Turn dissimilarities into clear maps for interpretation now. Choose dimensions, scaling, and missing-value handling options. Download tables, plots, and diagnostics in one click securely.
Tip: For best results, use symmetric matrices and zero diagonals.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| A | 0 | 2 | 3 | 6 | 7 |
| B | 2 | 0 | 4 | 5 | 8 |
| C | 3 | 4 | 0 | 6 | 9 |
| D | 6 | 5 | 6 | 0 | 2 |
| E | 7 | 8 | 9 | 2 | 0 |
This calculator expects a square matrix describing pairwise relationships. Use true distances when you have measurements like Euclidean, Manhattan, or travel time. When you have similarities, switch modes so values are converted into dissimilarities consistently. Keep the diagonal at zero and aim for symmetry, because classical scaling assumes mirrored pairs. If your matrix comes from ratings, consider normalizing to reduce dominance by extreme scales. Document units so maps remain interpretable across datasets.
The target dimension setting controls how many coordinates are returned, but the method can only use positive eigenvalues. Eigenvalues represent how much centered squared-distance information each axis explains. A sharp drop after the first two eigenvalues suggests a strong low-dimensional structure, while many moderate eigenvalues indicate complexity. The variance explained percentage summarizes the share captured by the selected dimensions among all positive eigenvalues, helping justify a 2D or 3D map for stakeholders.
Stress-1 quantifies mismatch between original distances and distances reconstructed from the map. Lower values indicate better fidelity; practical targets are often below 0.10 for strong representations and below 0.20 for exploratory views, depending on noise and sample size. The distance-fit correlation r complements stress by showing linear agreement across all pairs, with r² expressing variance captured. Use both metrics alongside the plot to avoid overinterpreting clustered labels in operational dashboards and reports.
Real matrices frequently contain missing cells or slight asymmetry from measurement error. The calculator symmetrizes entries and fills remaining gaps with the mean, producing a usable distance surface without manual imputation. If you allow triangular input, provide either upper or lower values; the rest will be mirrored. Min-max scaling preserves ranks while standardizing range, whereas z-score emphasizes departures from the average and is shifted to keep distances nonnegative for stable overall geometry.
Coordinates are ready for downstream tasks such as clustering, segmentation, or detecting outliers in product, survey, or document spaces. Because classical scaling is deterministic for a fixed matrix, exported CSV coordinates provide a reproducible feature set for reports and models. Use the PDF export when you need a quick appendix with diagnostics and a coordinate table. When comparing runs, keep preprocessing choices identical so movement reflects only data change, not scaling artifacts.
Distances increase as items differ, while similarities increase as items match. When you choose similarity mode, values are converted using max(similarity) minus similarity so larger similarities become smaller dissimilarities.
Classical MDS can only form axes from positive eigenvalues. If the distance matrix is not perfectly Euclidean, some eigenvalues become zero or negative, so fewer usable dimensions remain.
Stress-1 compares original distances with map distances. Lower is better. As a rule of thumb, values under 0.10 are strong, under 0.20 are usable for exploration, and higher values suggest caution.
Yes. Enable triangular input and paste either the upper or lower triangle. The calculator mirrors values to enforce symmetry and fills any remaining blanks with the mean of available distances.
No. If you omit labels, the tool generates Item 1, Item 2, and so on. Labels improve readability in the coordinate table and the 2D plot annotations.
It is the fraction of total positive eigenvalue mass captured by the chosen dimensions. Higher percentages indicate that the low-dimensional map preserves more of the centered squared-distance structure.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.