Many relative indices are used in general clustering applications

Performance of Modified Indices

Many relative indices are used in general clustering applications. Well-known ones are Dunn's, Davies and Bouldin's (DB) and silhouette indices. General clustering literature shall be referred to for their definitions and details. They involve distance metrics in their formulations. New indices have been defined by modifying the initial definitions. Specifically the distance factors have been replaced by reciprocal of the similarity.

As indicators of clustering quality, Dunn's index is considered to be positively-correlated such that higher value is regarded as indicating higher quality. DB index is negatively-correlated and silhouette index positively correlated.

Following plots in Figure 1 indicates that modified Dunn's index is negatively correlated with QI in two cases. This significantly diminishes the its robustness as a clustering quality indicator. DB index shows quite strong correlation in one case, but the degree is too low in two other cases. Silhouette index is negatively correlated in all cases, contrary to its positive correlation assumption. CU is seen to possess positive correlation with QI in all cases, and its linearity is higher than other modified indices.

Set 1.