# 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.