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CDalgs - Community detection algorithms

Overview

CDalgs is a framework for communities detection on graphs. The library implements the four following approaches:

  1. Louvain method
  2. CDEP
  3. ModMax method which performs direct maximization of modularity (exponential problem).
  4. NCClustering greedy method to finding near clique (dense) subgraphs.

Furthermore there are implemented two methods to create similarity graphs:

  1. Method based on Pearson correlation with usage of LinRegOutliers package (Satman et al., (2021). LinRegOutliers: A Julia package for detecting outliers in linear regression. Journal of Open Source Software, 6(57), 2892, https://doi.org/10.21105/joss.02892).
  2. Method based on Dynamic time warping algorithm.

Example of usage

Introduction

The simple example of detection of communities on MNIST dataset is presented.

Codes & commands

The following commands are in also in exmaples folder.

Load libraries.

julia> using CDalgs
       using MLDatasets
       using LinearAlgebra, StatsBase
       using Graphs, SimpleWeightedGraphs
       using Plots

Load dataset & define clustering and graph methods.

julia> dataset = MNIST(:train).features
       clustering = g -> louvain_clustering(g) # modmax_clustering(g) cdep_clustering(g) nc_clustering(g)
       create_graph = d -> correlation_graph(d)

Prepare data and correlation graph.

julia> n = size(dataset)[1]
julia> data_vec = collect(hcat(
julia> map(x -> vec(x), eachslice(dataset, dims=3))...)')
julia> g = create_graph(data_vec)

Perform community detection (graph clustering).

julia> clusters = clustering(g)
julia> clusters_matrix = transpose(reshape(clusters, (n, n)))

Create color map.

julia> clusters_matrix_colors = fill(RGB(0, 0, 0), (n, n))
julia> colors_vec = map(x->RGB(rand(1)[1], rand(1)[1], rand(1)[1]), 1:length(unique(clusters)))
julia> for i::Int64=1:n for j::Int64=1:n
          clusters_matrix_colors[i, j] = colors_vec[clusters_matrix[i, j]]
       end end
julia> gr(size=(400, 400), html_output_format=:png)
       plot(clusters_matrix_colors)

Display clustering of different methods.

julia> function clusterdataset(g::SimpleWeightedGraph, clustering::Function)
          n::Int64 = sqrt(length(vertices(g)))
          clusters::Vector{Int64} = clustering(g)
          clusters_matrix::Matrix{Int64} = transpose(reshape(clusters, (n, n)))
          clusters_matrix_colors = fill(RGB(0, 0, 0), (n, n))
          colors_vec = map(x->RGB(rand(1)[1], rand(1)[1], rand(1)[1]), 1:length(unique(clusters)))
          for i::Int64=1:n for j::Int64=1:n
             clusters_matrix_colors[i, j] = colors_vec[clusters_matrix[i, j]]
          end end
          clusters_matrix, plot(clusters_matrix_colors, title=String(Symbol(clustering)))
       end
julia> imgs = []
julia> append!(imgs, [clusterdataset(g, louvain_clustering)[2]])
julia> nc_clustering_95(g) = nc_clustering(g, α=.95)
julia> nc_clustering_99(g) = nc_clustering(g, α=.99)
julia> append!(imgs, [clusterdataset(g, nc_clustering_95)[2]])
julia> append!(imgs, [clusterdataset(g, nc_clustering_99)[2]])

Plot heatmaps.

julia> gr(size=(700, 700), html_output_format=:png)
       plot(imgs..., layout=(2, 2))

License

GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007