Bi-Selection of Instances and Features Based on Neighborhood Importance Degree

As one of the most important concepts for classification learning, neighborhood granules obtained by dividing adjacent objects or instances can be regarded as the minimal elements to simulate human cognition. At present, neighborhood granules have been successfully applied to knowledge acquisition. Nevertheless, little work has been devoted to the simultaneous selection of features and instances by the use of neighborhood granules. To fill this gap, we investigate in this paper the issue of bi-selection of instances and features based on neighborhood importance degree (NID). First, the conditional neighborhood entropy is defined to measure decision uncertainty of a neighborhood granule. Considering both decision uncertainty and coverage ability of a neighborhood granule, we propose the concept of NID. Then, an instance selection algorithm is formulated to select representative instances based on NID. Furthermore, an NID-based feature selection algorithm is provided for a neighborhood decision system. By integrating the instance selection and feature selection methods, a bi-selection approach based on NID (BSNID) is finally proposed to select instances and features. Lastly, some numerical experiments are conducted to evaluate the performance of BSNID. The results demonstrate that BSNID can take account of both reduction ratio and classification accuracy and, therefore, performs satisfactorily in effectiveness.