# One-sided Median¶

One-sided Median algorithm computes the median

$m_n^Y = \text{Median}\{Y_{n-2k}, \ldots, Y_{n-1}\}$

and the median

$m_n^Z = \text{Median}\{Z_{n-2k}, \ldots, Z_{n-1}\}$

with

$Z_n = Y_n - Y_{n-1}.$

$$2k$$ is the size of the neighborhood window. Defining

$\hat{m}_n = m_n^Y + k m_n^Z \, \text{,}$

$$Y_n$$ is treated as a value outside the region of interest if $$|Y_n - \hat{m}_n| \geq \tau$$.

Input Parameters

Parameter Type Constraint Description Remarks
$$Y$$ $$Y \in \mathbb R^N$$ $$N \in \mathbb{N}$$ Input data sequence 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

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.