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