Date(s) - 27/10/2023
11 h 00 - 12 h 00
CNAM, accès 35, salle 35.1.53
Speaker: Fabien Girka (CentraleSupélec)
Title: Tensor Generalized Canonical Correlation Analysis
Abstract:Studying a given phenomenon under multiple views can reveal a more signiﬁcant part of the mechanisms at stake rather than considering each view separately. In order to design a study under such a paradigm, measurements are usually acquired through different modalities resulting in multimodal/multiblock/multi-source data. One statistical framework suited explicitly for the joint analysis of such multi-source data is Regularized Generalized Canonical Correlation Analysis (RGCCA). RGCCA extracts canonical vectors and components that summarize the different views and their interactions. This framework subsumes many well-known multivariate analysis methods as special cases.
However, RGCCA only deals with vector-valued blocks, disregarding their possible higher-order structures. This is the case for example with excitation-emission spectroscopy (mixtures x emission wavelengths x excitation wavelengths), or electroencephalography (participants x channels x times x frequencies) data. In this talk, we present Tensor GCCA (TGCCA), a new method for analyzing higher-order tensors with canonical vectors admitting an orthogonal rank-R CP decomposition. Moreover, two algorithms for TGCCA, based on whether a separable covariance structure is imposed or not, are presented along with convergence guarantees. The efficiency and usefulness of TGCCA are evaluated on simulated and real data and compared favorably to state-of-the-art approaches.
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