Conformity evaluation and L_1-norm principal-component analysis of tensor data

摘要

Multi-modal tensor data sets arise with increasing frequency in modern day scienti c and engineering appli-cations, 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 (L_2-norm) eigenvectordecompositions across tensor domains. The algorithms are not joint-tensor-domain optimal and exhibit the fa-miliar sensitivity to faulty/corrupted/missing measurements that characterizes all L_2-norm principal-componentanalysis methods.In this work, we present a robustified method to evaluate the conformity of tensor data entries with respect tothe whole accessible data set. Conformity evaluation is based on a continuously refined sequence of calculated L_1-norm tensor subspaces. The theoretical developments are illustrated in the context of a multisensor localizationapplication that indicates unprecedented estimation performance and resistance to intermittent disturbances.An electroencephalogram (EEG) data analysis experiment is also presented.