A Sparse Functional SVD Method for Clustering Functional Data

Music City Center 

This work investigates the Sparse Multivariate Functional SVD (SMFSVD) method for clustering multivariate functional data. SMFSVD aims to construct a sparse, low-rank structured representation of multivariate functional data, serving as a novel exploratory tool for identifying interpretable clusters of subjects and functional variables. Within the SMFSVD framework, we introduce two approaches: the bicluster approach and the tricluster approach.

In the bicluster approach, adaptive Lasso and adaptive group Lasso penalties are applied to achieve sparsity in both subjects and functional variables. The tricluster approach extends this framework by introducing an additional adaptive Lasso penalty to select meaningful subregions within each functional variable, thereby capturing finer-grained structures.

Furthermore, recognizing that real-world data are often sparsely and irregularly sampled-conditions that traditional functional data analysis techniques struggle to handle-we incorporate a best- approximation computation within the SMFSVD framework. This enhancement ensures robust and effective performance when analyzing sparse and irregular functional data.

functional data analysis

sparse group lasso

functional SVD

iterative shrinkage-thresholding algorithm 

Section on Statistical Learning and Data Science