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.

The application of semi-nonnegative matrix factorization for detection of incipient faults in bearings

2019 ◽  
Vol 233 (13) ◽  
pp. 4543-4555 ◽  
Author(s):  
Akhand Rai ◽  
Sanjay H Upadhyay
Keyword(s):  
Frequency Domain ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Health Indicators ◽  
Data Matrix ◽  
Bearing Faults ◽  
Time Frequency ◽  
Factorization Algorithm ◽  
Incipient Faults

Bearing faults are a major reason for the catastrophic breakdown of rotating machinery. Therefore, the early detection of bearing faults becomes a necessity to attain an uninterrupted and safe operation. This paper proposes a novel approach based on semi-nonnegative matrix factorization for detection of incipient faults in bearings. The semi-nonnegative matrix factorization algorithm creates a sparse, localized, part-based representation of the original data and assists to capture the fault information in bearing signals more effectively. Through semi-nonnegative matrix factorization, two bearing health indicators are derived to fulfill the desired purpose. In doing so, the paper tries to address two critical issues: (i) how to reduce the dimensionality of feature space (ii) how to obtain a definite range of the indicator between 0 and 1. Firstly, a set of time domain, frequency domain, and time–frequency domain features are extracted from the bearing vibration signals. Secondly, the feature dataset is utilized to train the semi-nonnegative matrix factorization algorithm which decomposes the training data matrix into two new matrices of lower ranks. Thirdly, the test feature vectors are projected onto these lower dimensional matrices to obtain two statistics called as square prediction error and Q2. Finally, the Bayesian inference approach is exploited to convert the two statistics into health indicators that have a fixed range between [0–1]. The application of the advocated technique on experimental bearing signals demonstrates that it can effectively predict the weak defects in bearings as well as performs better than the earlier methods like principal component analysis and locality preserving projections.

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.

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