How many hashes will be needed for calculating Jaccard index with an expected error less than or equal to 0.10?

The Jaccard index, also known as the Jaccard similarity coefficient, is a statistic used in understanding the similarities between sample sets. The measurement emphasizes similarity between finite sample sets, and is formally defined as the size of the intersection divided by the size of the union of the sample sets.

To calculate the Jaccard index with an expected error less than or equal to 0.10 using MinHash, you would need to determine the number of hash functions required. The expected error (e) in the estimation of the Jaccard index can be approximated by 1/sqrt(k), where k is the number of hash functions.

So, to calculate the number of hash functions needed, you would rearrange the formula to solve for k:

k = (1/e)^2

Substituting 0.10 for e:

k = (1/0.10)^2 = 100

Therefore, you would need approximately 100 hash functions to calculate the Jaccard index with an expected error less than or equal to 0.10.