Cluster Analysis Results
Cluster Scatter Plot
Automatic Interpretation
Elbow analysis
Silhouette values
Cluster sizes
Within-cluster variance
Export Results
Formula Used
μₖ = (1 / nₖ) Σ xᵢ
Within-cluster sum of squares
WCSS = Σₖ Σᵢ∈Cₖ ||xᵢ − μₖ||²
s(i) = [b(i) − a(i)] / max[a(i), b(i)]
Explained variance ratio
EVR = BSS / TSS
The calculator measures cluster compactness using distances from each point to its centroid. It measures separation using distances between clusters and neighboring observations. Higher silhouette values usually indicate clearer, more distinct groups.
How to Use
- Paste observations or upload a CSV or TSV file.
- Detect columns, then choose the plotted numeric variables.
- Select an algorithm, distance metric, and cluster settings.
- Choose preprocessing, outlier rules, and visual options.
- Press Calculate and Plot to generate results.
- Inspect metrics, tables, diagnostic charts, and interpretations.
- Export the plot, summary, centroids, or processed dataset.
Example Data
| ID | X | Y | Z | Cluster |
|---|---|---|---|---|
| P01 | 1.2 | 2.1 | 12 | A |
| P05 | 6.3 | 7.1 | 22 | B |
| P09 | 10.1 | 2.5 | 28 | C |
| P13 | 13.8 | 10.9 | 9 | Noise |
Frequently Asked Questions
What does a cluster scatter plot show?
It places observations on two numeric axes and colors them by cluster. Centroids summarize each group’s central location. Hulls and ellipses reveal spread and overlap.
When should I standardize the variables?
Standardize when variables use different units or scales. This prevents large-valued features from dominating distances. Scaling often improves distance-based clustering.
How should I choose the number of clusters?
Compare the elbow curve, silhouette score, and practical meaning. Avoid relying on one metric alone. Stable and interpretable groups are usually preferable.
What is a good silhouette score?
Values near one indicate strong separation. Values near zero suggest overlapping clusters. Negative values may indicate incorrect assignments.
How does DBSCAN treat noise?
DBSCAN labels sparse observations as noise instead of forcing membership. Epsilon controls neighborhood distance. Minimum points controls local density requirements.
What is the difference between K-means and GMM?
K-means creates hard assignments around centroids. Gaussian mixtures estimate probabilistic component membership. GMM can better represent elliptical cluster shapes.
Why can PCA change the visual pattern?
PCA rotates data toward directions with the greatest variance. It may expose structure hidden in original axes. Some information is lost during reduction.
What do convex hulls represent?
A hull encloses the outermost observations in each cluster. It offers a simple visual boundary. Outliers can greatly expand hull size.
Can the chart prove meaningful segments exist?
No visual alone proves a useful segmentation. Validate clusters with metrics and domain knowledge. Test stability using new samples or settings.