Incremental feature selection approach to multi-dimensional variation based on matrix dominance conditional entropy for ordered data set

Rough set theory is a mathematical tool widely employed in various fields to handle uncertainty. Feature selection, as an essential and independent research area within rough set theory, aims to identify a small subset of important features by eliminating irrelevant, redundant, or noisy ones. In human life, data characteristics constantly change over time and other factors, resulting in ordered datasets with varying features. However, existing feature extraction methods are not suitable for handling such datasets since they do not consider previous reduction results when features change and need to be recomputed, leading to significant time consumption. To address this issue, the incremental attribute reduction algorithm utilizes prior reduction results effectively reducing computation time. Motivated by this approach, this paper investigates incremental feature selection algorithms for ordered datasets with changing features. Firstly, we discuss the dominant matrix and the dominance conditional entropy while introducing update principles for the new dominant matrix and dominance diagonal matrix when features change. Subsequently, we propose two incremental feature selection algorithms for adding (IFS-A) or deleting (IFS-D) features in ordered data set. Additionally, nine UCI datasets are utilized to evaluate the performance of our proposed algorithm. The experimental results validate that the average classification accuracy of IFS-A and IFS-D under four classifiers on twelve datasets is 82.05% and 80.75%, which increases by 5.48% and 3.68% respectively compared with the original data.