Interpretation of cosine & Jaccard similarity (similarity of histograms)

Rewritten Question

Given two bin counts arrays with a cosine similarity of 0.9547, why is the jaccard similarity only 0.07692?

The Jaccard similarity is calculated based on the number of common elements divided by the total number of unique elements in both sets.

In this case, since the cosine similarity is high (0.9547), it indicates that the two arrays have a high degree of similarity in terms of their values and distribution. However, the Jaccard similarity is low (0.07692) because it only considers the presence or absence of elements, regardless of their values or distribution.

Therefore, the Jaccard similarity is significantly lower than the cosine similarity because the two similarity metrics capture different aspects of the arrays’ characteristics.