Evaluating authorship distance methods using the positive Silhouette coefficient

Unsupervised Authorship Analysis (UAA) aims to cluster documents by authorship without knowing the authorship of any documents. An important factor in UAA is the method for calculating the distance between documents. This choice of the authorship distance method is considered more critical to the end result than the choice of cluster analysis algorithm. One method for measuring the correlation between a distance metric and a labelling (such as class values or clusters) is the Silhouette Coefficient (SC). The SC can be leveraged by measuring the correlation between the authorship distance method and the true authorship, evaluating the quality of the distance method. However, we show that the SC can be severely affected by outliers. To address this issue, we introduce the Positive Silhouette Coefficient, given as the proportion of instances with a positive SC value. This metric is not easily altered by outliers and produces a more robust metric. A large number of authorship distance methods are then compared using the PSC, and the findings are presented. This research provides an insight into the efficacy of methods for UAA and presents a framework for testing authorship distance methods.