The INCLude (InterNodal Complete Linkage) Hierarchical Clustering Method

Abstract

The goal of this project was to develop a general, complete linkage hierarchical clustering method that 1) substantially improves upon the accuracy of the standard complete linkage method and 2) can be fully automated or used with minimal operator supervision. For the first part of the project, a new, complete linkage hierarchical clustering method was developed. The INCLude (InterNodal Complete Linkage) hierarchical clustering method unwinds the assumptions that underlie the standard complete linkage method. Further, evaluating pairs of data points for linkage is decoupled from constructing cluster sets, and cluster sets are constructed de novo instead of updating previously constructed cluster sets. Thus, it is possible to construct only the cluster sets for select, possibly noncontiguous levels of an n(n - 1)/2 + 1-level hierarchical sequence. However, by unwinding the assumptions that underlie the standard complete linkage method, the size of a hierarchical sequence reverts back from n levels to n(n - 1)/2 + 1 levels, and the time complexity to construct cluster sets becomes O(n 4). For the second part of the project, a means was developed for finding meaningful levels of an n(n-1)/2 + 1-level hierarchical sequence prior to performing a cluster analysis. The means includes constructing at least one distance graph, which is visually examined for features that correlate with meaningful levels of the corresponding hierarchical sequence. Thus, it is possible to know which cluster sets to construct and construct only these cluster sets. This reduces the time complexity to construct cluster sets from O(n4) to O(ln2), where l is the number of meaningful levels. The second part also looked at how increasing the dimensionality of the data points helps reveal inherent structure in noisy data, which is necessary for finding meaningful levels. The third part of the project resolved how to mathematically capture the graphical relationships that underlie the above-described features and integrate the means into the new clustering method. By doing so, the new method becomes self-contained and incurs almost no extra cost to determine which cluster sets should be constructed and which should not. Empirical results from nine experiments are included.