For binary data, the L1 distance corresponds to the Hamming distance; that is, the number of bits that are different between two binary vec- tors. The Jaccard similarity is a measure of the similarity between two binary vectors. Compute the Hamming distance and the Jaccard simi- larity between the following two binary vectors.

Question

This exercise compares and contrasts some similarity and distance measures.

Answer 1

x = 0101010001
y = 0100011000
Hamming distance = number of different bits = 3
Jaccard Similarity = number of 1-1 matches /( number of bits - number
0-0 matches) = 2 / 5 = 0.4