Dynamic Multivariate Functional Data Modeling via Sparse Subspace Learning
This addresses the problem of analyzing high-dimensional, correlated functional data for researchers in fields like statistics or machine learning, but it appears incremental as it builds on existing subspace and sparse regression techniques.
The paper tackles modeling multivariate functional data with complex, time-varying cross-correlations by proposing a dynamic subspace learning method that groups functions into subspaces and uses sparse regression with regularization for temporal changes. Numerical studies show the method is efficient and applicable, though no concrete performance numbers are provided.
Multivariate functional data from a complex system are naturally high-dimensional and have 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 paper presents a dynamic subspace learning method for multivariate functional data modeling. In particular, we consider 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 (FISTA), and the features of every subspace can be extracted using the smooth multi-channel functional PCA. Numerical studies together with case studies demonstrate the efficiency and applicability of the proposed methodology.