Sparse tensor dimensionality reduction with application to clustering of functional connectivity

Gaëtan Frusque 1 Julien Jung 2 Pierre Borgnat 3 Paulo Gonçalves 1
1 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : Functional connectivity (FC) is a graph-like data structure commonly used by neuroscientists to study the dynamic behaviour of the brain activity. However , these analyses rapidly become complex and time-consuming, as the number of connectivity components to be studied is quadratic with the number of electrodes. In this work, we address the problem of clustering FC into relevant ensembles of simultaneously activated components that reveal characteristic patterns of the epileptic seizures of a given patient. While k−means is certainly the most popular method for data clustering, it is known to perform badly on large dimensional data sets, and to be highly sensitive to noise. To overcome the co-called curse of dimensionality, we propose a new tensor decomposition to reduce the size of the data set formed by FC time series recorded for several seizures, before applying k-means. The contribution of this paper is twofold: First, we derive a method that we compare to the state of the art, emphasizing one variant that imposes sparsity constraints. Second, we conduct a real case study, applying the proposed sparse tensor decomposition to epileptic data in order to infer the functional connectivity graph dynamics corresponding to the different stages of an epileptic seizure.
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Gaëtan Frusque, Julien Jung, Pierre Borgnat, Paulo Gonçalves. Sparse tensor dimensionality reduction with application to clustering of functional connectivity. 2019. ⟨hal-02154903⟩

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