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).