Two-sided MedianΒΆ
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
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.