Clustering Using Isoperimetric Number of Trees
This work addresses data clustering for researchers and practitioners, offering a novel method with outlier detection capabilities, but it appears incremental as it builds on graph-based clustering approaches.
The paper tackles the problem of data clustering by proposing a graph-based algorithm that clusters a minimum spanning tree using a minimum isoperimetry criteria, achieving an O(n log n) runtime for basic clustering and O(n^2) with post-processing, and shows effective performance on benchmarks and handmade examples.
In this paper we propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in $O(n \log n)$ and with post-processing in $O(n^2)$ (worst case) time where $n$ is the size of the data set. We also show that our generalized graph model which also allows the use of potentials at vertices can be used to extract a more detailed pack of information as the {\it outlier profile} of the data set. In this direction we show that our approach can be used to define the concept of an outlier-set in a precise way and we propose approximation algorithms for finding such sets. We also provide a comparative performance analysis of our algorithm with other related ones and we show that the new clustering algorithm (without the outlier extraction procedure) behaves quite effectively even on hard benchmarks and handmade examples.