Abstract
Many examples of multi-way or tensor-valued data, such as in climate studies, neuroimaging, chemometrics, and hyperspectral imaging, are structured meaning that variables are associated with locations. Tensor decompositions, or higher-order principal components analysis (HOPCA), are a classical method for dimension reduction and pattern recognition for this multi-way data. In this paper, we introduce novel methods for Functional HOPCA that decompose the tensor data into components that are smooth with respect to the known data structure. Through numerical experiments we demonstrate the comparative advantages of our methods for smooth signal recovery from multi-way data.
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