FuncICA for Time Series Pattern Discovery

We introduce FuncICA, a new independent component analysis method for pattern discovery in inherently functional data, such as time series data. We show how applying the dual of temporal ICA to temporal data, and likewise applying the dual of spatiotemporal ICA to spatiotemporal data, enables independent component regularization not afforded by the primal forms applied to their original domains. We call this family of regularized dual ICA algorithms FuncICA. FuncICA can be considered an analog to functional principal component analysis, where instead of extracting components to minimize L2 reconstruction error, we maximize independence of the components over the functional observations. In this work, we develop an algorithm for extracting independent component curves, derive a method for optimally smoothing the curves, and validate this method on both synthetic and real datasets. Results for synthetic, gene expression, and electroencephalographic event-related potential data indicate that FuncICA can recover well-known scientific phenomena and improve classification accuracy, highlighting its utility for unsupervised learning in continuous data. We conclude this work with a forward-looking, novel framework for fMRI data analysis by making use of the functional dual of spatiotemporal ICA.