Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 57 tok/s
Gemini 2.5 Pro 39 tok/s Pro
GPT-5 Medium 20 tok/s Pro
GPT-5 High 22 tok/s Pro
GPT-4o 82 tok/s Pro
Kimi K2 196 tok/s Pro
GPT OSS 120B 453 tok/s Pro
Claude Sonnet 4.5 27 tok/s Pro
2000 character limit reached

Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants (1612.02099v1)

Published 7 Dec 2016 in math.ST, cs.LG, stat.ML, and stat.TH

Abstract: Clustering is a fundamental problem in statistics and machine learning. Lloyd's algorithm, proposed in 1957, is still possibly the most widely used clustering algorithm in practice due to its simplicity and empirical performance. However, there has been little theoretical investigation on the statistical and computational guarantees of Lloyd's algorithm. This paper is an attempt to bridge this gap between practice and theory. We investigate the performance of Lloyd's algorithm on clustering sub-Gaussian mixtures. Under an appropriate initialization for labels or centers, we show that Lloyd's algorithm converges to an exponentially small clustering error after an order of $\log n$ iterations, where $n$ is the sample size. The error rate is shown to be minimax optimal. For the two-mixture case, we only require the initializer to be slightly better than random guess. In addition, we extend the Lloyd's algorithm and its analysis to community detection and crowdsourcing, two problems that have received a lot of attention recently in statistics and machine learning. Two variants of Lloyd's algorithm are proposed respectively for community detection and crowdsourcing. On the theoretical side, we provide statistical and computational guarantees of the two algorithms, and the results improve upon some previous signal-to-noise ratio conditions in literature for both problems. Experimental results on simulated and real data sets demonstrate competitive performance of our algorithms to the state-of-the-art methods.

Citations (104)

Summary

We haven't generated a summary for this paper yet.

Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (2)

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.