Distance metrics

Distance metrics are different formulas used by KNN/ANN to measure distance and select the nearest neighbors. The compatible ones vary depending on the backend.

Use the table below to select a distance metric(s) supported by the backend being used:

Legend

• ✅ Native support
• 🔁 Fallback to exact sklearn KNN
• ❌ Not supported

Metric	Why it matters for DES	KNN (exact)	FAISS flat/HNSW	FAISS IVF	Annoy	HNSW (hnswlib)	HNSW (nmslib)
euclidean	Standard L2 norm; best default for continuous feature spaces. Defines spherical local regions for selecting competent classifiers.	✅	✅	✅	✅	✅	✅
manhattan	L1 norm; robust to outliers and often preferable in high‑dimensional feature spaces (mitigates the curse of dimensionality for DES).	✅	✅	🔁	✅	❌	✅
chebyshev	L∞ norm; focuses on the worst‑case feature deviation. Useful when a single dominant feature dictates similarity (e.g., bounded grids).	✅	✅	🔁	❌	❌	✅
minkowski	Generalises L1/L2 via p; lets you tune the shape of the local neighbourhood between Manhattan and Euclidean.	✅	✅	🔁	❌	❌	❌
cosine	Angle between vectors, ignoring magnitude. Ideal for normalised embeddings (deep features, TF‑IDF) where direction, not scale, matters for classifier competence.	✅	✅	✅	✅	✅	✅
dot	Inner product (not a metric). Used for max‑inner‑product search (e.g., recommender systems). Generally not recommended for standard DES unless you specifically need relevance‑based ranking.	❌	❌	❌	✅	✅	✅
canberra	Weighted L1 that emphasises relative changes; sensitive to values near zero. Useful for sparse count data or features where zeros are meaningful.	✅	✅	🔁	❌	❌	❌
braycurtis	Normalised L1 bounded to [0,1]; common for compositional or ecological data (e.g., abundance vectors).	✅	✅	🔁	❌	❌	❌
jensenshannon	Symmetric KL divergence; requires non‑negative inputs. Ideal for measuring similarity between classifier output probability distributions or bag‑of‑word features.	❌	✅	🔁	❌	❌	❌
correlation	Pearson correlation distance (1‑ρ). Good for time‑series or features with linear trends – helps select classifiers that generalise across similar patterns.	✅	🔁	🔁	❌	❌	❌
hamming	Fraction of differing binary/categorical components. Directly applicable to binary feature spaces or binarised classifier predictions.	✅	🔁	🔁	✅	❌	❌
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