Some of the formulae that we have come across in Chapters 6 & 7 are listed below. Match each of these to the name they are most commonly known by, assuming two instances a and b and an m-dimensional feature space. 单项选择题
A
Euclidean Distance(a,b)
B
Manhattan Distance(a,b)
C
Minkowski Distance(a,b)

Question

Some of the formulae that we have come across in Chapters 6 & 7 are listed below. Match each of these to the name they are most commonly known by, assuming two instances a and b and an m-dimensional feature space. 单项选择题

A

Euclidean Distance(a,b)

B

Manhattan Distance(a,b)

C

Minkowski Distance(a,b)

BlackTom AI · Accepted Answer

The question asks us to identify which name corresponds to the general formula that takes two instances a and b in an m-dimensional feature space, and is commonly known by a specific term.
Option 1: Euclidean Distance(a,b) is the standard L2 distance, computed as the square root of the sum of squared coordinate differences. While closely related to the Minkowski distance (as a special case when p = 2), it is not the most general name for the whole family of Lp norms.
Option 2: Manhattan Distance(a,b) refers to the L1 distance, which sums the absolute differences across coordinates. This is also a specific instance within the Minkowski family, not the general name.
Option 3: Minkowski Distance(a,b) is the broad, canonical name for the family of distances defined by the p-norm: (sum_i |a_i - b_i|^p)^(1/p) for p >= 1. This general form encompasses both Euclidean (p=2) and Manhattan (p=1) as special cases, making it the correct umbrella term.
In summary, the general concept that covers all p-norm-based distances between two m-dimensional vectors is Minkowski Distance(a,b); Euclidean and Manhattan are particular instances within this family, not the overarching name.