Granular conditional entropy-based attribute reduction for partially
  labeled data with proxy labels
  Attribute reduction is one of the most important research topics in the
theory of rough sets, and many rough sets-based attribute reduction methods
have thus been presented. However, most of them are specifically designed for
dealing with either labeled data or unlabeled data, while many real-world
applications come in the form of partial supervision. In this paper, we propose
a rough sets-based semi-supervised attribute reduction method for partially
labeled data. Particularly, with the aid of prior class distribution
information about data, we first develop a simple yet effective strategy to
produce the proxy labels for unlabeled data. Then the concept of information
granularity is integrated into the information-theoretic measure, based on
which, a novel granular conditional entropy measure is proposed, and its
monotonicity is proved in theory. Furthermore, a fast heuristic algorithm is
provided to generate the optimal reduct of partially labeled data, which could
accelerate the process of attribute reduction by removing irrelevant examples
and excluding redundant attributes simultaneously. Extensive experiments
conducted on UCI data sets demonstrate that the proposed semi-supervised
attribute reduction method is promising and even compares favourably with the
supervised methods on labeled data and unlabeled data with true labels in terms
of classification performance.
