### Abstract

The nonparametric problem of detecting existence of an anomalous interval over a one-dimensional line network is studied. Nodes corresponding to an anomalous interval (if one exists) receive samples generated by a distribution q, which is different from the distribution p that generates samples for other nodes. If an anomalous interval does not exist, then all nodes receive samples generated by p. It is assumed that the distributions p and q are arbitrary, and are unknown. In order to detect whether an anomalous interval exists, a test is built based on mean embeddings of distributions into a reproducing kernel Hilbert space (RKHS) and the metric of maximum mean discrepancy (MMD). It is shown that as the network size n goes to infinity, if the minimum length of candidate anomalous intervals is larger than a threshold which has the order O(log n), the proposed test is asymptotically successful. An efficient algorithm to perform the test with substantial computational complexity reduction is proposed, and is shown to be asymptotically successful if the condition on the minimum length of candidate anomalous interval is satisfied. Numerical results are provided, which are consistent with the theoretical results.

Original language | English (US) |
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Title of host publication | IEEE International Workshop on Machine Learning for Signal Processing, MLSP |

Editors | Tulay Adali, Jan Larsen, Mamadou Mboup, Eric Moreau |

Publisher | IEEE Computer Society |

ISBN (Electronic) | 9781479936946 |

DOIs | |

State | Published - Nov 14 2014 |

Event | 2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014 - Reims, France Duration: Sep 21 2014 → Sep 24 2014 |

### Publication series

Name | IEEE International Workshop on Machine Learning for Signal Processing, MLSP |
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ISSN (Print) | 2161-0363 |

ISSN (Electronic) | 2161-0371 |

### Other

Other | 2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014 |
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Country | France |

City | Reims |

Period | 9/21/14 → 9/24/14 |

### All Science Journal Classification (ASJC) codes

- Human-Computer Interaction
- Signal Processing

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## Cite this

*IEEE International Workshop on Machine Learning for Signal Processing, MLSP*[6958913] (IEEE International Workshop on Machine Learning for Signal Processing, MLSP). IEEE Computer Society. https://doi.org/10.1109/MLSP.2014.6958913