axsk / pccaplus.jl

Julia implementation of PCCA+

PCCAPlus

A KISS style implementation of PCCA+ (Robust Perron Cluster Analysis) [1,2] with support for non-reversible systems [3]. For a similar python implementation see also the cmdtools package.

Basic usage

using PCCAPlus

P=rand(10,10)
P = P ./ sum(P, dims=2) # row stochastic matrix

# basic PCCA+ clustering with 2 clusters (using no weighting and the ISA initial guess only)
chi = pcca(P, 2)

using KrylovKit
using SparseArrays
P = sprand(100,100, 0.1)
P = P ./ sum(P, dims=2) # sparse row stochastic matrix

# solve the PCCA+ problem weighted with the stationary density 
# and optimize for crispness, using the KrylovKit.jl eigensolver
chi = pcca(P, 2; pi=:stationary, optimize=true, solver=KrylovSolver())

For sparse matrix support, add either the ArnoldiMethod.jl or KrylovKit.jl and pass the corresponding ArnoldiSolver() or KrylovSolver() as a solver.

References

1. 2006, M. Weber: Meshless Methods in Conformation Dynamics
2. 2013, S. Röblitz, M. Weber: Fuzzy Spectral Clustering by PCCA+
3. 2018, K. Fackeldey, A. Sikorski, M. Weber: Spectral Clustering for Non-Reversible Markov Chains

pccaplus.jl's Issues

Stationary density does not use sparse solvers

Should be fixable by making stationarydensity call schurvecs

innersimplexalgorithm should not feasiblize

check how marcus defined it

Write some documentation

• Make autodoc generation work
• Write a few lines about the design- and algorithmic choices

Write proper tests

The current tests look quite ugly.

• Test the different solver types
• Test dense and sparse matrices
• Test P and Q
• Test for consistency between the above
• Test for the PCCA+ guarantees (positivity, partition of unity, subspace)

Consistent treatment of complex conjugate subspace cutting

How do we want to handle this?

• error
• warn
• autofix

Make the schur solver dependencies optional

Should be easy using either Requires.jl or the new Pkg extensions.

also return the transformation A

pcca should also return the transformation A (and the eigenvectors? eigenvalues?)
For this makeprobabilistic needs to return A.

I think the latter should be renamed to basistransform and return only A.

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Add barycentric projection

I already have the code in https://github.com/axsk/InnocentMoTMo
Would be nice to have it here

Sparse Matrices are not well supported

I had to fix the method signatures, and I am not sure if all Sparse Eigensolver modules are really working.
Also one of the bigger ones (IterativeSolvers?) is missing.

Check the state of these

Find a good package name

• PCCA does not adhere to the Julia rules
• DynamicClustering
• MarkovClustering
• ProbabilisticSpectralClustering
• MarkovProjection

Publish the package

Once the other issues are fixed this should be finally published