Calculator
| Example observations | Feature 1 | Feature 2 | Feature 3 |
|---|---|---|---|
| A | 1.0 | 2.0 | 3.0 |
| B | 2.0 | 1.0 | 4.0 |
| C | 3.5 | 2.5 | 2.0 |
| D | 0.5 | 1.5 | 3.0 |
- Pick a distance metric for your data.
- Apply scaling to balance features.
- Handle missing entries without breaking the matrix.
- Export to CSV or PDF for reporting.
Formula used
- Euclidean: √( Σ (xᵢ − yᵢ)² )
- Manhattan: Σ |xᵢ − yᵢ|
- Chebyshev: max |xᵢ − yᵢ|
- Minkowski: ( Σ |xᵢ − yᵢ|ᵖ )¹ᐟᵖ
- Cosine: 1 − (x·y)/(||x||·||y||)
- Correlation: 1 − r(x,y)
How to use this calculator
- Paste your data so each row is one observation.
- Enable row labels if the first column is names.
- Select a metric and optional scaling method.
- Choose how to handle missing values.
- Click compute to view the full distance matrix.
- Use CSV or PDF buttons to export your results.
Why distance matrices matter A distance matrix summarizes how similar every observation is to every other observation. It underpins clustering, anomaly detection, record linkage, and prototype selection. For n observations it contains n×n values and is typically symmetric, so it becomes a compact map of structure in high-dimensional tables. Analysts use it to reveal groups, gaps, and outliers that raw columns hide.
Choosing the right metric Euclidean distance emphasizes straight-line separation and suits continuous features with comparable units. Manhattan distance is more robust to single-feature spikes because it aggregates absolute differences. Chebyshev highlights the largest single-feature deviation. Minkowski generalizes these with the power parameter p, allowing smooth tuning between behaviors. Cosine distance focuses on direction, useful for profiles where magnitude varies. Correlation distance removes mean level effects and compares shared patterns across features.
Scaling and missing data strategy Feature scaling is critical when variables have different ranges. Z-score standardization centers by the mean and scales by the sample standard deviation, making features comparable in variance. Min-max normalization compresses values into a 0–1 range, which can stabilize distance magnitudes for reporting. For missing entries, pairwise handling computes distances on shared non-missing dimensions, preserving available information. Zero-imputation can be useful when zeros have a real interpretation, but it may bias distances if zeros are merely placeholders.
Interpreting the matrix and neighbors The diagonal is always zero because each observation matches itself. Small off-diagonal values indicate close observations, and large values indicate separation. Look for blocks of low distances to spot clusters and for isolated rows with consistently large distances to spot potential anomalies. Nearest-neighbor lists convert the matrix into actionable comparisons for quality checks, deduplication, and similarity search. Heat shading helps users scan dense matrices by turning numeric gradients into visible structure.
Exporting results for workflows Exported matrices become inputs to downstream tools, including hierarchical clustering, multidimensional scaling, and graph-based methods. CSV is ideal for spreadsheets and scripting, while PDF is useful for peer review, audits, and stakeholder reporting. Consistent rounding improves readability without changing rankings. Recording the metric, p value, scaling, and missing-value rule alongside the export supports reproducibility across teams, projects, and time and reduces confusion when results are shared.
FAQs
What format should my data be in?
Paste one observation per line, with features separated by commas, tabs, semicolons, or spaces. Enable row labels if the first column is a name. Use the delimiter option when auto-detection misreads your input.
When should I use cosine distance?
Use cosine distance when you care about direction more than magnitude, such as comparing profiles, compositions, or normalized vectors. It is common in high-dimensional feature spaces where scale varies between observations.
How does pairwise missing handling affect results?
Pairwise handling computes each distance using only dimensions that both observations contain. This preserves information, but distances may be based on different feature subsets, so compare results cautiously when missingness is heavy.
What does the nearest-neighbor list show?
For each observation, the tool ranks other observations by smallest distance and returns the top k. This is useful for spotting likely duplicates, identifying closest matches, and quickly validating clustering intuition.
Why do some cells show dashes?
A dash appears when a distance cannot be computed, usually because two observations share no non-missing dimensions after parsing and missing-value rules. Switching to zero replacement can remove dashes if zeros are appropriate.
Can I compare matrices produced with different scaling?
Only compare matrices directly when the same scaling and metric are used. Changing scaling changes distance magnitudes and sometimes rankings. If you must compare, keep settings consistent and document them in exports.