guaranteed.  Experimental results with several datasets for clustering and classification have demonstrated that RPNMF achieves greater performance against the state-of-the-arts,  not only  in terms of  accuracy, but also interpretation of orderly data structure.

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.

scholarly journals Multi-Component Nonnegative Matrix Factorization

2017 ◽  
Author(s):  
Jing Wang ◽  
Feng Tian ◽  
Xiao Wang ◽  
Hongchuan Yu ◽  
Chang Hong Liu ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Multiple Representations ◽  
Nonnegative Matrix ◽  
Real Data ◽  
Multiple Components ◽  
Face Images ◽  
The Arts ◽  
Accurate Performance ◽  
Real World Datasets

Real data are usually complex and contain various components. For example, face images have expressions and genders. Each component mainly reflects one aspect of data and provides information others do not have. Therefore, exploring the semantic information of multiple components as well as the diversity among them is of great benefit to understand data comprehensively and in-depth. However, this cannot be achieved by current nonnegative matrix factorization (NMF)-based methods, despite that NMF has shown remarkable competitiveness in learning parts-based representation of data. To overcome this limitation, we propose a novel multi-component nonnegative matrix factorization (MCNMF). Instead of seeking for only one representation of data, MCNMF learns multiple representations simultaneously, with the help of the Hilbert Schmidt Independence Criterion (HSIC) as a diversity term. HSIC explores the diverse information among the representations, where each representation corresponds to a component. By integrating the multiple representations, a more comprehensive representation is then established. A new iterative updating optimization scheme is derived to solve the objective function of MCNMF, along with its correctness and convergence guarantees. Extensive experimental results on real-world datasets have shown that MCNMF not only achieves more accurate performance over the state-of-the-arts using the aggregated representation, but also interprets data from different aspects with the multiple representations, which is beyond what current NMFs can offer.

scholarly journals Robust Structure Preserving Nonnegative Matrix Factorization for Dimensionality Reduction

2016 ◽  
Vol 2016 ◽  
pp. 1-14
Author(s):  
Bingfeng Li ◽  
Yandong Tang ◽  
Zhi Han
Keyword(s):  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Noisy Data ◽  
Nonnegative Matrix ◽  
Structure Preserving ◽  
Structure Preservation ◽  
Significant Performance ◽  
Linear Dimensionality Reduction ◽  
Low Dimensional

As a linear dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in many fields, such as machine learning and data mining. However, there are still two major drawbacks for NMF: (a) NMF can only perform semantic factorization in Euclidean space, and it fails to discover the intrinsic geometrical structure of high-dimensional data distribution. (b) NMF suffers from noisy data, which are commonly encountered in real-world applications. To address these issues, in this paper, we present a new robust structure preserving nonnegative matrix factorization (RSPNMF) framework. In RSPNMF, a local affinity graph and a distant repulsion graph are constructed to encode the geometrical information, and noisy data influence is alleviated by characterizing the data reconstruction term of NMF withl2,1-norm instead ofl2-norm. With incorporation of the local and distant structure preservation regularization term into the robust NMF framework, our algorithm can discover a low-dimensional embedding subspace with the nature of structure preservation. RSPNMF is formulated as an optimization problem and solved by an effective iterative multiplicative update algorithm. Experimental results on some facial image datasets clustering show significant performance improvement of RSPNMF in comparison with the state-of-the-art algorithms.

scholarly journals Maximum Likelihood Estimation Based Nonnegative Matrix Factorization for Hyperspectral Unmixing

2021 ◽  
Vol 13 (13) ◽  
pp. 2637
Author(s):  
Qin Jiang ◽  
Yifei Dong ◽  
Jiangtao Peng ◽  
Mei Yan ◽  
Yi Sun
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Objective Function ◽  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Likelihood Estimation ◽  
Hyperspectral Data ◽  
Hyperspectral Unmixing

Hyperspectral unmixing (HU) is a research hotspot of hyperspectral remote sensing technology. As a classical HU method, the nonnegative matrix factorization (NMF) unmixing method can decompose an observed hyperspectral data matrix into the product of two nonnegative matrices, i.e., endmember and abundance matrices. Because the objective function of NMF is the traditional least-squares function, NMF is sensitive to noise. In order to improve the robustness of NMF, this paper proposes a maximum likelihood estimation (MLE) based NMF model (MLENMF) for unmixing of hyperspectral images (HSIs), which substitutes the least-squares objective function in traditional NMF by a robust MLE-based loss function. Experimental results on a simulated and two widely used real hyperspectral data sets demonstrate the superiority of our MLENMF over existing NMF methods.

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