Two-sided Median

Local Algorithm - One-Dimensional Algorithm

Two-sided Median algorithm computes the median

$$m_n^k = \text{Median}\{Y_{n-k}, \ldots, Y_{n-1}, Y_{n+1}, \ldots, Y_{n+k} \}.$$

$Y_n$ is the observed point and $2k$ is the size of the neighborhood window. If

$$|m_n^k - Y_n| \geq \tau \, \text{,}$$

$Y_n$ is treated as a value outside the region of interest.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
$Y$	$Y \in \mathbb R^N$	$N \in \mathbb{N}, N \geq 3$	Input data vector of length $N$
$\tau$	$\tau \in \mathbb R^+$		User-specified threshold

Output Parameters

Parameter	Type	Constraint	Description	Remarks
$\hat{Y}$	$\hat{Y} \in \mathbb R^N$		Values in the $Y$ list which are outside the region of interest are marked

Single Steps using the Algorithm

• Outlier Detection with Two-sided Median

References

• S. Basu, M. Meckesheimer, Automatic outlier detection for time series: an application to sensor data, Knowledge and Information Systems, vol. 11, Issue 2, pp 137-154, 2007.