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

2021/09/06 by Zhiyuan Liu, Liu, Zhiyuan, Jörn Schulz +11
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Computer and information sciences #Gene expression and cancer classification #Genetic Mapping and Diversity in Plants and Animals #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.2109.02230

openalex publication_date 2021/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

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