Learning Locally Adaptive Metrics that Enhance Structural Representation with LAMINAR

Christian Kleiber, William H. Oliver, Tobias Buck

Abstract:

We present 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. 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
LAMINAR by comparing its output to the Euclidean metric for structured data sets.