Fast and Low Memory Cost Matrix Factorization: Algorithm, Analysis, and Case Study

2020 ◽  
Vol 32 (2) ◽  
pp. 288-301
Author(s):  
Yan Yan ◽  
Mingkui Tan ◽  
Ivor W. Tsang ◽  
Yi Yang ◽  
Qinfeng Shi ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Algorithm Analysis ◽  
Cost Matrix ◽  
Factorization Algorithm ◽  
Memory Cost

scholarly journals Introducing an Educational Tool for Learning Branch & Bound Strategy

2017 ◽  
Vol 3 (1) ◽  
pp. 8 ◽  
Author(s):  
Sofriesilero Zumaytis ◽  
Oscar Karnalim
Keyword(s):  
Qualitative Evaluation ◽  
Performance Comparison ◽  
Brute Force ◽  
Educational Tool ◽  
Breadth First Search ◽  
Cost Matrix ◽  
Algorithm Visualization ◽  
Case Based

Abstract—According to our informal survey, Branch & Bound strategy is considerably difficult to learn compared to other strategies. This strategy consists of several complex algorithmic steps such as Reduced Cost Matrix (RCM) calculation and Breadth First Search. Thus, to help students understanding this strategy, AP-BB, an educational tool for learning Branch & Bound is developed. This tool includes four modules which are Brute Force solving visualization, Branch & Bound solving visualization, RCM calculator, and case-based performance comparison. These modules are expected to enhance student’s understanding about Branch & Bound strategy and its characteristics. Furthermore, our work incorporates TSP as its case study and Brute Force strategy as a baseline to provide a concrete impact of Branch & Bound strategy. According to our qualitative evaluation, AP-BB and all of its features fulfil student necessities for learning Branch & Bound strategy. Keywords— Educational Tool; Branch & Bound; Algorithm Strategy; Algorithm Visualization

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.

Sign in / Sign up

Export Citation Format

Share Document