General Rough Modeling of Cluster Analysis
This work addresses foundational issues in clustering theory by providing a contamination-free approach for clearer proofs, though it appears incremental as it builds on existing rough set concepts.
The authors propose a general theoretical framework for clustering based on partial algebraic systems, aiming to isolate minimal assumptions for clustering concepts and replace numeric validation with rough approximation methods.
In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). \emph{It is well-known that of the limited number of proofs in the theory of hard and soft clustering that are known to exist, most involve statistical assumptions}. Many methods seem to work because they seem to work in specific empirical practice. A new general rough method of analyzing clusterings is invented, and this opens the subject to clearer conceptions and contamination-free theoretical proofs. Numeric ideas of validation are also proposed to be replaced by those based on general rough approximation. The essence of the approach is explained in brief and supported by an example.