Chapter 2.4: Measures of Similarity and Dissimilarity

Question 1

similarity

Answer 1

The similarity between two objects is a numerical measure of the degree to which the two objects are alike.

Similarities are higher for pairs of objects that are more alike.

Similarities are usually non-negative and are often between 0 (no similarity) and 1 (complete similarity)

Question 2

dissimilarity

Answer 2

The dissimilarity between two objects is a numerical measure of the degree to which the two objects are different.

Dissimilarities are lower for more similar pairs of objects.

Question 3

3 Properties of distance metrics

Answer 3

• Positivity
• Symmetry
• Triangle inequality

Question 4

3 Properties of distance metrics

Positivity

Answer 4

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

Question 5

3 Properties of distance metrics

Symmetry

Answer 5

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

Question 6

3 Properties of distance metrics

Triangle inequality

Answer 6

d(x, z) ≤ d(x, y) + d(y, z)

for all points x, y and z

Question 7

2 typical properties of similarities

Answer 7

If s(x, y) is the similarity between points x and y:

1. s(x, y) = 1 only if x = y. (0 ≤ s ≤ 1)
2. s(x, y) = s(y, x) for all x and y (symmetry)

Question 8

Similarity coefficients

Answer 8

Similarity measures between objects that contain only binary attributes are called similarity coefficients.

Question 9

Simple Matching Coefficient

Answer 9

A similarity coefficient defined as:

SMC = number of matching attribute values / number of attributes

Question 10

Jaccard Coefficient

Answer 10

Used when we have a binary dataset (all attributes are either 0 or 1).

J = number of matching presences / number of attributes not involved in 00 matches

= f11 / (f11 + f10 + f01)

Question 11

Cosine Similarity

Answer 11

cos(x, y) = (x’y) / (||x|| ||y||)

Question 12

Extended Jaccard Coefficient

Answer 12

EJ = (x‘y) / (x’x + y’y - x’y)

Question 13

Correlation

Answer 13

corr(x, y) =
covariance(x, y)
/ [standard_dev(x) × standard_dev(y)]