Non-Euclidean Analysis of Joint Variations in Multi-Object Shapes

TL;DR

This paper introduces a novel non-Euclidean statistical method for analyzing joint variations in multi-object shapes, specifically applied to classify brain structures related to autism spectrum disorder with improved robustness and interpretability.

Contribution

It combines non-Euclidean statistics with a non-parametric integrative analysis to decompose multi-block data into joint, individual, and residual structures, advancing shape analysis methods.

Findings

Effective classification of ASD-related brain structures.

Robust and interpretable joint variation patterns.

Validated on shape data distinguishing ASD from controls.

Abstract

This paper considers joint analysis of multiple functionally related structures in classification tasks. In particular, our method developed is driven by how functionally correlated brain structures vary together between autism and control groups. To do so, we devised a method based on a novel combination of (1) non-Euclidean statistics that can faithfully represent non-Euclidean data in Euclidean spaces and (2) a non-parametric integrative analysis method that can decompose multi-block Euclidean data into joint, individual, and residual structures. We find that the resulting joint structure is effective, robust, and interpretable in recognizing the underlying patterns of the joint variation of multi-block non-Euclidean data. We verified the method in classifying the structural shape data collected from cases that developed and did not develop into Autistic Spectrum Disorder (ASD).