scholarly journals Graph Regularized Nonnegative Matrix Factorization with Sparse Coding

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Chuang Lin ◽  
Meng Pang
Keyword(s):  
Sparse Coding ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Geometrical Structure ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Target Function ◽  
Original Data ◽  
Data Space ◽  
Detailed Derivation

In this paper, we propose a sparseness constraint NMF method, named graph regularized matrix factorization with sparse coding (GRNMF_SC). By combining manifold learning and sparse coding techniques together, GRNMF_SC can efficiently extract the basic vectors from the data space, which preserves the intrinsic manifold structure and also the local features of original data. The target function of our method is easy to propose, while the solving procedures are really nontrivial; in the paper we gave the detailed derivation of solving the target function and also a strict proof of its convergence, which is a key contribution of the paper. Compared with sparseness constrained NMF and GNMF algorithms, GRNMF_SC can learn much sparser representation of the data and can also preserve the geometrical structure of the data, which endow it with powerful discriminating ability. Furthermore, the GRNMF_SC is generalized as supervised and unsupervised models to meet different demands. Experimental results demonstrate encouraging results of GRNMF_SC on image recognition and clustering when comparing with the other state-of-the-art NMF methods.

scholarly journals Two Efficient Algorithms for Orthogonal Nonnegative Matrix Factorization

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jing Wu ◽  
Bin Chen ◽  
Tao Han
Keyword(s):  
Gene Expression ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Alternating Direction Method ◽  
Data Matrix ◽  
Popular Method ◽  
Alternating Direction ◽  
Expression Classification

Nonnegative matrix factorization (NMF) is a popular method for the multivariate analysis of nonnegative data. It involves decomposing a data matrix into a product of two factor matrices with all entries restricted to being nonnegative. Orthogonal nonnegative matrix factorization (ONMF) has been introduced recently. This method has demonstrated remarkable performance in clustering tasks, such as gene expression classification. In this study, we introduce two convergence methods for solving ONMF. First, we design a convergent orthogonal algorithm based on the Lagrange multiplier method. Second, we propose an approach that is based on the alternating direction method. Finally, we demonstrate that the two proposed approaches tend to deliver higher-quality solutions and perform better in clustering tasks compared with a state-of-the-art ONMF.

scholarly journals Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation

2019 ◽  
Vol 31 (2) ◽  
pp. 417-439 ◽  
Author(s):  
Andersen Man Shun Ang ◽  
Nicolas Gillis
Keyword(s):  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Gradient Methods ◽  
Nonnegative Matrix ◽  
Synthetic Image ◽  
Data Sets ◽  
Extrapolation Scheme ◽  
Factorization Algorithms

We propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the exact coordinate descent algorithms tackling the nonconvex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms: accelerated hierarchical alternating least squares and alternating nonnegative least squares, using synthetic, image, and document data sets.

Hyperspectral unmixing via deep matrix factorization

2017 ◽  
Vol 15 (06) ◽  
pp. 1750058 ◽  
Author(s):  
Lei Tong ◽  
Jing Yu ◽  
Chuangbai Xiao ◽  
Bin Qian
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Real Data ◽  
Hyperspectral Unmixing ◽  
The Past ◽  
Factorization Model ◽  
Layer Structures ◽  
Hyperspectral Remote Sensing Image

Hyperspectral unmixing is one of the most important techniques in hyperspectral remote sensing image analysis. During the past decades, many models have been widely used in hyperspectral unmixing, such as nonnegative matrix factorization (NMF) model, sparse regression model, etc. Most recently, a new matrix factorization model, deep matrix, is proposed and shows good performance in face recognition area. In this paper, we introduce the deep matrix factorization (DMF) for hyperspectral unmixing. In this method, the DMF method is applied for hyperspectral unmixing. Compared with the traditional NMF-based unmixing methods, DMF could extract more information with multiple-layer structures. An optimization algorithm is also proposed for DMF with two designed processes. Results on both synthetic and real data have validated the effectiveness of this method, and shown that it has outperformed several state-of-the-art unmixing approaches.

Nonnegative matrix factorization with region sparsity learning for hyperspectral unmixing

2017 ◽  
Vol 15 (06) ◽  
pp. 1750063
Author(s):  
Bin Qian ◽  
Lei Tong ◽  
Zhenmin Tang ◽  
Xiaobo Shen
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Spatial Information ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Hyperspectral Data ◽  
Optimization Scheme ◽  
Hyperspectral Unmixing ◽  
Relationship Of ◽  
The Relationship

Hyperspectral unmixing is one of the most important techniques in the remote sensing image analysis tasks. In recent decades, nonnegative matrix factorization (NMF) has been shown to be effective for hyperspectral unmixing due to the strong discovery of the latent structure. Most NMFs put emphasize on the spectral information, but ignore the spatial information, which is very crucial for analyzing hyperspectral data. In this paper, we propose an improved NMF method, namely NMF with region sparsity learning (RSLNMF), to simultaneously consider both spectral and spatial information. RSLNMF defines a new sparsity learning model based on a small homogeneous region that is obtained via the graph cut algorithm. Thus RSLNMF is able to explore the relationship of spatial neighbor pixels within each region. An efficient optimization scheme is developed for the proposed RSLNMF, and its convergence is theoretically guaranteed. Experiments on both synthetic and real hyperspectral data validate the superiority of the proposed method over several state-of-the-art unmixing approaches.

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