Feature selection is an expensive challenging task in machine learning and data mining aimed at removing irrelevant and redundant features. This contributes to an improvement in classification accuracy, as well as the budget and memory requirements for classification, or any other post-processing task conducted after feature selection. In this regard, we define feature selection as a multi-objective binary optimization task with the objectives of maximizing classification accuracy and minimizing the number of selected features. In order to select optimal features, we have proposed a binary Compact NSGA-II (CNSGA-II) algorithm. Compactness represents the population as a probability distribution to enhance evolutionary algorithms not only to be more memory-efficient but also to reduce the number of fitness evaluations. Instead of holding two populations during the optimization process, our proposed method uses several Probability Vectors (PVs) to generate new individuals. Each PV efficiently explores a region of the search space to find non-dominated solutions instead of generating candidate solutions from a small population as is the common approach in most evolutionary algorithms. To the best of our knowledge, this is the first compact multi-objective algorithm proposed for feature selection. The reported results for expensive optimization cases with a limited budget on five datasets show that the CNSGA-II performs more efficiently than the well-known NSGA-II method in terms of the hypervolume (HV) performance metric requiring less memory. The proposed method and experimental results are explained and analyzed in detail.

翻译：特征选择是机器学习和数据挖掘中一项昂贵且具有挑战性的任务，旨在去除无关和冗余特征。这有助于提高分类精度，同时减少分类或特征选择后其他后处理任务的预算和内存需求。因此，我们将特征选择定义为多目标二元优化任务，其目标为最大化分类精度和最小化所选特征数量。为选择最优特征，我们提出了一种二元紧凑型NSGA-II（CNSGA-II）算法。紧凑性将种群表示为概率分布，以增强进化算法，使其不仅更节省内存，还能减少适应度评估次数。我们的方法在优化过程中不维持两个种群，而是使用多个概率向量（PV）生成新个体。与大多数进化算法中从少量种群中生成候选解的常见方法不同，每个概率向量高效地探索搜索空间中的某个区域以寻找非支配解。据我们所知，这是首个针对特征选择提出的紧凑型多目标算法。在五个数据集上有限预算下的昂贵优化案例的结果表明，CNSGA-II在超体积（HV）性能指标上比著名的NSGA-II方法效率更高，且所需内存更少。本文详细解释并分析了所提方法和实验结果。