Cosine Similarity

Select Connection: INPUT[inlineListSuggester(optionQuery(#permanent_note), optionQuery(#literature_note), optionQuery(#fleeting_note)):connections]

DEFINITION

Cosine similarity is the cosine of the angle between vectors; that is, it is the dot product of the vectors divided by the product of their lengths — https://en.wikipedia.org/wiki/Cosine_similarity

$$\text{cosine sim.}=\cos (\theta )=\frac{A\cdot B}{||A||\cdot ||B||}$$

where $||X||$ is the magnitude of vector $X$, which in general is defined as $||x||=\sqrt{x_1^2+...+x_n^2}$.

The cosine distance is defined as follows:

$$\text{dist}(A,B)=\sqrt{(A-B)\cdot (A-B)}=\sqrt{2(1-\text{sim}(A,B)}$$

but often it is defined without the square root, since it maintains the same relative order between the elements and it is easier to compute:

$$\text{dist}(A,B)=1-\text{sim}(A,B)$$

Note that the cosine distance is not a true metric distance, since it does not have the triangular inequality and violates the coindicence axiom. Convert to euclidean or Angular Distance.