The goal of this talk is to give an introduction to tensor decompositions for the analysis of multidimensional data. First, we recall some basic notions and operations on tensors. Then two tensor decompositions are presented: the Tucker decomposition (TD) and the Candecomp/Parafac decomposition (CPD). A particular focus is placed on the identifiability conditions of the CPD. Finally, various applications in biology are presented.
David Brie received the Ph.D. degree in 1992 and the Habilitation à Diriger des Recherches degree in 2000, both from Université de Lorraine, France. He is currently full professor at the Department of Telecommunications and Networking of the Institut Universitaire de Technologie, Université de Lorraine, France. He is editor-in-chief of the French journal “Traitement du Signal” since 2013 and will be co-general chair of the next IEEE CAMSAP 2019. His current research interests include vector-sensor-array processing, spectroscopy and hyperspectral image processing, non-negative matrix factorization, multidimensional signal processing, and tensor decompositions.
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