The similarity of signal processing effect between PCA and SVD and Its mechanism analysis

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (2) : 12-17.

NIE Zhen-guo，ZHAO Xue-zhi

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Abstract

The principal component analysis (PCA) is applied to signal processing and is compared with singular value decomposition (SVD). Firstly, the signal processing principles of PCA and SVD are analyzed and summarized. In view of the application of PCA in signal processing, the theory of eigenvalues difference spectrum based on PCA is proposed. It is pointed out that PCA has the very similar signal processing effect to that of SVD when applied to signal de-noising. Secondly, the reason for this similarity is analyzed theoretically, and it is found that this is because the right singular vectors of the original matrix are just the eigenvectors of its covariance matrix, and it is this reason that leads to the similarity of PCA and SVD in signal processing. Lastly, it is pointed out that the reconstruction error of SVD is smaller than that of PCA, and the reason is that SVD does not need to compute the covariance matrix, so the rounding errors is avoided.

Key words

principal component analysis / singular value decomposition / de-noising / similarity;error

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NIE Zhen-guo，ZHAO Xue-zhi. The similarity of signal processing effect between PCA and SVD and Its mechanism analysis[J]. Journal of Vibration and Shock, 2016, 35(2): 12-17

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