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ISFCClustering/Matlab_Scripts/2019_03_03_BCT/evaluate_generative_model.m
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evaluate_generative_model.m
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function [B,E,K] = evaluate_generative_model(A,Atgt,D,modeltype,modelvar,params)
% EVALUATE_GENERATIVE_MODEL Generation and evaluation of synthetic networks
%
% [B,E,K] = EVALUATE_GENERATIVE_MODEL(A,Atgt,D,m,modeltype,modelvar,params)
%
% Generates synthetic networks and evaluates their energy function (see
% below) using the models described in the study by Betzel et al (2016)
% in Neuroimage.
%
% Inputs:
% A, binary network of seed connections
% Atgt, binary network against which synthetic networks are
% compared
% D, Euclidean distance/fiber length matrix
% m, number of connections that should be present in
% final synthetic network
% modeltype, specifies the generative rule (see below)
% modelvar, specifies whether the generative rules are based on
% power-law or exponential relationship
% ({'powerlaw'}|{'exponential})
% params, either a vector (in the case of the geometric
% model) or a matrix (for all other models) of
% parameters at which the model should be evaluated.
%
% Outputs:
% B, m x number of networks matrix of connections
% E, energy for each synthetic network
% K, Kolmogorov-Smirnov statistics for each synthetic
% network.
%
% Full list of model types:
% (each model type realizes a different generative rule)
%
% 1. 'sptl' spatial model
% 2. 'neighbors' number of common neighbors
% 3. 'matching' matching index
% 4. 'clu-avg' average clustering coeff.
% 5. 'clu-min' minimum clustering coeff.
% 6. 'clu-max' maximum clustering coeff.
% 7. 'clu-diff' difference in clustering coeff.
% 8. 'clu-prod' product of clustering coeff.
% 9. 'deg-avg' average degree
% 10. 'deg-min' minimum degree
% 11. 'deg-max' maximum degree
% 12. 'deg-diff' difference in degree
% 13. 'deg-prod' product of degree
%
% Note: Energy is calculated in exactly the same way as in Betzel et
% al (2016). There are four components to the energy are KS statistics
% comparing degree, clustering coefficient, betweenness centrality, and
% edge length distributions. Energy is calculated as the maximum across
% all four statistics.
%
% Reference: Betzel et al (2016) Neuroimage 124:1054-64.
%
% Richard Betzel, Indiana University/University of Pennsylvania, 2015
m = nnz(Atgt)/2;
n = length(Atgt);
x = cell(4,1);
x{1} = sum(Atgt,2);
x{2} = clustering_coef_bu(Atgt);
x{3} = betweenness_bin(Atgt)';
x{4} = D(triu(Atgt,1) > 0);
B = generative_model(A,D,m,modeltype,modelvar,params);
nB = size(B,2);
K = zeros(nB,4);
for iB = 1:nB
b = zeros(n);
b(B(:,iB)) = 1;
b = b + b';
y = cell(4,1);
y{1} = sum(b,2);
y{2} = clustering_coef_bu(b);
y{3} = betweenness_bin(b)';
y{4} = D(triu(b,1) > 0);
for j = 1:4
K(iB,j) = fcn_ks(x{j},y{j});
end
end
E = max(K,[],2);
function kstat = fcn_ks(x1,x2)
binEdges = [-inf ; sort([x1;x2]) ; inf];
binCounts1 = histc (x1 , binEdges, 1);
binCounts2 = histc (x2 , binEdges, 1);
sumCounts1 = cumsum(binCounts1)./sum(binCounts1);
sumCounts2 = cumsum(binCounts2)./sum(binCounts2);
sampleCDF1 = sumCounts1(1:end-1);
sampleCDF2 = sumCounts2(1:end-1);
deltaCDF = abs(sampleCDF1 - sampleCDF2);
kstat = max(deltaCDF);
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