A Novel Nonnegative Matrix Factorization Algorithm for Multi-manifold Learning

2016 ◽  
pp. 575-582
Author(s):  
Qian Wang ◽  
Wen-Sheng Chen ◽  
Binbin Pan ◽  
Yugao Li
Keyword(s):  
Manifold Learning ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Factorization Algorithm

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 A Robust Manifold Graph Regularized Nonnegative Matrix Factorization Algorithm for Cancer Gene Clustering

Molecules ◽  
2017 ◽  
Vol 22 (12) ◽  
pp. 2131 ◽  
Author(s):  
Rong Zhu ◽  
Jin-Xing Liu ◽  
Yuan-Ke Zhang ◽  
Ying Guo
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Gene Clustering ◽  
Cancer Gene ◽  
Factorization Algorithm
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