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

arXiv: https://arxiv.org/abs/2109.02230 · HTML: https://mlsanity.com/paper/2109.02230/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 56 references that are in the map.
- First posted on arXiv 6 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [geomstats: a Python Package for Riemannian Geometry in Machine Learning](https://mlsanity.com/paper/1805.08308/) (2018)
- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Computational Anatomy for Multi-Organ Analysis in Medical Imaging: A Review](https://mlsanity.com/paper/1812.08577/) (2018)
- [Generalized Canonical Correlation Analysis for Classification](https://mlsanity.com/paper/1304.7981/) (2013)
- [Principal nested shape space analysis of molecular dynamics data](https://mlsanity.com/paper/1903.09445/) (2019)
- [Direction-Projection-Permutation for High Dimensional Hypothesis Tests](https://mlsanity.com/paper/1304.0796/) (2013)

## Abstract (arXiv)

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).