Modified PCA analysis script to run on simulated data.
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%% STEP 1: Generate synthetic image dataset
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%% STEP 1: Extract Images
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clear; close all; clc;
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% Parameters
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numImages = 50; % number of images in the dataset
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imgSize = [50 50]; % image dimensions
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baseDir = 'D:/Results - Numerics/Data_Full3D/PhaseTransition/DTS/Point2';
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JobNumber = 0;
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runFolder = sprintf('Run_%03d', JobNumber);
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savefileName = 'DropletsToStripes'; % Output file name
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datafileName = './DropletsToStripes.mat';
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reverseOrder = false; % Set this to true to reverse the theta ordering
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% Preallocate array
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images = zeros([imgSize, numImages]);
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TitleString = 'Droplets To Stripes';
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% Generate base features: a horizontal stripe + diagonal gradient
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[x, y] = meshgrid(1:imgSize(2), 1:imgSize(1));
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%%
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baseDir = 'D:/Results - Numerics/Data_Full3D/PhaseTransition/STD/Point2';
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JobNumber = 0;
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runFolder = sprintf('Run_%03d', JobNumber);
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savefileName = 'StripesToDroplets'; % Output file name
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datafileName = './StripesToDroplets.mat';
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reverseOrder = true; % Set this to true to reverse the theta ordering
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for k = 1:numImages
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% Feature 1: horizontal stripe
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stripe = double(y > 20 & y < 30);
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% Feature 2: diagonal gradient
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gradient = (x + y) / max(x(:) + y(:));
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% Random variation in stripe intensity
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stripeIntensity = 0.8 + 0.4*randn(1);
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% Random rotation of gradient strength
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gradIntensity = 0.5 + 0.2*randn(1);
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% Combine features + Gaussian noise
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images(:,:,k) = stripeIntensity*stripe + gradIntensity*gradient + 0.1*randn(imgSize);
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TitleString = 'Stripes To Droplets';
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%%
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folderList = dir(baseDir);
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isValid = [folderList.isdir] & ~ismember({folderList.name}, {'.', '..'});
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folderNames = {folderList(isValid).name};
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nimgs = numel(folderNames);
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% Extract theta values from folder names
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PolarAngleVals = zeros(1, nimgs);
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for k = 1:nimgs
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tokens = regexp(folderNames{k}, 'theta_(\d{3})', 'tokens');
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if isempty(tokens)
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warning('No theta found in folder name: %s', folderNames{k});
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PolarAngleVals(k) = NaN;
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else
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PolarAngleVals(k) = str2double(tokens{1}{1});
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end
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end
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%% STEP 2: Visualize some sample images
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figure;
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for i = 1:6
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subplot(2,3,i);
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imagesc(images(:,:,i));
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axis image off; colormap gray;
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title(sprintf('Image %d', i));
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% Choose sort direction
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sortDirection = 'ascend';
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if reverseOrder
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sortDirection = 'descend';
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end
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sgtitle('Sample Synthetic Images');
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% Sort folderNames based on polar angle
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[~, sortIdx] = sort(PolarAngleVals, sortDirection);
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folderNames = folderNames(sortIdx);
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PolarAngleVals = PolarAngleVals(sortIdx); % Optional: if you still want sorted list
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imgs = cell(1, nimgs);
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alphas = zeros(1, nimgs);
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for k = 1:nimgs
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folderName = folderNames{k};
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SaveDirectory = fullfile(baseDir, folderName, runFolder);
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% Extract alpha (theta) again from folder name
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tokens = regexp(folderName, 'theta_(\d{3})', 'tokens');
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alpha_val = str2double(tokens{1}{1});
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alphas(k) = alpha_val;
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matPath = fullfile(SaveDirectory, 'psi_gs.mat');
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if ~isfile(matPath)
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warning('Missing psi_gs.mat in %s', SaveDirectory);
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continue;
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end
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try
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Data = load(matPath, 'psi', 'Params', 'Transf', 'Observ');
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catch ME
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warning('Failed to load %s: %s', matPath, ME.message);
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continue;
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end
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Params = Data.Params;
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Transf = Data.Transf;
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Observ = Data.Observ;
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psi = Data.psi;
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if isgpuarray(psi)
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psi = gather(psi);
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end
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if isgpuarray(Observ.residual)
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Observ.residual = gather(Observ.residual);
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end
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% Axes and projection
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z = Transf.z * Params.l0 * 1e6;
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dz = z(2)-z(1);
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if k == 1
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x = Transf.x * Params.l0 * 1e6;
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y = Transf.y * Params.l0 * 1e6;
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% Calculate frequency increment (frequency axes)
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Nx = length(x); % grid size along X
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Ny = length(y); % grid size along Y
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dx = mean(diff(x)); % real space increment in the X direction (in micrometers)
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dy = mean(diff(y)); % real space increment in the Y direction (in micrometers)
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dvx = 1 / (Nx * dx); % reciprocal space increment in the X direction (in micrometers^-1)
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dvy = 1 / (Ny * dy); % reciprocal space increment in the Y direction (in micrometers^-1)
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% Create the frequency axes
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vx = (-Nx/2:Nx/2-1) * dvx; % Frequency axis in X (micrometers^-1)
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vy = (-Ny/2:Ny/2-1) * dvy; % Frequency axis in Y (micrometers^-1)
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% Create the Wavenumber axes
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kx_full = 2*pi*vx; % Wavenumber axis in X
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ky_full = 2*pi*vy; % Wavenumber axis in Y
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end
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n = abs(psi).^2;
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nxy = squeeze(trapz(n * dz, 3));
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imgs{k} = nxy;
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end
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%% STEP 2: Visualize images
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figure(1);
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set(gcf,'Position',[100 100 950 750])
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font = 'Bahnschrift';
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t = tiledlayout(4, 3, 'TileSpacing', 'compact', 'Padding', 'compact'); % 1x4 grid
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for i = 1:nimgs
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ax1 = nexttile;
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imagesc(x, y, imgs{i}')
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% Define normalized positions (relative to axis limits)
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x_offset = 0.025; % 5% offset from the edges
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y_offset = 0.025; % 5% offset from the edges
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axis square;
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hcb = colorbar;
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colormap(ax1, Colormaps.plasma());
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set(gca, 'FontSize', 14); % For tick labels only
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hL = ylabel(hcb, 'Optical Density');
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set(hL,'Rotation',-90);
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set(gca,'YDir','normal')
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% set(gca, 'YTick', linspace(y_min, y_max, 5)); % Define y ticks
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% set(gca, 'YTickLabel', flip(linspace(y_min, y_max, 5))); % Flip only the labels
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hXLabel = xlabel('x (µm)', 'Interpreter', 'tex');
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hYLabel = ylabel('y (µm)', 'Interpreter', 'tex');
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hTitle = title('Density', 'Interpreter', 'tex');
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set([hXLabel, hYLabel, hL], 'FontName', font)
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set([hXLabel, hYLabel, hL], 'FontSize', 14)
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set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold'); % Set font and size for title
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end
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sgtitle('Ground States');
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%% STEP 3: Reshape images into a 2D data matrix
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% Each image is a row, each pixel is a column
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X = reshape(images, [], numImages)'; % size: [numImages × numPixels]
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% Each image will be a row vector, so size(X) = [numImages × numPixels]
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% First, convert cell array to numeric 3D array
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allImgs = cat(3, imgs{:}); % size: [Nx × Ny × numImages]
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% Store image size for reshaping later
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imgSize = size(allImgs(:,:,1)); % [Nx, Ny]
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% Reshape into 2D matrix for PCA
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X = reshape(allImgs, [], nimgs)'; % [numImages × (Nx*Ny)]
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%% STEP 4: Perform PCA
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[coeff, score, latent, tsquared, explained] = pca(X);
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% coeff : principal component directions (eigenvectors) in pixel space
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% score : projection of each image onto the principal components
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% latent : eigenvalues (variance captured by each PC)
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% coeff : principal component directions (eigenvectors) in pixel space
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% score : projection of each image onto the principal components
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% latent : eigenvalues (variance captured by each PC)
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% explained : percentage variance explained by each PC
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%% STEP 5: Visualize variance explained
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figure;
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pareto(explained);
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xlabel('Principal Component');
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ylabel('Variance Explained (%)');
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title('PCA Variance Explained');
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%% Visualize cumulative variance
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figure(2);
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set(gcf,'Position',[100 100 950 750])
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cumVar = cumsum(explained);
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plot(cumVar, 'o-', 'LineWidth', 1.5);
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yline(95, '--r', '95% threshold');
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xlabel('Number of Principal Components');
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ylabel('Cumulative Variance (%)');
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title('Minimum number of PCA components required for a basis');
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grid on;
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%% STEP 6: View first few principal components as "eigenimages"
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numPCsToShow = 4;
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figure;
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%% Visualize first few principal components
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numPCsToShow = 7;
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figure(3);
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set(gcf,'Position',[100 100 950 750])
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t = tiledlayout(3, 3, 'TileSpacing', 'compact', 'Padding', 'compact'); % 1x4 grid
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for i = 1:numPCsToShow
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pcImage = reshape(coeff(:,i), imgSize); % reshape back to image form
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subplot(1,numPCsToShow,i);
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imagesc(pcImage);
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axis image off; colormap gray;
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title(sprintf('PC %d', i));
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nexttile;
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imagesc(pcImage)
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axis image off; colormap(Colormaps.coolwarm());
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title(sprintf('PC %d (%.1f%%)', i, explained(i)));
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end
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sgtitle('First Principal Components (Eigenimages)');
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%% STEP 7: View projection (scores) in PC space
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figure;
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scatter(score(:,1), score(:,2), 50, 'filled');
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xlabel('PC 1 Score');
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ylabel('PC 2 Score');
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title('Images in Principal Component Space');
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grid on;
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%% Visualize evolution of PCA scores
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figure(4);
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set(gcf,'Position',[100 100 950 750])
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plot(alphas, score(:,1), '-o', 'LineWidth', 1.5, 'DisplayName', 'PC1 Score');
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hold on;
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plot(alphas, score(:,2), '-o', 'LineWidth', 1.5, 'DisplayName', 'PC2 Score');
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% plot(alphas, score(:,3), '-o', 'LineWidth', 1.5, 'DisplayName', 'PC3 Score');
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% plot(alphas, score(:,4), '-o', 'LineWidth', 1.5, 'DisplayName', 'PC4 Score');
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% plot(alphas, score(:,5), '-o', 'LineWidth', 1.5, 'DisplayName', 'PC5 Score');
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% plot(alphas, score(:,6), '-o', 'LineWidth', 1.5, 'DisplayName', 'PC6 Score');
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% plot(alphas, score(:,7), '-o', 'LineWidth', 1.5, 'DisplayName', 'PC7 Score');
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legend('Location', 'northeast');
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xlabel('Polar Angle (°)'); ylabel('PC Score');
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title('Evolution of PC Scores');
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grid on;
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