## Abstract

We provide a deterministic data summarization algorithm that approximates the mean p = n EpepP f a set P f n vectors in Rd, by a weighted mean p of a subset of 0(l/e) vectors, i.e., independent of both n and d. We prove that the squared Euclidean distance between p and p is at most e multiplied by the variance of P. We use this algorithm to maintain an approximated sum of vectors from an unbounded stream, using memory that is independent of d, and logarithmic in the n vectors seen so far. Our main application is to extract and represent in a compact way friend groups and activity summaries of users from underlying data exchanges. For example, in the case of mobile networks, we can use GPS traces to identify meetings; in the case of social networks, we can use information exchange to identify friend groups. Our algorithm provably identifies the Heavy Hitter entries in a proximity (adjacency) matrix. The Heavy Hitters can be used to extract and represent in a compact way friend groups and activity summaries of users from underlying data exchanges. We evaluate the algorithm on several large data sets.

Original language | English |
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Title of host publication | 34th International Conference on Machine Learning, ICML 2017 |

Publisher | International Machine Learning Society (IMLS) |

Pages | 1847-1855 |

Number of pages | 9 |

ISBN (Electronic) | 9781510855144 |

State | Published - 2017 |

Event | 34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia Duration: 6 Aug 2017 → 11 Aug 2017 |

### Publication series

Name | 34th International Conference on Machine Learning, ICML 2017 |
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Volume | 3 |

### Conference

Conference | 34th International Conference on Machine Learning, ICML 2017 |
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Country/Territory | Australia |

City | Sydney |

Period | 6/08/17 → 11/08/17 |

### Bibliographical note

Publisher Copyright:Copyright 2017 by the author(s).

## ASJC Scopus subject areas

- Computational Theory and Mathematics
- Human-Computer Interaction
- Software