Customized dimetric dimension method for optimized attribute reduction with applications in uncertain clinical...

One of the basic problems in dimensionality reduction is determining minimal attribute subsets (reducts) for relational information systems that are not adequately described by traditional tabular methods because of their structural dependencies. This study introduces a new framework of optimized attribute reduction for rough graphs based on rough set theory and metric dimensions of graphs. The proposed methodology translates the information system into a rough graph and proposes four complementary dimetric formulations, namely, Standard Dimetric Distance, Product Dimetric Distance, Normalized Rough Degree Metric and Rough Membership-Weighted Dimetric, to describe the structural connectivity as well as the uncertainty. The basis with the minimum size of representative vertices that fully characterize vertices by their dimetric representations is then calculated, and this basis is called dimetric basis.The minimum set of representative vertices that fully characterise all vertices by their dimetric representations is then computed, which is called dimetric basis, and is used for efficient generation of relational reducts. The mathematical properties of the proposed formulations are proved for basic rough graph families, such as paths, cycles and complete graphs. The clinical applicability of the framework is illustrated through two clinical benchmark datasets, where a data reduction of up to 80 percent can be achieved with the proposed dimetric reducts without deteriorating classification performance and even with an improvement in it. The proposed framework is interpretable and has computation efficiency and is a flexible basis for uncertainty-aware graph analysis in complex information systems through the combination of structural graph information and rough approximations.