Title :
Multi-way functional principal components analysis
Author :
Allen, Genevera I.
Author_Institution :
Dept. of Stat. & Electr., Rice Univ., Houston, TX, USA
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.
Keywords :
functional analysis; hyperspectral imaging; pattern recognition; principal component analysis; signal processing; tensors; chemometrics; climate studies; dimension reduction; higher-order principal components analysis; hyperspectral imaging; multiway functional principal components analysis; neuroimaging; numerical experiments; pattern recognition; smooth signal recovery; tensor decompositions; tensor-valued data; Data models; Mathematical model; Matrix decomposition; Principal component analysis; Smoothing methods; Tensile stress; Vectors; CP decomposition; Tucker decomposition; functional data analysis; higher-order PCA; tensors;
Conference_Titel :
Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013 IEEE 5th International Workshop on
Conference_Location :
St. Martin
Print_ISBN :
978-1-4673-3144-9
DOI :
10.1109/CAMSAP.2013.6714047
