Unit 3: Clustering and Classification Algorithms

Question 1

3 Properties of a distance metric

Answer 1

1. Positivity
2. Symmetry
3. Triangle Inequality

Question 2

3 Properties of a distance metric

Positivity

Answer 2

a) d(x, y) ≥ 0 for all x and y
b) d(x, y) = 0 only if x = y

Question 3

3 Properties of a distance metric

Symmetry

Answer 3

d(x, y) = d(y, x) for any x and y

Question 4

3 Properties of a distance metric

Triangle inequality

Answer 4

d(x, z) ≤ d(x, y) + d(y, x)

for any x, y and z