136 lines
3.2 KiB
Matlab
136 lines
3.2 KiB
Matlab
function [ic_curves_pos, ic_coef_pos, Y_pos, h_Y_pos, pc_coef, pc_curves, pc_scores, mean_coef, W_pos, whitening_transform] = ...
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funcica(t, s, myfd_data, p, basis_curves, myfdPar, basis_inner_products);
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% funcica() - functional ICA
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% first call prelim_funcica
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% USAGE: [ic_curves_pos, ic_coef_pos, h_Y_pos] = funcica(t, s, data)
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data_coef = getcoef(myfd_data);
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pca_results = pca_fd(myfd_data, p, myfdPar);
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pc_coef = getcoef(pca_results.harmfd);
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%pc_curves = basis_curves * pc_coef;
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% pc_scores = pca_results.harmscr;% this doesn't work if lambda > 0
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% instead, we do:
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pc_scores = get_scores(data_coef, pc_coef', basis_inner_products);
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%mean_coef = getcoef(pca_results.meanfd);
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%figure(1); plot(t, pc_curves(:,1));
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%figure(2); plot(t, pc_curves(:,2));
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% p_small should be automatically selected according to some
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% reconstruction error threshold
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total_sum_var = 0;
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for i = 1:p
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total_sum_var = total_sum_var + sum(pc_scores(:,i).^2);
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end
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sum_var = 0;
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for p_small = 1:p
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sum_var = sum_var + sum(pc_scores(:,p_small).^2);
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disp(sprintf('i = %d, sum_var = %f', p_small, sum_var / total_sum_var));
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if sum_var / total_sum_var > 0.9
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break
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end
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end
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% p_small = 2;
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p_small
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sub_pc_coef = pc_coef(:,1:p_small);
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E = pc_scores(:,1:p_small)';
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%{
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inv_pc_coef = inv(pc_coef);
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calc_pc_scores = ...
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inv_pc_coef * (data_coef - ...
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repmat(getcoef(pca_results.meanfd), 1, ...
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size(data_coef, 2)));
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disp(sprintf('the difference is %f', maxall(calc_pc_scores' - pc_scores)));
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%}
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% check to ensure covariance matrix is orthogonal
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cov_E = cov(E');
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off_diag_max = maxall(cov_E - diag(diag(cov_E)));
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if off_diag_max > eps
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fprintf('covariance matrix is not orthogonal!\n');
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fprintf('off_diag_max = %f\n', off_diag_max);
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[V,D] = eig(cov_E);
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whitening_transform = V * (D^(-.5)) * V';
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else
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% the covariance matrix of E is already diagonal, but we need to
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% scale it so that cov(E') is white
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whitening_transform = diag(1./std(E'));
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end
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white_E = whitening_transform * E;
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[Y_pos, Y_neg, post_whitening_W_pos, post_whitening_W_neg] = ...
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find_opt_unmixing_matrix(white_E);
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%Y = Y_pos;
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W_pos = post_whitening_W_pos * whitening_transform;
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ic_coef_pos = (W_pos * sub_pc_coef')';
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%{
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W_neg = post_whitening_W_neg * whitening_transform;
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ic_coef_neg = (W_neg * sub_pc_coef')';
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W = W_pos;
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%save('YWE.mat', 'E', 'Y', 'W');
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h_E = zeros(p_small,1);
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h_white_E = zeros(size(h_E));
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h_Y_pos = zeros(size(h_E));
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h_Y_neg = zeros(size(h_E));
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for i = 1:p_small
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h_E(i) = get_vasicek_entropy_estimate(E(i,:));
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h_white_E(i) = get_vasicek_entropy_estimate(white_E(i,:));
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h_Y_pos(i) = get_vasicek_entropy_estimate(Y_pos(i,:));
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h_Y_neg(i) = get_vasicek_entropy_estimate(Y_neg(i,:));
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end
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%fprintf('joint entropy E = %f\n', sum(h_E));
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%fprintf('joint entropy white_E = %f\n', sum(h_white_E));
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fprintf('joint entropy Y = %f\n', sum(h_Y_pos));
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sub_pc_curves = basis_curves * sub_pc_coef;
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ic_curves_pos = basis_curves * ic_coef_pos;
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ic_curves_neg = basis_curves * ic_coef_neg;
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%}
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%{
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figure(1);
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clf;
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hold on;
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plot(s, 'b');
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plot(sub_pc_curves, 'r');
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plot(ic_curves_pos, 'g');
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plot(ic_curves_neg, 'c');
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%}
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ic_curves_pos = 0;
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Y_pos = 0;
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h_Y_pos = 0;
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pc_curves = 0;
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pc_scores = 0;
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mean_coef = 0;
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whitening_transform = 0;
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