Hamming Distance - count of positions where two equal-length sequences differ

Overview

d ≥ 0; d=0 iff a=b. Hamming Distance is symmetric.

Output

distance, lower is better

Data

Crisp, complete numeric matrix

Size

2+ alternatives, 3-12 criteria works best

Used for

Similarity assessment, clustering

How it works

1. 1

   Compute the Hamming Distance between vectors a and b.

   $$d_H(\mathbf{a},\mathbf{b})=|\{j:a_j\ne b_j\}|$$

   Hamming 1950, p.147 (error-detection; pending PDF page verification)

Edge cases and pitfalls

• Originally defined for binary/categorical data. For continuous MCDM data an epsilon-threshold extension is required.

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