UCD4IDS / MultiscaleSimplexSignalTransforms.jl

Signal processing on simplicial complexes, using basis dictionaries formed via hierarchical partitioning

MultiscaleSimplexSignalTransforms.jl

COPYRIGHT

Copyright 2023 The Regents of the University of California

Implemented by Eugene Shvarts

SETUP

MultiscaleSimplexSignalTransforms is not yet in the General registry, so either add via the Tetrapods registry

] registry add https://github.com/UCD4IDS/TetrapodsRegistry
] add MultiscaleSimplexSignalTransforms

or add manually by URL

] add https://github.com/UCD4IDS/MultiscaleSimplexSignalTransforms.jl

USAGE

• At top level are the graph basis dictionaries kGHWT and kHGLET, implementing the abstract type MSST, or MultiscaleSimplicialTransform.
• These dictionaries themselves rely on a method of partitioning simplicial complexes, which implements the abstract type SCPartition. The implementations are SubmatrixPartition (the default), and FullPartition.
• Each possesses an array of configuration options, Representation, SubRepresentation, Basis, PartitionInput, PartitionMethod, EigenMethod, which are extensible and allow for configurable, stackable, and repeatable experiments.
• The fundamental adjacency data structures are ZeroRegion and KRegion, which implement the abstract type Region, and the fundamental spectral representation for these is k_laplacian.
• The structure of a simplicial complex is stored in a SimplexTree, and generally speaking, when a function takes a SimplexTree, it will happily accept some g::AbstractGraph instead by passing in cliquecomplex(g, k) for an appropriate k.

If you have some g::AbstractGraph, then the easiest way to get started with analyzing, say, signals on the triangles of g with all defaults set is to construct the basis dictionary basis = kGHWT(KRegion(g, 2)). Then you can investigate the dictionary vector at level j, location k, tag l with ordinary indexing (i.e., basis[j,k,l]), and you can obtain a dictionary of expansion coefficients for some triangle signal s with analyze(basis, s).