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490e645ed3
* updating DIRECTORY.md
* types(maths): Fix pylance issues in maths
* reset(vsc): Reset settings changes
* Update maths/jaccard_similarity.py
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
* revert(erosion_operation): Revert erosion_operation
* test(jaccard_similarity): Add doctest to test alternative_union
* types(newton_raphson): Add typehints to func bodies
---------
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
96 lines
3.2 KiB
Python
96 lines
3.2 KiB
Python
"""
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The Jaccard similarity coefficient is a commonly used indicator of the
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similarity between two sets. Let U be a set and A and B be subsets of U,
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then the Jaccard index/similarity is defined to be the ratio of the number
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of elements of their intersection and the number of elements of their union.
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Inspired from Wikipedia and
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the book Mining of Massive Datasets [MMDS 2nd Edition, Chapter 3]
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https://en.wikipedia.org/wiki/Jaccard_index
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https://mmds.org
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Jaccard similarity is widely used with MinHashing.
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"""
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def jaccard_similarity(
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set_a: set[str] | list[str] | tuple[str],
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set_b: set[str] | list[str] | tuple[str],
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alternative_union=False,
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):
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"""
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Finds the jaccard similarity between two sets.
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Essentially, its intersection over union.
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The alternative way to calculate this is to take union as sum of the
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number of items in the two sets. This will lead to jaccard similarity
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of a set with itself be 1/2 instead of 1. [MMDS 2nd Edition, Page 77]
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Parameters:
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:set_a (set,list,tuple): A non-empty set/list
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:set_b (set,list,tuple): A non-empty set/list
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:alternativeUnion (boolean): If True, use sum of number of
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items as union
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Output:
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(float) The jaccard similarity between the two sets.
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Examples:
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>>> set_a = {'a', 'b', 'c', 'd', 'e'}
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>>> set_b = {'c', 'd', 'e', 'f', 'h', 'i'}
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>>> jaccard_similarity(set_a, set_b)
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0.375
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>>> jaccard_similarity(set_a, set_a)
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1.0
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>>> jaccard_similarity(set_a, set_a, True)
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0.5
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>>> set_a = ['a', 'b', 'c', 'd', 'e']
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>>> set_b = ('c', 'd', 'e', 'f', 'h', 'i')
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>>> jaccard_similarity(set_a, set_b)
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0.375
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>>> set_a = ('c', 'd', 'e', 'f', 'h', 'i')
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>>> set_b = ['a', 'b', 'c', 'd', 'e']
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>>> jaccard_similarity(set_a, set_b)
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0.375
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>>> set_a = ('c', 'd', 'e', 'f', 'h', 'i')
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>>> set_b = ['a', 'b', 'c', 'd']
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>>> jaccard_similarity(set_a, set_b, True)
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0.2
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>>> set_a = {'a', 'b'}
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>>> set_b = ['c', 'd']
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>>> jaccard_similarity(set_a, set_b)
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Traceback (most recent call last):
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...
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ValueError: Set a and b must either both be sets or be either a list or a tuple.
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"""
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if isinstance(set_a, set) and isinstance(set_b, set):
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intersection_length = len(set_a.intersection(set_b))
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if alternative_union:
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union_length = len(set_a) + len(set_b)
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else:
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union_length = len(set_a.union(set_b))
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return intersection_length / union_length
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elif isinstance(set_a, (list, tuple)) and isinstance(set_b, (list, tuple)):
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intersection = [element for element in set_a if element in set_b]
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if alternative_union:
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return len(intersection) / (len(set_a) + len(set_b))
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else:
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# Cast set_a to list because tuples cannot be mutated
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union = list(set_a) + [element for element in set_b if element not in set_a]
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return len(intersection) / len(union)
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raise ValueError(
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"Set a and b must either both be sets or be either a list or a tuple."
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)
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if __name__ == "__main__":
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set_a = {"a", "b", "c", "d", "e"}
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set_b = {"c", "d", "e", "f", "h", "i"}
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print(jaccard_similarity(set_a, set_b))
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