A Guide to the Tucker Tensor Decomposition for Data Mining: Exploratory Analysis, Clustering and Classification.

Tensors are powerful multi-dimensional mathematical objects, that easily embed various data models such as relational, graph or time series. Furthermore, tensor decomposition operators are of great utility to reveal hidden patterns and complex relationships in data. Among these decompositions, the Tucker decomposition allows to factorize a tensor into a smaller core tensor and a set of factor matrices. In this article, we propose to study the capabilities of the Tucker decomposition when it is used in data mining techniques such as exploratory analysis, clustering and classification of data. We apply these different techniques on practical examples using several datasets having a ground truth. It is a preliminary work to add the Tucker decomposition to the Tensor Data Model, a model aiming at making tensors data-centric, and at optimizing operators in order to enable the manipulation of large tensors.