SVM Classification of Crystal Phases from Synthetic Diffraction Peak Features

Project info

• Field of studyChemistry and Materials
• LevelMaster's thesis (S2)
• Method typeMachine Learning
• Estimated build time± 5 working days
• Toolsfitcsvm, predict, crossval, perfcurve (Statistics and Machine Learning Toolbox)
• PriceUS$28 - US$178

Research goal

Classify crystal phase with an SVM using the features main peak position and relative peak intensity.

Variables

Example result

• 0.906Test accuracy
• 0.927F1 score
• 88Support vectors
• 0.915Best CV accuracy
• 1Best box constraint
• 0.53Kernel scale

The RBF-kernel SVM classifies Crystal phase with a test accuracy of 0.906 and F1 of 0.927 using 88 support vectors; the best cross-validated accuracy of 0.915 occurs at C=1.00.

Computed from illustrative synthetic data, not from a real study.

About Support Vector Machine (fitcsvm)

fitcsvm trains a Support Vector Machine for binary classification with various kernels. It suits classification on small to medium data with complex class boundaries.

Steps

1. 1Prepare the feature matrix and class labels
2. 2Split into training and test sets with cvpartition
3. 3Fit fitcsvm with an RBF kernel and Standardize on
4. 4Tune BoxConstraint and KernelScale (or OptimizeHyperparameters)
5. 5Evaluate accuracy, confusion matrix, and AUC on the test set
6. 6Plot the decision boundary if features are two-dimensional

Assumptions to check

• Features are standardised because SVM is scale sensitive
• Hyperparameters are tuned by cross-validation on training data
• Classes are not heavily imbalanced

Reading and reporting the results

Report the kernel, hyperparameters, test metrics, and the number of support vectors. Acknowledge the limited interpretability of a black-box model.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(6);
n = 300;
main_peak_position = randn(n, 2);
crystal_phase = double(sum(main_peak_position.^2, 2) > 1.4);          % circular class boundary

cv = cvpartition(crystal_phase, 'HoldOut', 0.25);
Xtr = main_peak_position(training(cv), :);  ytr = crystal_phase(training(cv));
Xte = main_peak_position(test(cv), :);      yte = crystal_phase(test(cv));

best = inf;
for C = [0.1 1 10 100]
    m = fitcsvm(Xtr, ytr, 'KernelFunction', 'rbf', 'KernelScale', 'auto', ...
        'BoxConstraint', C, 'Standardize', true);
    err = kfoldLoss(crossval(m, 'KFold', 5));
    if err < best, best = err; Cbest = C; end
end
mdl = fitcsvm(Xtr, ytr, 'KernelFunction', 'rbf', 'KernelScale', 'auto', ...
    'BoxConstraint', Cbest, 'Standardize', true);
[pred, score] = predict(mdl, Xte);
[~, ~, ~, auc] = perfcurve(yte, score(:, 2), 1);
fprintf('Best C = %g, CV error = %.3f\n', Cbest, best);
fprintf('Test accuracy = %.3f, AUC = %.3f, support vectors = %d\n', mean(pred == yte), auc, sum(mdl.IsSupportVector));
disp(confusionmat(yte, pred));

[g1, g2] = meshgrid(linspace(-3, 3, 150));
gp = predict(mdl, [g1(:) g2(:)]);
figure; gscatter(g1(:), g2(:), gp, [0.9 0.9 1; 1 0.9 0.9]); hold on;
gscatter(Xte(:,1), Xte(:,2), yte, 'br', 'ox');
xlabel('x_1'); ylabel('x_2'); title('SVM decision regions');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions