Fuzzy Rough Choquet Distances for Classification
Adnan Theerens, Chris Cornelis
TL;DR
The paper addresses the need for flexible, information-rich distance measures in distance-based classifiers by fusing fuzzy rough set attribute measures with the Choquet integral. It introduces monotone measures derived from fuzzy rough dependencies, notably $\gamma_R(B)$ and $\delta_R(B)$, and integrates them into Choquet $p$-distances to capture non-linear attribute interactions toward the decision attribute. The authors propose two monotoneization schemes to ensure valid Choquet measures and demonstrate the approach with gamma-based distances (e.g., $d^\gamma_p$), showing improved neighbor relations over standard additive or Manhattan distances in illustrative scenarios. The work lays a foundation for more expressive classification distances and points to future experiments, extensions to Choquet-Mahalanobis operators, and metric-learning-inspired optimization of the measure.
Abstract
This paper introduces a novel Choquet distance using fuzzy rough set based measures. The proposed distance measure combines the attribute information received from fuzzy rough set theory with the flexibility of the Choquet integral. This approach is designed to adeptly capture non-linear relationships within the data, acknowledging the interplay of the conditional attributes towards the decision attribute and resulting in a more flexible and accurate distance. We explore its application in the context of machine learning, with a specific emphasis on distance-based classification approaches (e.g. k-nearest neighbours). The paper examines two fuzzy rough set based measures that are based on the positive region. Moreover, we explore two procedures for monotonizing the measures derived from fuzzy rough set theory, making them suitable for use with the Choquet integral, and investigate their differences.