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Squared Euclidean

The squared Euclidean distance between two points, computed as the sum of the squared differences of their features without the final square root applied by Euclidean. This distance is not a metric — it fails the triangle inequality — but it is symmetric and coordinatewise monotone. It is the natural cost function for Ward agglomerative clustering.

\[ SquaredEuclidean\left(a,b\right) = \sum _{i=1}^{n} \left( a_{i}-b_{i}\right)^2 \]

Interfaces: Monotonic, Symmetric

Data Type Compatibility: Continuous

Parameters

This kernel does not have any parameters.

Example

use Rubix\ML\Kernels\Distance\SquaredEuclidean;

$kernel = new SquaredEuclidean();

References

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1. J. K. Dixon. (1978). Pattern Recognition with Partly Missing Data. ↩