## Abstract

Consider a stream of dd-dimensional rows (points in RdRd) arriving sequentially. An ϵϵ-coreset is a positively weighted subset that approximates their sum of squared distances to any linear subspace of RdRd, up to a 1 pm ϵ1±ϵ factor. Unlike other data summarizations, such a coreset: (1) can be used to minimize faster any optimization function that uses this sum, such as regularized or constrained regression, (2) preserves input sparsity; (3) easily interpretable; (4) avoids numerical errors; (5) applies to problems with constraints on the input, such as subspaces that are spanned by few input points. Our main result is the first algorithm that returns such an ϵϵ-coreset using finite and constant memory during the streaming, i.e., independent of nn, the number of rows seen so far. The coreset consists of O(d °2d / ϵ 2)O(dlog2d/ϵ2) weighted rows, which is nearly optimal according to existing lower bounds of Ω (d / ϵ 2)Ω(d/ϵ2). We support our findings with experiments on the Wikipedia dataset benchmarked against state-of-the-art algorithms.

Original language | English |
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Pages (from-to) | 8699-8712 |

Number of pages | 14 |

Journal | IEEE Transactions on Knowledge and Data Engineering |

Volume | 35 |

Issue number | 9 |

DOIs | |

State | Published - 1 Sep 2023 |

### Bibliographical note

Publisher Copyright:© 1989-2012 IEEE.

## Keywords

- Big data
- coresets
- optimization
- streaming algorithms

## ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics