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Dynamic Multivariate Functional Data Modeling via Sparse Subspace Learning

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posted on 2021-09-15, 18:41 authored by Chen Zhang, Hao Yan, Seungho Lee, Jianjun Shi

Multivariate functional data from a complex system are naturally high-dimensional and have a complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar features, while some others may have almost no cross-correlations with quite diverse features; and (2) the cross-correlation structure may also change over time due to the system evolution. With this regard, this article presents a dynamic subspace learning method for multivariate functional data modeling. In particular, we consider that different functions come from different subspaces, and only functions of the same subspace have cross-correlations with each other. The subspaces can be automatically formulated and learned by reformatting the problem as a sparse regression. By allowing but regularizing the regression change over time, we can describe the cross-correlation dynamics. The model can be efficiently estimated by the fast iterative shrinkage-thresholding algorithm, and the features of each subspace can be extracted using the smooth multi-channel functional principal component analysis. Some theoretical properties of the model are presented. Numerical studies, together with case studies, demonstrate the efficiency and applicability of the proposed methodology.


This work was partially supported by NSFC 71901131, NSFC 71932006, NSF CCF 1740776, NSF DMS 1830363, NSF CMMI 1922739, and Tsinghua University Intelligent Logistics and Supply Chain Research Center grant THUCSL20182911756-001.