scholarly journals Robust Nonnegative Matrix Factorization via Joint Graph Laplacian and Discriminative Information for Identifying Differentially Expressed Genes

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ling-Yun Dai ◽  
Chun-Mei Feng ◽  
Jin-Xing Liu ◽  
Chun-Hou Zheng ◽  
Jiguo Yu ◽  
...  
Keyword(s):  
Differentially Expressed Genes ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Gene Selection ◽  
Error Function ◽  
Recognition Rate ◽  
Nonnegative Matrix ◽  
Graph Laplacian ◽  
Differentially Expressed ◽  
Update Rules

Differential expression plays an important role in cancer diagnosis and classification. In recent years, many methods have been used to identify differentially expressed genes. However, the recognition rate and reliability of gene selection still need to be improved. In this paper, a novel constrained method named robust nonnegative matrix factorization via joint graph Laplacian and discriminative information (GLD-RNMF) is proposed for identifying differentially expressed genes, in which manifold learning and the discriminative label information are incorporated into the traditional nonnegative matrix factorization model to train the objective matrix. Specifically,L2,1-norm minimization is enforced on both the error function and the regularization term which is robust to outliers and noise in gene data. Furthermore, the multiplicative update rules and the details of convergence proof are shown for the new model. The experimental results on two publicly available cancer datasets demonstrate that GLD-RNMF is an effective method for identifying differentially expressed genes.

scholarly journals Incremental Graph Regulated Nonnegative Matrix Factorization for Face Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhe-Zhou Yu ◽  
Yu-Hao Liu ◽  
Bin Li ◽  
Shu-Chao Pang ◽  
Cheng-Cheng Jia
Keyword(s):  
Face Recognition ◽  
Matrix Factorization ◽  
Information Needs ◽  
Nonnegative Matrix Factorization ◽  
Recognition Rate ◽  
Nonnegative Matrix ◽  
Recognition Algorithm ◽  
Incremental Method ◽  
Real World Application ◽  
The Face

In a real world application, we seldom get all images at one time. Considering this case, if a company hired an employee, all his images information needs to be recorded into the system; if we rerun the face recognition algorithm, it will be time consuming. To address this problem, In this paper, firstly, we proposed a novel subspace incremental method called incremental graph regularized nonnegative matrix factorization (IGNMF) algorithm which imposes manifold into incremental nonnegative matrix factorization algorithm (INMF); thus, our new algorithm is able to preserve the geometric structure in the data under incremental study framework; secondly, considering we always get many face images belonging to one person or many different people as a batch, we improved our IGNMF algorithms to Batch-IGNMF algorithms (B-IGNMF), which implements incremental study in batches. Experiments show that (1) the recognition rate of our IGNMF and B-IGNMF algorithms is close to GNMF algorithm while it runs faster than GNMF. (2) The running times of our IGNMF and B-IGNMF algorithms are close to INMF while the recognition rate outperforms INMF. (3) Comparing with other popular NMF-based face recognition incremental algorithms, our IGNMF and B-IGNMF also outperform then both the recognition rate and the running time.

scholarly journals Research of SWNMF with New Iteration Rules for Facial Feature Extraction and Recognition

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 354
Author(s):  
Jing Zhou
Keyword(s):  
Feature Extraction ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Recognition Rate ◽  
Nonnegative Matrix ◽  
Facial Feature ◽  
Face Database ◽  
Base Matrix ◽  
Sparse Nonnegative Matrix Factorization ◽  
Pca Method

Weighted nonnegative matrix factorization (WNMF) is a technology for feature extraction, which can extract the feature of face dataset, and then the feature can be recognized by the classifier. To improve the performance of WNMF for feature extraction, a new iteration rule is proposed in this paper. Meanwhile, the base matrix U is sparse based on the threshold, and the new method is named sparse weighted nonnegative matrix factorization (SWNMF). The new iteration rules are based on the smaller iteration steps, thus, the search is more precise, therefore, the recognition rate can be improved. In addition, the sparse method based on the threshold is adopted to update the base matrix U, which can make the extracted feature more sparse and concentrate, and then easier to recognize. The SWNMF method is applied on the ORL and JAFEE datasets, and from the experiment results we can find that the recognition rates are improved extensively based on the new iteration rules proposed in this paper. The recognition rate of new SWNMF method reached 98% for ORL face database and 100% for JAFEE face database, respectively, which are higher than the PCA method, the sparse nonnegative matrix factorization (SNMF) method, the convex non-negative matrix factorization (CNMF) method and multi-layer NMF method.

A Generalized Divergence Measure for Nonnegative Matrix Factorization

2007 ◽  
Vol 19 (3) ◽  
pp. 780-791 ◽  
Author(s):  
Raul Kompass
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Auxiliary Function ◽  
Divergence Measure ◽  
Factorization Problem ◽  
Special Cases ◽  
Leibler Divergence ◽  
Update Rules ◽  
Quadratic Distance

This letter presents a general parametric divergence measure. The metric includes as special cases quadratic error and Kullback-Leibler divergence. A parametric generalization of the two different multiplicative update rules for nonnegative matrix factorization by Lee and Seung (2001) is shown to lead to locally optimal solutions of the nonnegative matrix factorization problem with this new cost function. Numeric simulations demonstrate that the new update rule may improve the quadratic distance convergence speed. A proof of convergence is given that, as in Lee and Seung, uses an auxiliary function known from the expectation-maximization theoretical framework.

scholarly journals Hypergraph Regularized Discriminative Nonnegative Matrix Factorization on Sample Classification and Co-Differentially Expressed Gene Selection

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yong-Jing Hao ◽  
Ying-Lian Gao ◽  
Mi-Xiao Hou ◽  
Ling-Yun Dai ◽  
Jin-Xing Liu
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Gene Selection ◽  
Differentially Expressed Gene ◽  
Nonnegative Matrix ◽  
Intrinsic Geometry ◽  
Sample Classification ◽  
Analysis Technique ◽  
Label Information ◽  
Discriminative Function

Nonnegative Matrix Factorization (NMF) is a significant big data analysis technique. However, standard NMF regularized by simple graph does not have discriminative function, and traditional graph models cannot accurately reflect the problem of multigeometry information between data. To solve the above problem, this paper proposed a new method called Hypergraph Regularized Discriminative Nonnegative Matrix Factorization (HDNMF), which captures intrinsic geometry by constructing hypergraphs rather than simple graphs. The introduction of the hypergraph method allows high-order relationships between samples to be considered, and the introduction of label information enables the method to have discriminative effect. Both the hypergraph Laplace and the discriminative label information are utilized together to learn the projection matrix in the standard method. In addition, we offered a corresponding multiplication update solution for the optimization. Experiments indicate that the method proposed is more effective by comparing with the earlier methods.

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