Convolutional PCA for Multiple Time Series
Xi-Lin Li · IEEE Signal Processing Letters · 2020
We study a fundamental generalization of principal component analysis (PCA) that looks for a small set of common time series, i.e., principal components (PCs), whose filtered versions can explain most of the variances of multiple observed time series. This problem boils down to PCA in the frequency domain, in principle. But, frequency domain processing suffers from aliasing, and brings inconveniences when handling certain time domain properties like nonstationarity, and sparsity. We propose novel time, and z-domain costs for such PCA, and study its properties in detail with setting of either finite or diverging filter lengths. We further discuss its implementations, and possible extensions, and present numerical results for empirical performance study. Convolution is used to extract these PCs, thus the name convolutional PCA.