arXiv Machine Learning

A Sub-4 Approximation for Fair $k$-Means

arXiv AI
Sep 10

Parameterized and Streaming Algorithms for Euclidean Fair $k$-Center Clustering

The paper presents new algorithms for fair k‑center clustering in Euclidean spaces, where a dataset is divided into groups and each group has a limit on the number of centers that can be chosen. A parameterized approximation algorithm achieves a 2.732 ratio, which is improved to 2.414 with exponential time in k. By integrating this into a one‑pass streaming framework, the authors obtain streaming approximations of 4.464 (improvable to 3.828) and a polynomial‑time streaming algorithm with a 4.732 ratio, further reduced to 4.42, surpassing previous state‑of‑the‑art results. Experiments confirm that these methods outperform existing approaches in clustering accuracy.

By Zeyu Lin, Chaoqi Jia, Longkun Guo, Chao Chen
arXiv Machine Learning
Jul 30

Randomizing the Number of Centers in k-means++

arXiv:2607. 26202v1 Announce Type: cross Abstract: The $k$-means++ algorithm is a standard and widely used seeding method for $k$-means clustering, but for a fixed number $k$ of centers its worst-case expected approximation ratio is $\Theta(\log k)$.

By Vaclav Rozhon
arXiv Machine Learning
Jul 14

Learning Partition Trees for Nearest Neighbor Search

arXiv:2607. 09909v1 Announce Type: cross Abstract: We study nearest neighbor search from the perspective of data-driven algorithm design: given a dataset $P \subset \mathbb{R}^d$ of size $n$ and sample access to a query distribution over $\mathbb{R}^d$, the goal is to learn a data structure optimized for queries drawn from that specific distribution.

By Sanjeev Khanna, Ashwin Padaki, Erik Waingarten