Optimal scale selection in dynamic multi-scale decision tables based on sequential three-way decisions

A novel ANN-based feature subset selection in multi-scale granular ball neighborhood decision tables

As an effective data preprocessing method, feature subset selection has been widely explored in recent years. However, the feature subset selection for the Wu-Leung model and its extended model involves high time complexity. Therefore, we combine the granular ball neighborhood rough set with the Wu-Leung model. A multi-scale granular ball neighborhood decision table is designed. Meanwhile, the weight of features are not the same at different scales and are correlated with the decision. We combine the artificial neural network (ANN) with the multi-scale granular ball neighborhood decision table to calculate feature weights. Based on this, the weight-based feature subset selection algorithm, and the positive region increment-based feature subset selection algorithm are designed. Most importantly, in order to overcome the situation of missing or missing labels during data collection, we design an unsupervised feature subset selection algorithm. Finally, the effectiveness and feasibility of the proposed three algorithms are verified through experimental comparison and analysis. The advantages of the proposed algorithm are analyzed.

Optimal Scale Combination Selection Integrating Three-Way Decision With Hasse Diagram

Multi-scale decision system (MDS) is an effective tool to describe hierarchical data in machine learning. Optimal scale combination (OSC) selection and attribute reduction are two key issues related to knowledge discovery in MDSs. However, searching for all OSCs may result in a combinatorial explosion, and the existing approaches typically incur excessive time consumption. In this study, searching for all OSCs is considered as an optimization problem with the scale space as the search space. Accordingly, a sequential three-way decision model of the scale space is established to reduce the search space by integrating three-way decision with the Hasse diagram. First, a novel scale combination is proposed to perform scale selection and attribute reduction simultaneously, and then an extended stepwise optimal scale selection (ESOSS) method is introduced to quickly search for a single local OSC on a subset of the scale space. Second, based on the obtained local OSCs, a sequential three-way decision model of the scale space is established to divide the search space into three pair-wise disjoint regions, namely the positive, negative, and boundary regions. The boundary region is regarded as a new search space, and it can be proved that a local OSC on the boundary region is also a global OSC. Therefore, all OSCs of a given MDS can be obtained by searching for the local OSCs on the boundary regions in a step-by-step manner. Finally, according to the properties of the Hasse diagram, a formula for calculating the maximal elements of a given boundary region is provided to alleviate space complexity. Accordingly, an efficient OSC selection algorithm is proposed to improve the efficiency of searching for all OSCs by reducing the search space. The experimental results demonstrate that the proposed method can significantly reduce computational time.

Optimal scale combination selection for inconsistent multi-scale decision tables

Hierarchical structured data are very common for data mining and other tasks in real-life world. How to select the optimal scale combination from a multi-scale decision table is critical for subsequent tasks. At present, the models for calculating the optimal scale combination mainly include lattice model, complement model and stepwise optimal scale selection model, which are mainly based on consistent multi-scale decision tables. The optimal scale selection model for inconsistent multi-scale decision tables has not been given. Based on this, firstly, this paper introduces the concept of complement and lattice model proposed by Li and Hu. Secondly, based on the concept of positive region consistency of inconsistent multi-scale decision tables, the paper proposes complement model and lattice model based on positive region consistent and gives the algorithm. Finally, some numerical experiments are employed to verify that the model has the same properties in processing inconsistent multi-scale decision tables as the complement model and lattice model in processing consistent multi-scale decision tables. And for the consistent multi-scale decision table, the same results can be obtained by using the model based on positive region consistent. However, the lattice model based on positive region consistent is more time-consuming and costly. The model proposed in this paper provides a new theoretical method for the optimal scale combination selection of the inconsistent multi-scale decision table.