# Hausdorff metric (hausdorff)#

## Description#

The hausdorff function computes the Hausdorff metric which measures the worst prediction error. Assume a set of change point indexes $$t_1,t_2,\dots$$ and their estimates $$\hat{t}_1, \hat{t}_2,\dots$$. The Hausdorff metric is then equal to

$\text{Hausdorff}(\{t_k\}_k, \{\hat{t}_k\}_k) := \max \{ \max_k \min_l |t_k - \hat{t}_l| \, , \max_k \min_l |\hat{t}_k - t_l|\}.$

Schematic example: true segmentation in gray, estimated segmentation in dashed lines. Here, Hausdorff is equal to $$\max(\Delta t_1, \Delta t_2, \Delta t_3)$$.

## Usage#

from ruptures.metrics import hausdorff