Feature selection based on multi-perspective dynamic neighbourhood entropy measures in a dynamic neighbourhood rough set

Neighbourhood rough set (NRS)-based feature selection has been extensively applied in data mining. However, the effectiveness of the NRS model is limited by its reliance on the grid search method to determine the optimal neighbourhood parameter, insensitivity to data distribution under different features, and consideration of uncertainty measures from only one single perspective. To address the aforementioned issues, this study first defines a spatial function that can obtain information about the distribution of samples in space according to the change in the feature subset. On this basis, three perspectives of dynamic neighbourhoods are proposed: pessimistic, neutral, and optimistic. Next, the concept of the dynamic neighbourhood rough set (DNRS) model is developed. The most significant feature of this model is its adaptive ability to dynamically update the neighbourhood radius of samples on the basis of the information of their distribution in space, without the necessity of setting neighbourhood parameters artificially. Then, algebraic and information-theoretic views are introduced to propose multi-perspective dynamic neighbourhood entropy measures, which effectively measure the uncertainty of the data. In addition, a nonmonotonic feature selection algorithm based on mutual information is designed to overcome the limitations of feature selection algorithms that rely on monotonic evaluation functions. This algorithm utilizes multi-perspective dynamic neighbourhood entropy measures from a neutral perspective. Finally, to mitigate the high time complexity in feature selection for high-dimensional datasets, the Fisher score is introduced in an initial dimensionality reduction method. The results of the experiment show that the algorithm effectively eliminates redundant features and improves accuracy.