Evolutionary algorithms (EAs) have shown their competitiveness in solving the problem of feature selection. However, limited by their encoding scheme, most of them face the challenge of “curse of dimensionality”. To address the issue, in this paper, an objective space constraint-based evolutionary algorithm, named OSC-EA, is proposed for high-dimensional feature selection (HDFS). Although the decision space of EAs for HDFS is very huge, its objective space is the same as that of the low-dimensional feature selection. Based on this fact, in the proposed OSC-EA, the HDFS is firstly modeled as a constrained problem, where a constraint of the objective space is introduced and used to partition the whole objective space into the “feasible region” and the “infeasible region”. To handle the constrained problem, a two-stage $\varepsilon$ɛ constraint-based evolutionary scheme is designed. In the first stage, the value of $\varepsilon$ɛ is set to be very small, which ensures that the search concentrates on the “feasible region”, and the latent high-quality feature subsets can be found quickly. Then, in the second stage, the value of $\varepsilon$ɛ increases gradually, so that more solutions in the “infeasible region” are considered. Until the end of the scheme, $\varepsilon \rightarrow \infty$ɛ→∞; all the solutions in the objective space are considered. By using the search in the second stage, the quality of the obtained feature subsets is further improved. The empirical results on different high-dimensional datasets demonstrate the effectiveness and efficiency of the proposed OSC-EA.

中文翻译：

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一种基于客观空间约束的高维特征选择进化方法【研究前沿】

进化算法（EA）在解决特征选择问题方面表现出了其竞争力。然而，由于编码方案的限制，大多数都面临着“维数灾难”的挑战。为了解决这个问题，本文提出了一种基于客观空间约束的进化算法，称为 OSC-EA，用于高维特征选择（HDFS）。虽然HDFS的EA的决策空间非常巨大，但其目标空间与低维特征选择的目标空间相同。基于这一事实，在所提出的OSC-EA中，HDFS首先被建模为一个约束问题，其中引入了目标空间的约束，并将整个目标空间划分为“可行区域”和“不可行区域” ”。为了处理约束问题，设计了一个基于约束的两阶段 $\varepsilon$ɛ 进化方案。在第一阶段，$\varepsilon$ɛ的值设置得非常小，这保证了搜索集中在“可行区域”，并且可以快速找到潜在的高质量特征子集。然后，在第二阶段，$\varepsilon$ɛ的值逐渐增加，从而在“不可行区域”考虑更多的解决方案。直到方案结束，$\varepsilon \rightarrow \infty$ɛ→∞；考虑目标空间中的所有解决方案。通过第二阶段的搜索，得到的特征子集的质量进一步提高。不同高维数据集上的实证结果证明了所提出的 OSC-EA 的有效性和效率。