# k-Center Clustering with Outliers in Sliding Windows

arXiv: https://arxiv.org/abs/2201.02448 · HTML: https://mlsanity.com/paper/2201.02448/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 7 Jan 2022.

## Builds on (most cited first, 9 of 9)

- [Near-Linear Time Approximation Schemes for Clustering in Doubling Metrics](https://mlsanity.com/paper/1812.08664/) (2018)
- [Efficient Classification for Metric Data](https://mlsanity.com/paper/1306.2547/) (2013)
- [The Non-Uniform k-Center Problem](https://mlsanity.com/paper/1605.03692/) (2016)
- [A Lottery Model for Center-type Problems With Outliers](https://mlsanity.com/paper/1710.00287/) (2017)
- [Solving k-center Clustering (with Outliers) in MapReduce and Streaming, almost as Accurately as Sequentially](https://mlsanity.com/paper/1802.09205/) (2018)
- [Sliding Window Algorithms for k-Clustering Problems](https://mlsanity.com/paper/2006.05850/) (2020)
- [The Parameterized Hardness of the k-Center Problem in Transportation Networks](https://mlsanity.com/paper/1802.08563/) (2018)
- [k-Center Clustering with Outliers in the Sliding-Window Model](https://mlsanity.com/paper/2109.11853/) (2021)
- [Scalable Distributed Approximation of Internal Measures for Clustering Evaluation](https://mlsanity.com/paper/2003.01430/) (2020)

## Abstract (arXiv)

Metric k-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so that a more sensible variant seeks for the best solution that disregards a given number z of points of the dataset, called outliers. We provide efficient algorithms for this important variant in the streaming model under the sliding window setting, where, at each time step, the dataset to be clustered is the window W of the most recent data items. Our algorithms achieve O(1) approximation and, remarkably, require a working memory linear in k+z and only logarithmic in |W|. As a by-product, we show how to estimate the effective diameter of the window W, which is a measure of the spread of the window points, disregarding a given fraction of noisy distances. We also provide experimental evidence of the practical viability of our theoretical results.