diff --git a/Data-Analyzer/StructuralPhaseTransition/SpectralAnalysisRoutines/analyzewithPCA.m b/Data-Analyzer/StructuralPhaseTransition/SpectralAnalysisRoutines/analyzewithPCA.m
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+++ b/Data-Analyzer/StructuralPhaseTransition/SpectralAnalysisRoutines/analyzewithPCA.m
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+%% STEP 1: Generate synthetic image dataset
+clear; close all; clc;
+
+% Parameters
+numImages = 50;   % number of images in the dataset
+imgSize   = [50 50]; % image dimensions
+
+% Preallocate array
+images = zeros([imgSize, numImages]);
+
+% Generate base features: a horizontal stripe + diagonal gradient
+[x, y] = meshgrid(1:imgSize(2), 1:imgSize(1));
+
+for k = 1:numImages
+    % Feature 1: horizontal stripe
+    stripe = double(y > 20 & y < 30);
+    
+    % Feature 2: diagonal gradient
+    gradient = (x + y) / max(x(:) + y(:));
+    
+    % Random variation in stripe intensity
+    stripeIntensity = 0.8 + 0.4*randn(1);
+    
+    % Random rotation of gradient strength
+    gradIntensity = 0.5 + 0.2*randn(1);
+    
+    % Combine features + Gaussian noise
+    images(:,:,k) = stripeIntensity*stripe + gradIntensity*gradient + 0.1*randn(imgSize);
+end
+
+%% STEP 2: Visualize some sample images
+figure;
+for i = 1:6
+    subplot(2,3,i);
+    imagesc(images(:,:,i));
+    axis image off; colormap gray;
+    title(sprintf('Image %d', i));
+end
+sgtitle('Sample Synthetic Images');
+
+%% STEP 3: Reshape images into a 2D data matrix
+% Each image is a row, each pixel is a column
+X = reshape(images, [], numImages)';  % size: [numImages × numPixels]
+
+%% STEP 4: Perform PCA
+[coeff, score, latent, tsquared, explained] = pca(X);
+
+% coeff  : principal component directions (eigenvectors) in pixel space
+% score  : projection of each image onto the principal components
+% latent : eigenvalues (variance captured by each PC)
+% explained : percentage variance explained by each PC
+
+%% STEP 5: Visualize variance explained
+figure;
+pareto(explained);
+xlabel('Principal Component');
+ylabel('Variance Explained (%)');
+title('PCA Variance Explained');
+
+%% STEP 6: View first few principal components as "eigenimages"
+numPCsToShow = 4;
+figure;
+for i = 1:numPCsToShow
+    pcImage = reshape(coeff(:,i), imgSize); % reshape back to image form
+    subplot(1,numPCsToShow,i);
+    imagesc(pcImage);
+    axis image off; colormap gray;
+    title(sprintf('PC %d', i));
+end
+sgtitle('First Principal Components (Eigenimages)');
+
+%% STEP 7: View projection (scores) in PC space
+figure;
+scatter(score(:,1), score(:,2), 50, 'filled');
+xlabel('PC 1 Score');
+ylabel('PC 2 Score');
+title('Images in Principal Component Space');
+grid on;