Module: Measurable::Jaccard

Extended by:

Jaccard

Included in:

Jaccard

Defined in:

lib/measurable/jaccard.rb

Instance Method Summary

• #jaccard(u, v) ⇒ Object

  call-seq: jaccard(u, v) -> Float.

• #jaccard_index(u, v) ⇒ Object

  call-seq: jaccard_index(u, v) -> Float.

Instance Method Details

#jaccard(u, v) ⇒ Object

call-seq:

jaccard(u, v) -> Float

The jaccard distance is a measure of dissimilarity between two sets. It is calculated as:

jaccard_distance = 1 - jaccard_index

This is a proper metric, i.e. the following conditions hold:

- Symmetry:              jaccard(u, v) == jaccard(v, u)
- Non-negative:          jaccard(u, v) >= 0
- Coincidence axiom:     jaccard(u, v) == 0 if u == v
- Triangular inequality: jaccard(u, v) <= jaccard(u, w) + jaccard(w, v)

Arguments:

• u -> Array.

• v -> Array.

Returns:

• Float value representing the dissimilarity between u and v.

Raises:

• ArgumentError -> The size of the input arrays doesn’t match.

# File 'lib/measurable/jaccard.rb', line 52

def jaccard(u, v)
  1 - jaccard_index(u, v)
end

#jaccard_index(u, v) ⇒ Object

call-seq:

jaccard_index(u, v) -> Float

Give the similarity between two binary vectors u and v. Calculated as:

jaccard_index = |intersection| / |union|

In which intersection and union refer to u and v and |x| is the cardinality of set x.

For example:

jaccard_index([1, 0], [1]) == 0.5

Because |intersection| = |(1)| = 1 and |union| = |(0, 1)| = 2.

See: en.wikipedia.org/wiki/Jaccard_coefficient

Arguments:

• u -> Array.

• v -> Array.

Returns:

• Float value representing the Jaccard similarity coefficient between u and v.

# File 'lib/measurable/jaccard.rb', line 26

def jaccard_index(u, v)
  intersection = u & v
  union = u | v
  intersection.length.to_f / union.length
end