Information theoretical-based methods have attracted a great attention in recent years and gained promising results for multilabel feature selection (MLFS). Nevertheless, most of the existing methods consider a heuristic way to the grid search of important features, and they may also suffer from the issue of fully utilizing labeling information. Thus, they are probable to deliver a suboptimal result with heavy computational burden. In this article, we propose a general optimization framework global relevance and redundancy optimization (GRRO) to solve the learning problem. The main technical contribution in GRRO is a formulation for MLFS while feature relevance, label relevance (i.e., label correlation), and feature redundancy are taken into account, which can avoid repetitive entropy calculations to obtain a global optimal solution efficiently. To further improve the efficiency, we extend GRRO to filter out inessential labels and features, thus facilitating fast MLFS. We call the extension as GRROfast, in which the key insights are twofold: 1) promising labels and related relevant features are investigated to reduce ineffective calculations in terms of features, even labels and 2) the framework of GRRO is reconstructed to generate the optimal result with an ensemble. Moreover, our proposed algorithms have an excellent mechanism for exploiting the inherent properties of multilabel data; specifically, we provide a formulation to enhance the proposal with label-specific features. Extensive experiments clearly reveal the effectiveness and efficiency of our proposed algorithms.

Recently several novel cost-sensitive attribute-scale selection approaches have been proposed based on measurement errors. They are significant because they can simultaneously select attributes and scale combination to minimize the cost consumed in data processing. However, these approaches cannot deal with hybrid data with test cost constraint, and most of them do not consider the scale diversity between different attributes; and these approaches do not touch the uncertainty measurement, all of which are important issues in real applications. To address this situation, in this paper an effective cost-sensitive attribute-scale selection approach is presented based on the rough set theory, and multiple relevant uncertainty measures are developed. The main contributions of the paper are threefold. First, a generalized confidence level vector-based neighborhood rough set model is constructed. It takes into account the scale diversity between different attributes of hybrid data. Then, multiple uncertainty measures are developed. They consider both attributes and scales, thus are more general than existing ones which consider only attributes or only scales. Finally, an efficient heuristic attribute-scale selection algorithm is designed, which can select attributes and their respective scales to minimize the consumed total cost of hybrid data under any rational value of test cost upper bound. Detailed experiments thoroughly confirm the effectiveness of the proposed cost-sensitive attribute-scale selection approach. The experiments also reveal the influences of different test cost upper bounds to the attribute-scale selection and some related quantities including the uncertainty measures. This study would enrich the rough set theory to some extent, and provide an effective support for some test cost-constrained decision makings.

Information theoretical based methods have attracted a great attention in recent years, and gained promising results to deal with multi-label data with high dimensionality. However, most of the existing methods are either directly transformed from heuristic single-label feature selection methods or inefficient in exploiting labeling information. Thus, they may not be able to get an optimal feature selection result shared by multiple labels. In this paper, we propose a general global optimization framework, in which feature relevance, label relevance (i.e., label correlation), and feature redundancy are taken into account, thus facilitating multi-label feature selection. Moreover, the proposed method has an excellent mechanism for utilizing inherent properties of multi-label learning. Specially, we provide a formulation to extend the proposed method with label-specific features. Empirical studies on twenty multi-label data sets reveal the effectiveness and efficiency of the proposed method. Our implementation of the proposed method is available online at: https://jiazhang-ml.pub/GRRO-master.zip.

Topological base plays a foundational role in topology theory. However, few works have been done to find the minimal base, which would make us difficult to interpret the internal structure of topological spaces. To address this issue, we provide a method to convert the finite topological space into Boolean matrix and some properties of minimal base are investigated. According to the properties, an algorithm(URMB) is proposed. Subsequently, the relationship between topological space and its sub-space with respect to the base is concentrated on by Boolean matrix. Then, a fast algorithm(MMB) is presented, which can avoid a mass of redundant computations. Finally, some numerical experiments are given to show the advantage and the effectiveness of MMB compared with URMB.