期刊
IEEE ACCESS
卷 10, 期 -, 页码 114223-114231出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/ACCESS.2022.3218163
关键词
Principal component analysis; Kernel; Time series analysis; Correlation; Covariance matrices; Eigenvalues and eigenfunctions; Discrete Fourier transforms; PCA; discrete Fourier transform; filter; correlation; time series; kernel PCA; circulant matrices
资金
- German Research Foundation (DFG) [SCHW 623/7-1]
This paper presents a novel generalization of Principal Component Analysis (PCA) that allows for decorrelation of data based on desired correlation patterns. By generalizing the projection onto a multi-dimensional subspace, this method can incorporate known statistical dependencies between input variables, thereby enhancing overall performance. Additionally, the paper discusses the role of this method in relation to other well-known time series analysis techniques.
Principal component analysis (PCA) and kernel PCA allow the decorrelation of data with respect to a basis that is found via variance maximization. However, these techniques are based on pointwise correlations. Especially in the context of time series analysis this is not optimal. We present a novel generalization of PCA that allows to imprint any desired correlation pattern. Thus the proposed method can be used to incorporate previously known statistical dependencies between input variables into the model which is increasing the overall performance. This is achieved by generalizing the projection onto the direction of maximum variance-as known from PCA-to a projection onto a multi-dimensional subspace. We focus on the use of cyclic correlation patterns, which is especially of interest in the domain of time series analysis. Beneath introducing the presented variation of PCA, we discuss the role of this method with respect to other well-known time series analysis techniques.
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