Clustering with a new distance measure based on a dual-rooted tree

Abstract

39 pagesInternational audienceThis paper introduces a novel distance measure for clustering high dimensional data based on the hitting time of two Minimal Spanning Trees (MST) grown sequentially from a pair of points by Prim's algorithm. When the proposed measure is used in conjunction with spectral clustering, we obtain a powerful clustering algorithm that is able to separate neighboring non-convex shaped clusters and to account for local as well as global geometric features of the data set. Remarkably, the new distance measure is a true metric even if the Prim algorithm uses a non-metric dissimilarity measure to compute the edges of the MST. This metric property brings added flexibility to the proposed method. In particular, the method is applied to clustering non Euclidean quantities, such as probability distributions or spectra, using the Kullback-Liebler divergence as a base measure. We reduce computational complexity by applying consensus clustering to a small ensemble of dual rooted MSTs. We show that the resultant consensus spectral clustering with dual rooted MST is competitive with other clustering methods, both in terms of clustering performance and computational complexity. We illustrate the proposed clustering algorithm on public domain benchmark data for which the ground truth is known, on one hand, and on real-world astrophysical data on the other hand

Image patch analysis of sunspots and active regions

“…Section 4 describes the clustering procedures that take the metrics' output as input. The method called Evidence Accumulating Clustering with Dual rooted Prim tree Cuts' (EAC-DC) was introduced by Galluccio et al (2013) and is used to cluster the ARs. By combining the two matrix factorization methods, a total of two procedures are used to analyze the data.…”

“…The clustering algorithm we use is the Evidence Accumulating Clustering with Dual rooted Prim tree Cuts (EAC-DC) method in Galluccio et al (2013) which scales well for clustering in high dimensions. EAC-DC clusters the data by defining a metric based on the growth of two minimal spanning trees (MSTs) grown sequentially from a pair of points.…”

“…It is fed into a spectral clustering algorithm that groups together inputs which are most similar. The similarity measure based on the MSTs adapts to the geometry of the data, and this results in a clustering method that is robust and competitive with other algorithms (Galluccio et al 2013). See Appendix A.2 for more details.…”

An agent-based algorithm exploiting multiple local dissimilarities for clusters mining and knowledge discovery

“…In particular LD-ABCD identifies clusters on a dataset that is represented through a labeled graph: graph clustering is a well-known problem and it has been addressed in many other works [10,46,18,20,21,38]. Such clusters are discovered by different agents, which operate according to a paradigm inspired by the multi-agent systems that can be found in the literature [6,36,13,12,16,2,38].…”

“…Clustering [27,37,11,39,9,26,51] is a well-established approach that can be used to this end. Among the many solutions available in this field, it is worth citing those clustering techniques based on graph-theoretical results and multi-agent systems [10,46,18,20,21,6,38,1,22]. Graph-based techniques have the fundamental advantage of mapping the original problem onto a "dimensionless" object: the graph.…”