Manhattan Distance - L1 norm (city-block distance) between two vectors

Overview

d ≥ 0; d=0 iff a=b. Manhattan 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 Manhattan Distance between vectors a and b.

   $$d_M(\mathbf{a},\mathbf{b})=\sum _{j=1}^n|a_j-b_j|$$

   Dezert et al. 2020 (L1 distance; pending PDF page verification)

Edge cases and pitfalls

• L1 is less sensitive to outliers than L2 (Euclidean). Also used in CODAS as secondary distance.

Works with

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