Beyond kNN: Adaptive, Sparse Neighborhood Graphs via Optimal Transport
This work addresses a fundamental issue in graph-based machine learning for researchers and practitioners, offering a more robust alternative to kNN graphs with fewer tuning parameters.
The paper tackles the problem of constructing neighborhood graphs that adapt to varying data density and noise levels, proposing a method based on quadratically regularized optimal transport that outperforms fixed-k nearest neighbor graphs in unsupervised and semi-supervised learning tasks.
Nearest neighbour graphs are widely used to capture the geometry or topology of a dataset. One of the most common strategies to construct such a graph is based on selecting a fixed number k of nearest neighbours (kNN) for each point. However, the kNN heuristic may become inappropriate when sampling density or noise level varies across datasets. Strategies that try to get around this typically introduce additional parameters that need to be tuned. We propose a simple approach to construct an adaptive neighbourhood graph from a single parameter, based on quadratically regularised optimal transport. Our numerical experiments show that graphs constructed in this manner perform favourably in unsupervised and semi-supervised learning applications.