Learning Locally Adaptive Metrics that Enhance Structural Representation with $\texttt{LAMINAR}$

TL;DR

LAMINAR is an unsupervised learning pipeline that creates a locally adaptive, density-based metric to better capture the underlying structure of complex data sets without prior metric specification.

Contribution

It introduces a novel method using normalising flows and inverse sampling to define a Riemannian manifold, enabling more informative structural representations in data.

Findings

LAMINAR outperforms Euclidean metrics on structured data.

It effectively captures complex data structures.

The method is unsupervised and does not require predefined metrics.

Abstract

We present $\texttt{LAMINAR}$, a novel unsupervised machine learning pipeline designed to enhance the representation of structure within data via producing a more-informative distance metric. Analysis methods in the physical sciences often rely on standard metrics to define geometric relationships in data, which may fail to capture the underlying structure of complex data sets. $\texttt{LAMINAR}$ addresses this by using a continuous-normalising-flow and inverse-transform-sampling to define a Riemannian manifold in the data space without the need for the user to specify a metric over the data a-priori. The result is a locally-adaptive-metric that produces structurally-informative density-based distances. We demonstrate the utility of $\texttt{LAMINAR}$ by comparing its output to the Euclidean metric for structured data sets.