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http://dx.doi.org/10.5351/KJAS.2017.30.3.441

Principal component analysis in the frequency domain: a review and their application to climate data  

Jo, You-Jung (Department of Statistics, Seoul National University)
Oh, Hee-Seok (Department of Statistics, Seoul National University)
Lim, Yaeji (Department of Statistics, Pukyong National University)
Publication Information
The Korean Journal of Applied Statistics / v.30, no.3, 2017 , pp. 441-451 More about this Journal
Abstract
In this paper, we review principal component analysis (PCA) procedures in the frequency domain and apply them to analyze sea surface temperature data. The classical PCA defined in the time domain is a popular dimension reduction technique. Extending the conventional PCA to the frequency domain makes it possible to define PCA in the frequency domain, which is useful for dimension reduction as well as a feature extraction of multiple time series. We focus on two PCA methods in the frequency domain, Hilbert PCA (HPCA) and frequency domain PCA (FDPCA). We review these two PCAs in order for potential readers to easily understand insights as well as perform a numerical study for comparison with conventional PCA. Furthermore, we apply PCA methods in the frequency domain to sea surface temperature data on the tropical Pacific Ocean. Results from numerical experiments demonstrate that PCA in the frequency domain is effective for the analysis of time series data.
Keywords
frequency domain; principal component analysis; sea surface temperature; spectral envelope;
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