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Environmental Multiway Data Mining

Abstract : Among commonly used data mining techniques, few are those which are able to take advantage of the multiway structure of data in the form of a multiway array. In contrast, tensor decomposition techniques specifically look intricate processes underlying the data, where each of these processes can be used to describe all ways of the data array. The work reported in the following pages aims at incorporating various external knowledge into the tensor canonical polyadic decomposition, which is usually understood as a blind model. The first two chapters of this manuscript introduce tensor decomposition techniques making use respectively of a mathematical and application framework. In the third chapter, the many faces of constrained decompositions are explored, including a unifying framework for constrained decomposition, some decomposition algorithms, compression and dictionary-based tensor decomposition. The fourth chapter discusses the inclusion of subject variability modeling when multiple arrays of data are available stemming from one or multiple subjects sharing similarities. State of the art techniques are studied and expressed as particular cases of a more general flexible coupling model later introduced. The chapter ends on a discussion on dimensionality reduction when subject variability is involved, as well a some open problems.
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Submitted on : Wednesday, November 23, 2016 - 12:00:08 PM
Last modification on : Wednesday, August 25, 2021 - 4:10:17 PM


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  • HAL Id : tel-01371777, version 3



Jérémy E. Cohen. Environmental Multiway Data Mining. Signal and Image processing. Université Grenoble Alpes, 2016. English. ⟨NNT : 2016GREAT054⟩. ⟨tel-01371777v3⟩



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