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Statistics > Machine Learning

arXiv:2109.02230 (stat)
[Submitted on 6 Sep 2021 (v1), last revised 7 Sep 2021 (this version, v2)]

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

Authors:Zhiyuan Liu, Jörn Schulz, Mohsen Taheri, Martin Styner, James Damon, Stephen Pizer, J. S. Marron
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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).
Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as: arXiv:2109.02230 [stat.ML]
  (or arXiv:2109.02230v2 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.2109.02230

Submission history

From: Zhiyuan Liu [view email]
[v1] Mon, 6 Sep 2021 03:45:42 UTC (13,146 KB)
[v2] Tue, 7 Sep 2021 13:44:43 UTC (13,145 KB)
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