Cosine distance#

The Cosine distance is a measure of distance between two non-zero vectors of an inner product space.


Computational methods



Mathematical formulation#


Given a set \(U\) of \(n\) feature vectors \(u_1 = (u_{11}, \ldots, u_{1k}), \ldots, u_n = (u_{n1}, \ldots, u_{nk})\) of dimension \(k\) and a set \(V\) of \(m\) feature vectors \(v_1 = (v_{11}, \ldots, v_{1k}), \ldots, v_m = (v_{m1}, \ldots, v_{mk})\) of dimension \(k\), the problem is to compute the Cosine distance \(D_{cos}(u_i, v_j)\) for any pair of input vectors:

\[D_{cos}(u_i, v_j) = 1 - \frac{\sum_{l=1}^{k}u_{il}v_{jl}}{\sqrt{\sum_{l=1}^{k}u_{il}^{2}}\sqrt{\sum_{l=1}^{k}v_{jl}^{2}}},\]

where \(\quad 1 \leq i \leq n, \quad 1 \leq j \leq m\).

Computation method: dense#

The method defines Cosine distance metric, which is used in other algorithms for the distance computation. There is no separate computation mode to compute the distance manually.

Programming Interface#

Refer to API Reference: Cosine distance.