Comparison of silhouette-based reallocation methods for vegetation classification

Aims Vegetation classification seeks to partition the variability of vegetation into relatively homogeneous but distinct types. There are many ways to evaluate, and potentially improve, such a partitioning. One effective approach involves calculating silhouette widths which measure the goodness-of-fit of plots to their cluster. We introduce a new iterative reallocation clustering method - Reallocation of Misclassified Objects based on Silhouette width (REMOS) - and compare its performance with an existing algorithm - OPTimizing SILhouette widths (OPTSIL). REMOS reallocates misclassified objects to their nearest-neighbour cluster iteratively. Of its two variants, REMOS1 reallocates only the object with the lowest silhouette width, while REMOS2 reallocates all objects with negative silhouette width in each iteration. We test how REMOS1, REMOS2 and OPTSIL perform in terms of: (a) cluster homogeneity and separation; (b) the number of diagnostic species; and (c) runtime. Methods We classified simulated data with the flexible-beta algorithm for values of beta from -1 to 0. These classifications were subsequently optimized by REMOS1, REMOS2 and OPTSIL and compared for mean silhouette widths, misclassification rate, and runtime. We classified three vegetation data sets from two to ten clusters, optimized all outcomes with the three reallocation methods, and compared their mean silhouette widths, misclassification rate, and number of diagnostic species. Results OPTSIL achieved the highest mean silhouette width across the majority of the data sets. REMOS achieved zero or negligible misclassifications, outperforming OPTSIL on this criterion. REMOS algorithms were typically more than an order of magnitude faster to calculate than OPTSIL. There was no clear difference between REMOS and OPTSIL in the number of diagnostic species. Conclusions REMOS algorithms may be preferable to OPTSIL when: (a) the primary objective is to reduce the number of negative silhouette widths in a classification, as opposed to maximizing mean silhouette width; or (b) when the time efficiency of the algorithm is important.