DEMO for "Latent Variable Graphical Model Selection using Harmonic Analysis"
Won Hwa Kim*, Hyunwoo J. Kim*, Nagesh Adluru, Vikas Singh, Latent Variable Graphical Model Selection using Harmonic Analysis: Applications to the Human Connectome Project (HCP), Computer Vision and Pattern Recognition (CVPR) , June, 2016 (Spotlight). Both * are the joint first authors.
Github repository: http://github.com/MLman/lvgm-cvpr2016/
Github page: http://mlman.github.io/lvgm-cvpr2016/
The last update by Hyunwoo J Kim 2016/06/24 13:43:24 (CDT) (CST)
Contents
Data synthesis
clc;clear;close all; rng default N = 70; NO = 50; NC = 10; density = .5e-1; % a rough estimate of the amount of edges [theta,theta_GT]= random_sparse_network(NO, NC, N, density); % covariance matrix sigma = pinv(theta); sigma = (sigma+sigma')./2; mu = zeros(1,N); nsamples = 2000; r = mvnrnd(mu,sigma,nsamples); Xo = r(1:nsamples, 1:NO+NC); Cov = Xo'*Xo./nsamples; P = pinv(Cov);
Proposed method.
A0 = inv(Cov); invA0 = Cov; [V, D] = eig(Cov); lambda = diag(D); % kernel function kid = 1; kernel = mysgwt_func(kid); option.c1 =0.01; % step size option.gamma = 2; % sparsity parmeter option.s0 = .2; % intial point option.tol = 1e-5; % tolerance option.niter = 20000; % number of iteration option.kernel = kernel; % Normalized Kernel function and derivative. tic; [A, s_opt, ghistory, fhistory] = faster_solverK(V, D, option); toc; thetaO = theta(1:NO+NC, 1:NO+NC) ; AA = abs(A); PP = abs(P); low = 0.01; high = .5;
iter 1, f=2.284884 |grad|=0.000055, s=0.200001 iter 2, f=2.284894 |grad|=0.000055, s=0.200001 iter 3, f=2.284905 |grad|=0.000055, s=0.200002 iter 4, f=2.284916 |grad|=0.000055, s=0.200002 iter 5, f=2.284927 |grad|=0.000055, s=0.200003 iter 6, f=2.284938 |grad|=0.000055, s=0.200003 iter 7, f=2.284949 |grad|=0.000055, s=0.200004 iter 8, f=2.284960 |grad|=0.000055, s=0.200004 iter 9, f=2.284971 |grad|=0.000055, s=0.200005 iter 10, f=2.284982 |grad|=0.000055, s=0.200005 ... iter 5811, f=2.313952 |grad|=0.000010, s=0.201447 iter 5812, f=2.313954 |grad|=0.000010, s=0.201447 iter 5813, f=2.313956 |grad|=0.000010, s=0.201447 iter 5814, f=2.313958 |grad|=0.000010, s=0.201447 iter 5815, f=2.313960 |grad|=0.000010, s=0.201447 iter 5816, f=2.313962 |grad|=0.000010, s=0.201448 Elapsed time is 3.016885 seconds.
visualization
low = 0.1; high = 1; figure; set(gcf,'units','normalized','position',[0 0 1 1]); subplot(1,3,1);imagesc(abs(theta_GT(1:(NO+NC),1:(NO+NC))));colorbar;caxis([low high]) title('Ground Truth'); subplot(1,3,2);imagesc(abs(AA));colorbar;caxis([low high]) title('Ours'); subplot(1,3,3);imagesc(abs(P));colorbar;caxis([low high]) title('Raw precision matrix'); colormap hot
