Semi-supervised shadowed sets for three-way classification on partial labeled data

Abstract

Shadowed set divides a fuzzy set into three regions through fuzzy-rough transformation to denote acceptance, rejection and uncertain decision. Based on the tri-partition property, shadowed sets are utilized to implement the machine learning methods for uncertain data analysis. The extant uncertain machine learning methods with shadowed sets include the unsupervised clustering on only unlabeled data and the supervised classification on only labeled data. However, for the partial labeled data containing both labeled and unlabeled data instances, the studies of uncertain learning methods with shadowed sets are very limited. Aiming at the requirement, in this paper, we propose a novel semi-supervised shadowed set on partial labeled data and thereby construct semi-supervised shadowed neighborhoods to implement the three-way classification of uncertain data. To construct the semi-supervised shadowed set, we reformulate the objective function of shadowed sets, in which the membership loss in fuzzy-rough transformation is weighted by labeled and unlabeled data. We also analyze the influence of labeled data to the shadowed set construction. Experiments validate that the proposed three-way classification method with semi-supervised shadowed sets is effective to utilize partial labeled data to achieve low-risk uncertain data classification.