Linear Storage and Potentially Constant Time Hierarchical Clustering Using the Baire Metric and Random Spanning Paths

We study how random projections can be used with large data sets in order (i) to cluster the data using a fast, binning approach which is characterized in terms of direct inducing of a hierarchy through use of the Baire metric; and (ii) based on clusters found, selecting subsets of the original data for further analysis. In this work, we focus on random projection that is used for processing high dimensional data. A random projection, outputting a random permutation of the observation set, provides a random spanning path. We show how a spanning path relates to contiguity- or adjacency-constrained clustering. We study performance properties of hierarchical clustering constructed from random spanning paths, and we introduce a novel visualization of the results.