## Abstract

Life-logging video streams, financial time series, and Twitter tweets are a few examples of high-dimensional signals over practically unbounded time. We consider the problem of computing optimal segmentation of such signals by a k-piecewise linear function, using only one pass over the data by maintaining a coreset for the signal. The coreset enables fast further analysis such as automatic summarization and analysis of such signals. A coreset (core-set) is a compact representation of the data seen so far, which approximates the data well for a specific task - in our case, segmentation of the stream. We show that, perhaps surprisingly, the segmentation problem admits coresets of cardinality only linear in the number of segments k, independently of both the dimension d of the signal, and its number n of points. More precisely, we construct a representation of size O(k log n/ε^{2}) that provides a (1+ε)-approximation for the sum of squared distances to any given k-piecewise linear function. Moreover, such coresets can be constructed in a parallel streaming approach. Our results rely on a novel reduction of statistical estimations to problems in computational geometry. We empirically evaluate our algorithms on very large synthetic and real data sets from GPS, video and financial domains, using 255 machines in Amazon cloud.

Original language | English |
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Title of host publication | Advances in Neural Information Processing Systems )NIPS) 2014 |

Pages | 559-567 |

Number of pages | 9 |

Volume | 1 |

Edition | January |

State | Published - 2014 |

Externally published | Yes |

Event | 28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 - Montreal, Canada Duration: 8 Dec 2014 → 13 Dec 2014 |

### Conference

Conference | 28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 |
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Country/Territory | Canada |

City | Montreal |

Period | 8/12/14 → 13/12/14 |

## ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing