A comprehensive collection of distance and similarity functions for vectors, sequences, and distributions. Designed for machine learning, data science, and scientific computing applications.
- 50+ Distance Functions across multiple categories
- Pure Python + NumPy - no external dependencies
- Comprehensive Documentation with examples and formulas
- Type Hints for better IDE support
- Modular Architecture - import by category or use flat API
git clone https://github.com/rehanguha/interspace.git
cd interspace
pip install -e .
import interspace
# Direct access (flat API)
interspace.euclidean([1, 2, 3], [4, 5, 6])
# 5.196152422706632
interspace.levenshtein_distance("kitten", "sitting")
# 3
interspace.haversine((42.52, 15.28), (51.51, -0.13))
# 1231910.73... (Zagreb to London in meters)
# Categorized access
interspace.distances.vector.euclidean([1, 2], [3, 4])
interspace.distances.string.levenshtein_distance("hello", "hallo")
interspace.distances.geographic.haversine((0, 0), (1, 1))
| Function |
Description |
Formula |
euclidean(x, y) |
L2 norm distance |
√Σ(xᵢ - yᵢ)² |
manhattan(x, y) |
L1 norm / cityblock distance |
`Σ |
minkowski(x, y, p) |
Generalized p-norm distance |
`(Σ |
chebyshev_distance(x, y) |
L∞ norm / maximum distance |
`max |
cosine_similarity(x, y) |
Angular similarity |
x·y / (‖x‖‖y‖) |
cosine_distance(x, y) |
1 - cosine_similarity |
1 - (x·y / (‖x‖‖y‖)) |
mahalanobis(u, v, VI) |
Distance with covariance |
√((u-v)ᵀVI(u-v)) |
>>> interspace.euclidean([1, 2, 3], [4, 5, 6])
5.196152422706632
>>> interspace.minkowski([1, 2], [4, 6], p=1) # Manhattan
7.0
>>> interspace.cosine_similarity([1, 0], [0, 1])
0.0
| Function |
Description |
weighted_euclidean(x, y, w) |
Weighted Euclidean distance |
weighted_manhattan(x, y, w) |
Weighted Manhattan distance |
weighted_minkowski(x, y, w, p) |
Weighted Minkowski distance |
>>> interspace.weighted_euclidean([1, 2], [4, 6], [1, 0.5])
4.301162633521313
| Function |
Description |
jaccard_distance(x, y) |
1 - |
dice_distance(x, y) |
1 - 2 |
matching_distance(x, y) |
Proportion of mismatched positions |
overlap_distance(x, y) |
1 - |
tanimoto_distance(x, y) |
Extended Jaccard for vectors |
>>> interspace.jaccard_distance([1, 2, 3], [2, 3, 4])
0.5
>>> interspace.dice_distance([1, 2, 3], [2, 3, 4])
0.4
| Function |
Description |
canberra_distance(x, y) |
Weighted Manhattan distance |
braycurtis_distance(x, y) |
Bray-Curtis dissimilarity |
correlation_distance(x, y) |
1 - Pearson correlation |
pearson_distance(x, y) |
Alias for correlation_distance |
squared_chord_distance(x, y) |
Squared chord distance |
>>> interspace.canberra_distance([1, 2, 3], [2, 2, 4])
0.47619047619047616
>>> interspace.correlation_distance([1, 2, 3], [3, 2, 1])
2.0
| Function |
Description |
kl_divergence(p, q) |
Kullback-Leibler divergence |
js_distance(p, q) |
Jensen-Shannon distance |
bhattacharyya_distance(p, q) |
Distribution overlap measure |
hellinger_distance(p, q) |
Fidelity-based distance |
total_variation_distance(p, q) |
L1 distribution distance |
wasserstein_distance(p, q) |
Earth Mover's Distance (1D) |
>>> interspace.kl_divergence([0.5, 0.5], [0.5, 0.5])
0.0
>>> interspace.js_distance([1.0, 0.0], [0.5, 0.5])
0.4645034044881785
| Function |
Description |
hamming(a, b) |
Bitwise or per-position mismatches |
hamming_distance_normalized(a, b) |
Normalized Hamming distance |
levenshtein_distance(s1, s2) |
Edit distance |
damerau_levenshtein_distance(s1, s2) |
Edit + transpositions |
jaro_distance(s1, s2) |
String similarity |
jaro_winkler_distance(s1, s2) |
Jaro with prefix weighting |
>>> interspace.levenshtein_distance("kitten", "sitting")
3
>>> interspace.jaro_winkler_distance("MARTHA", "MARHTA")
0.9666666666666667
>>> interspace.hamming(0b1010, 0b0011)
2
| Function |
Description |
haversine(coord1, coord2, R) |
Great-circle distance |
vincenty_distance(coord1, coord2) |
Geodesic on ellipsoid |
bearing(coord1, coord2) |
Direction between points |
midpoint(coord1, coord2) |
Geographic midpoint |
destination_point(coord, bearing, distance) |
Point along bearing |
>>> zagreb = (45.8150, 15.9819)
>>> london = (51.5074, -0.1278)
>>> interspace.haversine(zagreb, london)
1230000.0 # meters
>>> interspace.bearing((0, 0), (1, 0))
0.0 # North
| Function |
Description |
dtw_distance(x, y) |
Dynamic Time Warping |
euclidean_distance_1d(x, y) |
1D Euclidean distance |
longest_common_subsequence(x, y) |
LCS length |
>>> interspace.dtw_distance([1, 2, 3], [1, 2, 2, 3])
0.0
>>> interspace.longest_common_subsequence([1, 2, 3, 4], [2, 3, 5])
2
| Function |
Description |
frobenius_distance(A, B) |
Frobenius norm distance |
spectral_distance(A, B) |
Largest singular value |
trace_distance(A, B) |
Nuclear norm distance / 2 |
>>> A = [[1, 0], [0, 1]]
>>> B = [[1, 0], [0, 2]]
>>> interspace.spectral_distance(A, B)
1.0
| Function |
Description |
russell_rao_distance(x, y) |
Russell-Rao distance |
sokal_sneath_distance(x, y) |
Sokal-Sneath distance |
kulczynski_distance(x, y) |
Kulczynski distance |
>>> interspace.russell_rao_distance([1, 0, 1, 0], [1, 1, 0, 0])
0.75
| Function |
Description |
normalized_euclidean(x, y) |
Euclidean / √n |
standardized_euclidean(x, y, variances) |
Variance-weighted |
seuclidean(x, y, V) |
Alias for standardized_euclidean |
chi2_distance(x, y) |
Chi-squared distance |
gower_distance(x, y, types, ranges) |
Mixed variable types |
>>> interspace.chi2_distance([1, 2, 3], [2, 3, 4])
0.2777777777777778
| Function |
Description |
angular_distance(angle1, angle2) |
Shortest angular distance |
spherical_law_of_cosines(coord1, coord2) |
Alternative great-circle |
euclidean_3d(point1, point2) |
3D Euclidean distance |
>>> interspace.angular_distance(10, 350)
20.0
>>> interspace.euclidean_3d([0, 0, 0], [1, 2, 2])
3.0
| Function |
Description |
entropy(p, base) |
Shannon entropy |
cross_entropy(p, q, base) |
Cross-entropy |
mutual_information(x, y, base) |
Mutual information |
>>> interspace.entropy([0.5, 0.5])
1.0
>>> interspace.mutual_information([0, 0, 1, 1], [0, 0, 1, 1])
1.0
| Function |
Description |
pairwise_distance(X, Y, metric) |
Compute distance matrix |
is_distance_metric(func) |
Validate metric properties |
>>> X = [[1, 2], [3, 4], [5, 6]]
>>> interspace.pairwise_distance(X, metric="euclidean")
array([[0. , 2.82842712, 5.65685425],
[2.82842712, 0. , 2.82842712],
[5.65685425, 2.82842712, 0. ]])
interspace/
├── __init__.py # Main exports (flat API)
├── _validators.py # Internal validation helpers
├── distances/
│ ├── vector.py # Euclidean, Manhattan, Minkowski, etc.
│ ├── weighted.py # Weighted distance functions
│ ├── set.py # Jaccard, Dice, Tanimoto, etc.
│ ├── distribution.py # Canberra, Bray-Curtis, etc.
│ ├── probability.py # KL, JS, Bhattacharyya, etc.
│ ├── string.py # Levenshtein, Jaro, Hamming, etc.
│ ├── geographic.py # Haversine, Vincenty, Bearing, etc.
│ ├── time_series.py # DTW, LCS, etc.
│ ├── matrix.py # Frobenius, Spectral, Trace
│ ├── binary.py # Russell-Rao, Sokal-Sneath, etc.
│ ├── normalized.py # Chi-squared, Gower, etc.
│ └── physics.py # Angular, 3D Euclidean, etc.
├── information/
│ └── theory.py # Entropy, Cross-entropy, MI
├── metrics/
│ ├── pairwise.py # Pairwise distance matrix
│ └── validation.py # Metric property validation
└── misc/
└── misc.py # Experimental functions
# Run all tests
pytest
# Run with coverage
pytest --cov=interspace --cov-report=html
# Format code
black interspace/
# Lint
ruff check interspace/
# Type check
mypy interspace/
Contributions are welcome! Please see CONTRIBUTING.md for guidelines.
See CHANGELOG.md for version history.
This project is licensed under the MIT License - see the LICENSE file for details.
Rehan Guha
Inspired by scipy.spatial.distance and designed for simplicity and ease of use.
