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- function som_iris_ex4()
- % SOM on IRIS for different final neighborhood sizes
- % (port of your Python code to MATLAB)
- rng(7); % reproducible random generator
- R = 12;
- C = 12; % bigger lattice
- M = R * C;
- iters = 4000; % more iterations for bigger maps
- eta0 = 0.12;
- sigma0 = max(R, C) / 2; % initial neighborhood (global ordering)
- sigma_final_list = [1 2 3]; % final sigmas to test
- % --- load and scale iris data (150x4, each feature to [0,1]) ---
- load fisheriris % variables: meas (150x4), species
- X = meas; % 150x4
- S = size(X, 1);
- Xmin = min(X, [], 1);
- Xmax = max(X, [], 1);
- X = (X - Xmin) ./ (Xmax - Xmin); % min-max scaling to [0,1]
- fprintf('loaded iris: %d samples, %d features\n', S, size(X, 2));
- fprintf('grid: %dx%d = %d neurons\n', R, C, M);
- fprintf('testing sigma_final: [');
- fprintf('%d ', sigma_final_list);
- fprintf(']\n');
- % grid coordinates (same idea as Python meshgrid + ravel)
- [gx, gy] = meshgrid(1:C, 1:R); % gx,gy: R x C
- grid2d = [gx(:), gy(:)]; % M x 2
- % --- figure for topographic error ---
- fig1 = figure('Color', 'w', 'Position', [100 100 800 500]);
- ax1 = axes('Parent', fig1);
- hold(ax1, 'on');
- xlabel(ax1, 'Iteration');
- ylabel(ax1, 'Topographic Error');
- title(ax1, sprintf('R=%d, C=%d — Effect of final \\sigma in {1,2,3}', R, C));
- grid(ax1, 'on');
- box(ax1, 'on');
- results = struct('sigma_final', {}, 'W', {}, 'topoErr', {}, 'topoErr_s', {});
- tau = iters; % single time constant for whole run
- for k = 1:numel(sigma_final_list)
- sigma_final = sigma_final_list(k);
- fprintf('\n=== Testing sigma_final = %d ===\n', sigma_final);
- % weights in [0,1], same scale as X
- W = rand(M, size(X, 2));
- topoErr = zeros(iters, 1);
- for t = 1:iters
- % --- time-dependent sigma and eta ---
- sigma_t = sigma_final + (sigma0 - sigma_final) * exp(-t / tau);
- eta_t = eta0 * exp(-t / tau);
- % --- random sample from X ---
- idx_sample = randi(S);
- x = X(idx_sample, :); % 1 x D
- % --- BMU1, BMU2 ---
- dists = sum((W - x).^2, 2); % M x 1
- [~, idx_sorted] = sort(dists, 'ascend');
- bmu1 = idx_sorted(1);
- bmu2 = idx_sorted(2);
- % --- Gaussian neighborhood around BMU1 in grid space ---
- dgrid2 = sum((grid2d - grid2d(bmu1, :)).^2, 2); % M x 1
- h = exp(-dgrid2 / (2 * sigma_t^2));
- h = h / max(h); % normalize
- % --- update weights ---
- % implicit expansion: h (M x 1) with (x - W) (M x D)
- W = W + eta_t * (h .* (x - W));
- % --- topographic error: 0 if BMU1,BMU2 are neighbors, else 1 ---
- topoErr(t) = ~are_neighbors(grid2d, bmu1, bmu2);
- if mod(t, 1000) == 0
- fprintf(' iteration %d/%d, sigma=%.3f, eta=%.5f\n', ...
- t, iters, sigma_t, eta_t);
- end
- end
- % smoothing TE with moving average (okno = 50)
- win = 50;
- topoErr_s = movmean(topoErr, win);
- results(k).sigma_final = sigma_final;
- results(k).W = W;
- results(k).topoErr = topoErr;
- results(k).topoErr_s = topoErr_s;
- % plot TE curve
- plot(ax1, 1:iters, topoErr_s, 'LineWidth', 1.5, ...
- 'DisplayName', sprintf('\\sigma_{final}=%d', sigma_final));
- end
- legend(ax1, 'Location', 'northeast');
- % --- PCA projection and final lattices ---
- fig2 = figure('Color', 'w', 'Position', [100 100 1200 350]);
- for k = 1:numel(results)
- W = results(k).W;
- % PCA to 2D
- [coeff, score] = pca(W); %#ok<ASGLU>
- W2 = score(:, 1:2); % M x 2
- WX = reshape(W2(:, 1), R, C);
- WY = reshape(W2(:, 2), R, C);
- ax = subplot(1, numel(results), k, 'Parent', fig2);
- hold(ax, 'on');
- axis(ax, 'equal');
- box(ax, 'on');
- title(ax, sprintf('\\sigma_{final}=%d', results(k).sigma_final));
- % horizontal lines (rows)
- for r = 1:R
- plot(ax, WX(r, :), WY(r, :), '-', 'LineWidth', 1.0);
- end
- % vertical lines (columns)
- for c = 1:C
- plot(ax, WX(:, c), WY(:, c), '-', 'LineWidth', 1.0);
- end
- % neuron markers
- plot(ax, W2(:, 1), W2(:, 2), 'ko', 'MarkerSize', 2, 'MarkerFaceColor', 'k');
- end
- sgtitle('Final Lattices Projected by PCA');
- % --- summary ---
- fprintf('\n== Summary (lower TE is better) ==\n');
- for k = 1:numel(results)
- topoErr = results(k).topoErr;
- last500 = topoErr(end-499:end);
- te_mean = mean(last500);
- fprintf('sigma_final=%d -> mean TE (last 500 iters): %.4f\n', ...
- results(k).sigma_final, te_mean);
- end
- end
- % =======================================================================
- % local helpers
- % =======================================================================
- function tf = are_neighbors(grid2d, i, j)
- % odleglosc Chebyshev = 1 (8-neighborhood)
- % grid2d: M x 2, i,j: indices of neurons
- di = abs(grid2d(i,1) - grid2d(j,1));
- dj = abs(grid2d(i,2) - grid2d(j,2));
- tf = max(di, dj) == 1; % true if neighbors
- end
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