Trigonometric distance and similarity measures

​Dr. Rahul Remanan

CEO, Moad Computer

Described in this article are the concepts behind the distance and similarity measures using trigonometric functions.  Specifically, the computation of cosine similarity, cosine distance, angular similarity and angular distance, using Python.

Consider two vectors: A and B. ​

Cosine similarity
The cosine similarity, cos(θ), is represented using the dot product and the magnitude of those two vectors, as follows:

Cosine distance

The cosine distance is the complement of cosine similarity in positive space. It is computed as follows:​

Angular distance

The angular distance is a formal distance metric and can be calculated from the cosine similarity. It is computed as follows:

Angular similarity

The angular similarity is the complement of the angular distance metric. It is computed as follows:

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Implementing cosine similarity, cosine distance, angular similarity and angular distance

Library imports

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Using SciPy

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Using SciKit Learn

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Using Keras losses API

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Using Keras layers API

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