In multi-dimensional classification (MDC), each instance is associated with labels from multiple potentially interdependent class dimensions. However, existing approaches often overlook the fact that different semantic dimensions may require distinct feature representations. Additionally, irrelevant and redundant features in the feature space can adversely affect model performance. To address these issues, a feature selection approach based on evolutionary multi-tasking named Fest is proposed for MDC. It treats feature selection for each class dimension as a separate subtask for evolution, ensuring the selected features effectively capture the semantics of each dimension. To effectively identify and select shared features between correlated class dimensions, Fest introduces an exploration mechanism for feature interaction that considers class dependencies. Extensive experiments are conducted on eleven benchmark datasets as well as on four state-of-the-art MDC approaches. Experimental results clearly demonstrate that selecting dimension-specific features instead of all features can significantly improve the classification performance of existing MDC approaches.

In multi-dimensional classification (MDC), the classifier chain approach is based on a chain structure to model dependencies between class spaces. However, current research on constructing a chain order is usually based on a greedy criterion or random generation, which is highly likely to lead to an incorrect chain order and fit incorrect class dependencies. Moreover, existing classifier chain-based approaches do not consider the misleading effects of irrelevant input features on the classifiers. To fill the above gap, a classifier chain-based approach incorporating evolutionary chain order optimization and feature selection (ECCO) is proposed. Specifically, this approach designs a meta-heuristic algorithm to optimize the chain order of multiple classifiers. Simultaneously, the approach selects dimension-specific feature combinations that are more conducive to class prediction of each dimension. These strategies enhance the class prediction capability of the constructed MDC model. Comparative experiments on 14 real datasets validate that ECCO outperforms 7 state-of-the-art MDC approaches.

In multiobjective feature selection, different feature subsets with the same number of selected features can achieve identical classification accuracy, meaning that it is a multimodal optimization problem. To effectively search for multimodal feature subsets within the vast search spaces of high-dimensional datasets, it is crucial to adopt reasonable encoding and search methods. Generally, applying a uniform evolutionary operator based on a single encoding method across the entire feature space is inefficient and prone to falling into local optima. To address the above issues, this article proposes a multimodal multiobjective feature selection method based on a joint encoding mechanism that combines discrete encoding and continuous encoding. It provides new perspectives to solve the high-dimensional feature selection problem from encoding methods to search operators. First, the search space is divided into a discrete encoding region and a continuous encoding region based on the knee points of feature importance ranking curve. A tailored initialization strategy is used to obtain the initial population for joint encoding. Second, an adaptive niche strategy based on three priorities is proposed, which ensures the similarity of individuals within a niche and the difference between niches. In addition, different search operators are cooperated with the two encoding strategies, respectively, to achieve effective and efficient search. The experimental results on 24 datasets show that the proposed algorithm achieves a better-classification performance than the state-of-the-art feature selection methods.

Unbalanced classification problems have attracted significant academic attention due to their widespread existence in the real world. The lack of recognition accuracy of minority class samples and the “curse of dimensionality” are two major difficulties in unbalanced classification problems. Existing unbalanced classification methods run the risk of losing the original feature information and are prone to bias toward the majority class. Multiform optimization is famous for capturing useful knowledge from alternative forms to help solve the original task. Motivated by this, this article introduces a multiform evolutionary framework that addresses the issue of multiobjective feature selection in unbalanced classification scenarios. It aims to utilize the advanced experience of selecting features on balanced datasets to assist in the search for feature subsets that can more accurately identify minority classes on the original dataset. Specifically, a knowledge transfer strategy is proposed to draw on the search experience of the auxiliary task from the oversampled dataset to help the cost-sensitive learning task based on the original dataset jump out of the local optimum. In addition, an offspring repairing mechanism is proposed to filter redundant features by considering the frequency of selected features. Experimental results on 23 real-world benchmark datasets demonstrate that the proposed method can select fewer features and achieve better classification results compared to six state-of-the-art multiobjective feature selection algorithms and three classical oversampling algorithms. Furthermore, the difference in performance of four base classifiers is investigated through a series of comparative experiments.

Feature selection in machine learning as a key data processing technique has two conflicting goals: minimizing the classification error rate and minimizing the number of features selected. However, most of the existing multi-objective feature selection methods face the problems of easily falling into local optima and slow convergence by virtue of their problem characteristics, such as partially conflicting objectives and highly discontinuous Pareto fronts. To solve these problems, this article proposes a multiform optimization framework to solve a multi-objective feature selection task together with several auxiliary single-objective feature selection tasks in a multitask environment. The proposed framework uses the problem-solving experience of single-objective tasks to assist the multi-objective feature selection task in exploring more promising regions and accelerating the convergence speed. Specifically, a knowledge transfer strategy based on the search experience of different tasks is developed to accomplish multiform optimization. In addition, a diversity enhancement mechanism is presented to improve search ability in promising decision space areas by considering historical information about the population. In most cases, the experiment results on 27 datasets demonstrate that the proposed technique can uncover more diversified feature subsets on the Pareto front in less time than existing state-of-the-art methods.