Qualitative and quantitative combinations of crisp and rough clustering schemes using dominance relations

Due to their unsupervised learning nature, analyzing the semantics of clustering schemes can be difficult. Qualitative information such as preference relations may be useful in semantic analysis of clustering process. This paper describes a framework based on preference or dominance relations that helps us qualitatively analyze a clustering scheme. This qualitative interpretation is shown to be useful for combining clustering schemes that are based on different criteria. The qualitative combination can be used to analyze its quantitative counterpart and can also be used instead of the quantitative combination. The paper further extends the framework to accommodate rough set based clustering. The usefulness of the approach is illustrated using a synthetic retail database.