pyts.metrics.boss

pyts.metrics.boss(x, y)[source]

Return the BOSS distance between two arrays.

Parameters:
x : array-like, shape = (n_timestamps,)

First array.

y : array-like, shape = (n_timestamps,)

Second array.
Returns:
dist : float

The BOSS distance between both arrays.

Notes

The BOSS metric is defined as

BOSS(x, y) = \sum_{\substack{i=1\\ x_i > 0}}^n (x_i - y_i)^2

where x and y are vectors of non-negative integers. The BOSS distance is not a distance metric as it neither satisfies the symmetry condition nor the triangle inequality.

References

[1]P. Schäfer, “The BOSS is concerned with time series classification in the presence of noise”. Data Mining and Knowledge Discovery, 29(6), 1505-1530 (2015).

Examples

>>> from pyts.metrics import boss
>>> x = [0, 5, 5, 3, 4, 5]
>>> y = [3, 0, 0, 0, 8, 0]
>>> boss(x, y)
10.0
>>> boss(y, x)
5.0