Resampling and averaging coordinates on data

TL;DR

This paper presents a robust method for computing intrinsic coordinates on point clouds by generating multiple embeddings, clustering to find representative ones, and averaging them to improve stability and accuracy, validated on synthetic and genomics data.

Contribution

The authors introduce a novel algorithm combining subsampling, clustering, and topological analysis to enhance the robustness of coordinate embeddings on point clouds.

Findings

Robustness to noise and outliers demonstrated on synthetic data.

Effective application to genomics data.

Improved stability of embeddings through averaging.

Abstract

We introduce algorithms for robustly computing intrinsic coordinates on point clouds. Our approach relies on generating many candidate coordinates by subsampling the data and varying hyperparameters of the embedding algorithm (e.g., manifold learning). We then identify a subset of representative embeddings by clustering the collection of candidate coordinates and using shape descriptors from topological data analysis. The final output is the embedding obtained as an average of the representative embeddings using generalized Procrustes analysis. We validate our algorithm on both synthetic data and experimental measurements from genomics, demonstrating robustness to noise and outliers.