A comparison of central‐tendency and interconnectivity approaches to clustering multivariate data with irregular structure

Abstract

Abstract Questions Most clustering methods assume data are structured as discrete hyperspheroidal clusters to be evaluated by measures of central tendency. If vegetation data do not conform to this model, then vegetation data may be clustered incorrectly. What are the implications for cluster stability and evaluation if clusters are of irregular shape or density? Location Southeast Australia. Methods We define misplacement as the placement of a sample in a cluster other than (distinct from) its nearest neighbor and hypothesize that optimizing homogeneity incurs the cost of higher rates of misplacement. Chameleon is a graph‐theoretic algorithm that emphasizes interconnectivity and thus is sensitive to the shape and distribution of clusters. We contrasted its solutions with those of traditional nonhierarchical and hierarchical (agglomerative and divisive) approaches. Results Chameleon‐derived solutions had lower rates of misplacement and only marginally higher heterogeneity than those of k‐means in the range of 15–60 clusters, but their metrics converged with larger numbers of clusters. Solutions derived by agglomerative clustering had the best metrics (and divisive clustering the worst) but both produced inferior high‐level solutions to those of Chameleon by merging distantly‐related clusters. Conclusions Graph‐theoretic algorithms, such as Chameleon, have an advantage over traditional algorithms when data exhibit discontinuities and variable structure, typically producing more stable solutions (due to lower rates of misplacement) but scoring lower on traditional metrics of central tendency. Advantages are less obvious in the partitioning of data from continuous gradients; however, graph‐based partitioning protocols facilitate the hierarchical integration of solutions.

Keywords

• Chameleon
• classification
• cluster metrics
• cluster optimization
• clustering
• CLUTO