High-dimensional and weakly supervised (HiDWS) data present significant challenges for traditional machine learning and pattern recognition. Although semi-supervised feature selection has shown effectiveness in improving the quality of HiDWS data, existing methods remain sensitive and lack robustness due to the unreliability of unlabeled data learning and the uncertainty in modeling processes. Hence, this study focuses on a multi-granularity zentropy modeling (Ze-MGM) framework with model-agnostic for highly-accuracy and robust semi-supervised feature selection. Unlike existing methods, Ze-MGM does not rely on specific settings such as rough or fuzzy set assumptions and can effectively capture the granularity of information under high-dimensional and weakly supervised data scenarios. Specifically, we first introduce a strategic soft label ($S2-$S2-Label) learning method that integrates object proximity and classification certainty to reduce uncertainty between features and labels. This method also enables the selection of compatible instances, thereby mitigating the negative impact of incompatible objects on label learning. Subsequently, a multi-granularity knowledge space and zentropy uncertainty measure are constructed by analyzing the hierarchical relationships among labels, decisions, and specific classes, which enables accurate multi-granularity knowledge representation and multi-granularity uncertainty characterization in HiDWS data modeling processing. Finally, two multi-granularity significance measures based on multi-granularity uncertainty are defined for feature evaluation and selection via a semi-supervised paradigm. Extensive experiments on multiple benchmark datasets demonstrate that the proposed Ze-MGM method achieves superior generalization performance and robustness compared to state-of-the-art methods.

Multigranularity knowledge modeling is an influential study for information processing and knowledge discovery in artificial intelligence (AI). A central research focus is the multigranularity representation and learning of knowledge structures. Among them, fuzzy rough sets (FRSs) have emerged as a representative method for characterizing uncertain knowledge. However, the existing FRS studies still exhibit two limitations: low robustness in knowledge acquisition and incomplete characterization of uncertainty. Hence, this article proposes a zentropy-enhanced multigranularity knowledge modeling framework for robust feature selection (ZeMG-FS). Specifically, we design a fast and adaptive multigranularity information granulation mechanism based on generalized granular-ball generation to effectively capture data distributions embedded in complex data. Then, the fuzzy rough approximation method is incorporated into the representation of multigranularity knowledge. Furthermore, we analyze the fundamental relationships and structures of the multigranularity knowledge model to introduce a novel multilevel zentropy. Unlike existing entropy measures, the primary consideration of the proposed zentropy is to match and enhance the performance of the proposed model. Finally, we design two feature evaluation criteria grounded in the model and apply them to feature selection. Extensive experiments demonstrate that our proposed methods achieve superior robustness and effectiveness compared with state-of-the-art approaches.

In many real-world scenarios, data unreliability and information-processing uncertainty seriously affect the credibility and reliability of artificial intelligence models. Probing a valuable cognitive learning paradigm is crucial for supporting and implementing the proposed artificial intelligence hypothesis. Concept-cognitive learning (CCL), as an emerging cognitive learning technology, investigates the knowledge-learning process using limited data through the lens of concepts. However, the existing CCL research has one prevalent disadvantage: instability and complex cognition. Thus, this work focuses on constructing an effective and interpretable cognitive learning paradigm for acquiring knowledge. Inspired by a multi-granularity knowledge representation, this paper proposes an adaptive and robust fuzzy knowledge representation paradigm, namely granular-ball concept-cognitive learning(GB-CCL). Unlike existing CCL systems, GB-CCL is a non-parameter cognitive learning system that achieves more accurate, faster adaptive capabilities for concept learning. The concept acquired through cognitive learning is structured conceptual knowledge, which is naturally interpretable and robust. Finally, extensive experiments verify that GB-CCL is an effective cognitive learning method with significantly better performance than state-of-the-art models in classification and robust learning.

Multigranularity data analysis has recently become an active research topic in the intelligent computing and data mining fields. Feature selection via multigranularity data analysis is an effective tool for characterizing hierarchical data and enhancing the accuracy of the results. Although the multigranularity data analysis method has been widely adopted for feature selection, existing studies still present one prevalent disadvantage: multigranularity data analysis mostly focuses on information presented at a single granularity while ignoring the hierarchical structure of multigranularity data, which is contrary to the nature of multigranularity. Hence, this article proposes a multigranularity data analysis with a zentropy uncertainty measure for efficient and robust feature selection. Specifically, a consistent degree is first introduced to obtain optimal granularity combinations and establish an efficient neighborhood model for multigranularity information processing. Then, a novel and robust uncertainty measure is developed by integrating the multigranularity information, namely the zentropy-based measure. Considering its accuracy among uncertainty measures, two important measures are further designed and applied to feature selection. Extensive experiments demonstrate that the proposed method can achieve better robustness and classification performance than other state-of-the-art methods.

The feature selection based on the rough set (RS) theory has been an active research topic in data mining and knowledge discovery. Fuzzy RSs (FRSs), an efficient tool to process the inconsistency between features and decisions, have attracted attention to the problems of feature selection. However, most FRSs-based feature selection methods pay much attention to the approximation space while ignoring the interaction between different levels. Note that the single-level feature selection method, depending on the boundary objects, is easily influenced by the noise data and cannot integrate multiple granular levels to evaluate features accurately. Therefore, this article proposes an efficient and robust feature selection approach based on the neighborhood-aware model and zentropy measure. Specifically, we first define a neighborhood-aware FRS (NAFRS) with weighted fuzzy relation to improve the antinoise ability of FRSs. Then, we propose a fuzzy granule zentropy (FGZE) measure based on zentropy by analyzing the granular level relation in NAFRS. Moreover, a significance measure with FGZE is designed and applied to feature selection. Finally, the experimental results of our method on 22 datasets by comparing it with 12 representative feature selection methods demonstrate the antinoise and the classification ability of the proposed method.

Feature selection and entropy theory are two efficacious data analysis tools for investigating uncertainty information processing in artificial intelligence. The fruitful marriage of the two has been an active research topic in knowledge discovery. Currently, most feature selection methods via entropy theory mainly focus on the information measures at a single granular level. However, it ignores the interaction between granular levels, which leads to the poor stability and accuracy of related methods. Hence, this article proposes a novel zentropy-based uncertainty measure to design a feature selection method by exploiting the granular level structure in knowledge space. Subsequently, by analyzing the granular level structure in decision data, the zentropy-based uncertainty measure and its properties are designed and analyzed to depict the uncertainty knowledge from whole and internal. Moreover, two importance measures are defined to evaluate features based on the designed uncertainty measure, and then a corresponding feature selection algorithm is developed. Finally, some experiments are carried out on public datasets to demonstrate that the proposed method can achieve state-of-the-art performance among methods, especially regarding stability and classification accuracy.

Knowledge discovery of heterogeneous data is an active topic in knowledge engineering. Feature selection for heterogeneous data is an important part of effective data analysis. Although there have been many attempts to study the feature selection for heterogeneous data, there are still some challenges, such as the unbalanced problem between the stability and validity of the designed model. Hence, this paper focuses on how to design an effective and robust heterogeneous feature selection method, namely a zentropy-based uncertainty measure for heterogeneous feature selection(Ze-HFS). Different from other entropy-based uncertainty measures, the proposed method does not consider single-level information measures but systematically analyzes and integrates the information between different granular levels, which has an obvious advantage in the study of heterogeneous data knowledge discovery. Specifically, a heterogeneous distance metric is first introduced to construct heterogeneous neighborhood granules and heterogeneous neighborhood rough sets(HNRS). Then, the zentropy-based uncertainty measure is developed by analyzing the granular level structure in the HNRS model. Finally, two significant measures based on the above research are designed for heterogeneous feature selection. Compared with other state-of-the-art methods, the experimental results on 18 public datasets demonstrate the robustness and effectiveness of the proposed method.

Abstract The semantic link network (SLN) is the extension of the hyperlink Web by attaching semantics to hyperlinks. It is an approach to construct a semantic overlay on Web resources. The specification of the semantics of the SLN model is an essential issue of SLN application. This paper proposes a modeling language for SLN consisting of an algebraic definition for SLN, a SLN metamodel and a Unified Modeling Language (UML) profile for SLN. The SLN metamodel specifies the primitives of the modeling language. The UML profile for SLN defines the specific syntax on SLN to make the modeling language understandable and usable. The development of the SLN builder implementing this language and the graphical SLN browser is introduced. This work is a part of the SLN model. Copyright © 2007 John Wiley & Sons, Ltd.