Minkowski distance#
The Minkowski distances are the set of distance metrics with different degree \((p > 0)\) and are widely used for distance computation in different algorithms. The most commonly used distance metric, Euclidean distance, is also a Minkowski distance with \(p = 2.0\).
Operation |
Computational methods |
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Mathematical formulation#
Computing#
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 Minkowski distance \(||u_i, v_j||_{p}\) for any pair of input vectors:
where \(\quad 1 \leq i \leq n, \quad 1 \leq j \leq m, \quad p > 0\).
Computation method: dense#
The method defines Minkowski distance metric, which is used in other algorithms for the distance computation. There are no separate computation mode to compute distance manually.
Programming Interface#
Refer to API Reference: Minkowski distance.