Conformity evaluation and L1-norm principal-component analysis of tensor data

Abstract

Multi-modal tensor data sets arise with increasing frequency in modern day scientific and engineering applications, for example in biomedical sciences and autonomous engineered systems. Over the past twenty years, tensor-domain data analysis has been attempted primarily in the context of standard (<i>L</i>₂-norm) eigenvector decompositions across tensor domains. The algorithms are not joint-tensor-domain optimal and exhibit the familiar sensitivity to faulty/corrupted/missing measurements that characterizes all <i>L</i>₂-norm principal-component analysis methods. In this work, we present a robustified method to evaluate the conformity of tensor data entries with respect to the whole accessible data set. Conformity evaluation is based on a continuously refined sequence of calculated <i>L</i>₁- norm tensor subspaces. The theoretical developments are illustrated in the context of a multisensor localization application that indicates unprecedented estimation performance and resistance to intermittent disturbances. An electroencephalogram (EEG) data analysis experiment is also presented.