Functional Subspace Clustering with Application to Time Series
Mohammad Taha Bahadori, David C. Kale, Yingying Fan, Yan Liu · 2015
Functional data, where samples are random func-tions, are increasingly common and important in a variety of applications, such as health care and traffic analysis. They are naturally high dimen-sional and lie along complex manifolds. These properties warrant use of the subspace assump-tion, but most state-of-the-art subspace learning algorithms are limited to linear or other simple settings. To address these challenges, we pro-pose a new framework called Functional Sub-space Clustering (FSC). FSC assumes that func-tional samples lie in deformed linear subspaces and formulates the subspace learning problem as a sparse regression over operators. The result-ing problem can be efficiently solved via greedy variable selection, given access to a fast defor-mation oracle. We provide theoretical guaran-tees for FSC and show how it can be applied to time series with warped alignments. Experimen-tal results on both synthetic data and real clini-cal time series show that FSC outperforms both standard time series clustering and state-of-the-art subspace clustering. 1.