A Space Transformation-Based Multiform Approach for Multiobjective Feature Selection in High-Dimensional Classification

Improving classification performance and reducing the number of selected features are two conflicting objectives of feature selection, which can be well solved by multiobjective algorithms. However, as the dimensionality of the data increases, the search space for feature selection will grow exponentially, which leads to high-computational costs. Additionally, the complex interaction among features makes the population prone to falling into local optimal. To address these issues, feature grouping can treat one dimension as a group of features instead of one feature, effectively transforming the high-dimensional search space into a lower-dimensional one. Since different grouping forms can be converted into different feature combination spaces, the search directions of the population also vary. Inspired by this, a multiform optimization approach based on space transformation (MOFS-MST) is proposed in this article. Specifically, two different grouping forms are set based on the ranking of features in different evaluation criteria to construct a multiform framework, thereby increasing the diversity of the population. During the evolutionary process, a knowledge transfer strategy based on feature groups is executed between the two forms of grouping in order to help each other escape local optima. Moreover, it can dynamically adjust the state of feature grouping to enhance the potential for feature interaction. Experimental results demonstrate that this method outperforms six other state-of-the-art multiobjective high-dimensional feature selection methods on 12 high-dimensional datasets.