Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
R. Kannan , Dept. of Comput. Sci., Yale Univ., New Haven, CT, USA
S. Vempala , Dept. of Comput. Sci., Yale Univ., New Haven, CT, USA
A. Veta , Dept. of Comput. Sci., Yale Univ., New Haven, CT, USA
We propose a new measure for assessing the quality of a clustering. A simple heuristic is shown to give worst-case guarantees under the new measure. Then we present two results regarding the quality of the clustering found by a popular spectral algorithm. One proffers worst case guarantees whilst the other shows that if there exists a "good" clustering then the spectral algorithm will find one close to it.
randomised algorithms; computational complexity; pattern clustering; heuristic programming; clustering quality assessment measure; heuristic; worst-case guarantees; spectral algorithm; spectral clustering; randomized algorithm; polynomial time algorithms
S. Vempala, R. Kannan and A. Veta, "On clusterings-good, bad and spectral," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 367.