K-Means Clustering of Flight Mission Profiles by Duration and Cruise Altitude

Project info

• Field of studyAerospace and Aviation
• LevelUndergraduate thesis (S1)
• Method typeMachine Learning
• Estimated build time± 3 working days
• Toolskmeans, silhouette, zscore (Statistics and Machine Learning Toolbox)
• PriceUS$19 - US$128

Research goal

Cluster data related to mission profile cluster with K-Means using the features flight duration and cruise altitude.

Variables

Example result

• 3Clusters k
• 847.225Within-cluster SS
• 0.888Mean silhouette
• 783.553Calinski-Harabasz
• 26.25Smallest cluster (%)
• 37.083Largest cluster (%)

K-means splits the Mission profile cluster, Flight duration and Cruise altitude data into 3 clusters with a mean silhouette of 0.888 and a Calinski-Harabasz index of 783.6; the smallest cluster holds 26.2% of observations.

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

About K-Means (kmeans)

kmeans partitions data into k clusters by minimising the distance of points to cluster centres. It suits segmentation of numeric data when the number of clusters can be estimated, such as customer or regional segmentation.

Steps

1. 1Select numeric features and standardise with zscore
2. 2Run kmeans for several values of k with Replicates
3. 3Choose k by mean silhouette or evalclusters
4. 4Fit the final model with kmeans++ initialisation
5. 5Profile clusters with feature means
6. 6Plot clusters and centroids

Assumptions to check

• Clusters are roughly spherical and similar in size
• Features are standardised because it is distance based
• Outliers are handled because they affect centroids

Reading and reporting the results

Report why k was chosen (silhouette or elbow), and the size and profile of each cluster. Stress that clusters are exploratory findings that depend on features and scaling.

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(8);
mu = [0 0; 4 4; 0 5; 5 0];
X = [];
for k = 1:4
    X = [X; mvnrnd(mu(k,:), eye(2), 100)];
end
X = zscore(X);
flight_duration = X(:, 1);
cruise_altitude = X(:, 2);

ks = 2:8;
sil = zeros(size(ks));  sse = zeros(size(ks));
for i = 1:numel(ks)
    [idx, ~, sumd] = kmeans(X, ks(i), 'Replicates', 10, 'Start', 'plus');
    sil(i) = mean(silhouette(X, idx));
    sse(i) = sum(sumd);
    fprintf('k = %d  silhouette = %.3f  SSE = %.1f\n', ks(i), sil(i), sse(i));
end
[~, ib] = max(sil);
kbest = ks(ib);
[mission_profile_cluster, C] = kmeans(X, kbest, 'Replicates', 10, 'Start', 'plus');
fprintf('Chosen k = %d, cluster sizes: %s\n', kbest, mat2str(accumarray(mission_profile_cluster, 1)'));

figure;
subplot(1,2,1); plot(ks, sse, '-o'); xlabel('k'); ylabel('Total within-cluster SSE');
subplot(1,2,2); gscatter(flight_duration, cruise_altitude, mission_profile_cluster); hold on;
plot(C(:,1), C(:,2), 'kx', 'MarkerSize', 12, 'LineWidth', 2);

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