Investigation on PCA in frequency domain

• Main Author: Duan, Zhaoming
• Other Authors: Pan Guangming
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2022
• Subjects: Science::Mathematics::Analysis
• Online Access: https://hdl.handle.net/10356/156932
• Institution: Nanyang Technological University

With the development of science and technology, the dimension of dataset has grown to be be higher and higher. To conveniently cope with them, a method called principal component analysis (PCA) has been invented to reduce the dimension while maintain most information of dataset. Nowadays, data in the signal format has shown up in many industry fields. To decompose the multivariate non-stationary signal into components that have zero coherency, PCA in the frequency domain is applied. It is usually applied in Factor Analysis and Signal Analysis. In our study, the dependencies of PCA in the frequency domain were explored. With the factor model and spiked model, the synthetic data was generated. Based on the dataset and PCA in frequency domain, the result of this technique was able to be analyzed. Periodic and symmetric behavior of the PCA result was revealed. We found that the dataset ratio and the type of distribution for data generation would affect the PCA result. This research is valuable for signal processing field, which may help researchers to improve the performance of PCA in the frequency domain in electroencephalogram, fault diagnosis, factor analysis and etc.