Shadowed-set-based three-way clustering methods: An investigation of new optimization-based principles

Shadowed set approximation form a cornerstone for the explainable decision advice provided by shadowed C means (SCM) clustering in unsupervised learning. Due to its advantage of managing uncertainty in fuzzy clustering, it has been used in data classification. Existing SCM clustering method requires the overall amount of uncertainty associated with a fuzzy cluster ck to be preserved in its boundary region. This requirement may suffer serious risk of having high number of unclassified patterns, especially when the uncertainty in ck is very high. Consequently, the ensuing clustering may not adequately maximize the inter-cluster separation necessary for achieving optimum cluster validity results. To tackle this problem, this paper considers new SCM clustering methods arising from (i) trade-off between uncertain and certain regions, which is necessary for refraining from making uncertain classification as much as possible, (ii) measure of sharpness balance, which helps to leverage on the location of a pattern from borderline and identify included or excluded patterns by means of their location from borderline, (iii) measure of gradualness balance, which exploits the degree of transition of a pattern out of or into ck. Each method comes with some advantages. For instance, the first and third methods may minimize the overall amount of unclassified patterns. To provide an overall evaluation of the performance of the proposed methods, a comparative study with some other shadowed set-based optimization methods are involved by considering some data sets from UCI Machine Learning repository. Friedman testing followed by Holm-Bonferroni testing are also exploited to provide statistical analysis on the performance significance of the compared methods.