Uncertainty measurement for a three heterogeneous information system based on <i>k</i> -nearest neighborhood: Application to unsupervised attribute reduction

Abstract The <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> </m:math> k -nearest-neighbor (KNN) rule is a widely adopted classification technique in machine learning and pattern recognition. Notably, rough set models exhibit a robust capability for decision approximation, making them particularly valuable in handling complex and imprecise data. In practical applications, information systems (IS) often comprise diverse structures of information values. A three-way heterogeneous information system (3HIS) refers to an IS where attribute values encompass three distinct data types: scaled (continuous), ordinal (ranked), and nominal (categorical). This article investigates uncertainty measurement in a 3HIS by leveraging the KNN approach. First, we introduce a specialized distance function designed to compute the dissimilarity between any two information values within each attribute, accounting for the heterogeneity of data types. Building upon this, we propose an enhanced KNN model tailored for a 3HIS, which effectively captures local data structures. By using this model, we construct information granules that facilitate granular computing in heterogeneous data environments. Subsequently, we develop uncertainty quantification tools based on information entropy and information granulation, enabling a rigorous assessment of data inconsistency and ambiguity. To validate the effectiveness of these measurements, we conduct dispersion analysis from a statistical perspective, comparing various uncertainty metrics. Furthermore, we introduce a novel unsupervised attribute reduction algorithm for a 3HIS. The algorithm optimizes feature selection by minimizing redundancy while preserving discriminative power. To evaluate its performance, we employ cluster analysis to demonstrate its efficacy in enhancing data interpret-ability and classification accuracy. These findings provide significant insights into the fundamental nature of uncertainty in a 3HIS.