Representation-Based Decision-Theoretic Rough Sets for Three-Way Classification

Three-valued reasoning or three-way decision modelling theory (3WD) offers a natural, human-intuitive method for dealing with uncertainty. Rough set theory is a paradigm which mimics 3WD by providing a set of concepts which broadly reflect the three different modelling scenarios; certainty, uncertainty and exclusion. A further development known as decision-theoretic rough sets utilises a neighbourhood relation to partition the universe and offers further flexibility in the framing of 3WD by allowing for a probabilistic extension to rough sets. However, the traditional approach to discovering the neighbourhood is based upon one-to-one metrics which suffer from some inherent weaknesses, such as ignoring some holistic information including data distribution and class structure. In order to address this shortcoming and improve existing 3WD classification models, this paper proposes a linear reconstruction neighbourhood membership and associated representation-based decision-theoretic rough set (RDTRS) approach in order to implement 3WD classification. The work employs a linear reconstruction metric (LRM), which is a one-to-many mapping. This allows the exploration of inherent geometric similarities and the complete consideration of the neighbourhood relationships of objects. LRM can be deemed a hybrid approach, since it has the ability to reflect both the distribution of the training objects and the significance of objects in constructing the representation subspace. The experimental results demonstrate that the use of this novel RDTRS technique harnesses the representation power of 3WD classification and results in improved classification performance for both benchmark and face image datasets.