On Clusterings - Good, Bad and Spectral

We motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have polylogarithmic worst-case guarantees under the new measure. The main result of the article is the analysis of a popular spectral algorithm. One variant of spectral clustering turns out to have effective worst-case guarantees; another finds a “good” clustering, if one exists. Categories and Subject Descriptors: F2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; H3 [Information Systems]: Information Storage and Retrieval General Terms: Algorithms, Theory Additional Key Words and Phrases: Clustering, graph algorithms, spectral methods

• Type: Conference
• Year: 2000
• Where: FOCS
• Authors: Ravi Kannan, Santosh Vempala, Adrian Vetta
• Keywords: Effective Worst-case Guarantees, FOCS 2000, Polylogarithmic Worst-case Guarantees, Theoretical Computer Science, Worst-case Guarantees