Cosine Similarity
a measure of similarity between two non-zero vectors of an inner product space
the cosine of the trigonometric angle between two vectors
the inner product of two vectors normalized to length 1
applied to vectors of low and high dimensionality
not a measure of vector magnitude, just the angle between vectors
Euclidean Vector Dot Product Cosine Similarity
A Euclidean Vector is a geometric object that has a magnitude and direction.
Interpreting Results
The illustration below indicates how to interpret the cosine similarity in terms of the angle of separation between two vectors:
Applications
Applications include:
Embedded Values Analysis - such as word embeddings and causal embeddings
Image Processing - such as comparing shapes, arrangements, positions
Natural Language Processing - such as comparing phrases, documents, queries