Quiver Laplacians and Feature Selection

Code produced for the paper Quiver Laplacians and Feature Selection¹.

Use

topology.py contains classes for constructing simplicial complexes and covers. The Cover class takes as input a numpy array of data points (rows are data points), and an OrderedSet of frozensets of indices of the rows of the data points. The Nerve class constructs a simplicial complex from a Cover object.

harmonic.py contains classes to compute compatible features. OriginalFeatureSelectionProblem and DualFeatureSelectionProblem correspond to the constructs in Theorem 7.1 and Theorem 7.2 of ¹ respectively. They both take: a Simplicial Complex and a dictionary of points associated to each simplex; a kernel. OriginalFeatureSelectionProblem also takes a particular simplex to reduce the problem onto.

Footnotes

1. Quiver Laplacians and Feature Selection, Otto Sumray, Heather A. Harrington, Vidit Nanda, 2024. ↩ ↩²