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Graph neural networks (GNNs) have gained sufficient attention and are applied to various domain tasks. At present, numerous pooling approaches are being proposed to aggregate node features and obtain node embeddings. However, current GNNs are black-box models that typically use a flat or single pooling step to aggregate nodes, which only considers the similarity between nodes within the cluster. These approaches ignore the influence of relationships within and between clusters in the learning process. To address this issue, we propose a novel multi-granular pooling method that aggregates nodes by simultaneously considering density and relationships among nodes and clusters. This method allows us to obtain multi-granular node-embedding clusters from GNN layers. The clusters in the current layer are built upon those in the previous layer, and these clusters change from fine to coarse as the number of clusters decreases during learning, which is achieved by using multi-granular pooling (MgrPool). Additionally, there is an inclusion relation between adjacent layers, and the node representation of each layer is established through the ratio of node distance within clusters to that between clusters. Finally, we conducted several experiments on node and graph classification tasks by combining GNN models with this pooling approach. The results demonstrate that our GNN-MgrPool model outperforms similar state-of-the-art algorithms and largely improves the interpretability of the learning process. [ABSTRACT FROM AUTHOR]

• We propose the concept of local rough approximation measures(LRAMs), which related theorems keep the property of RAMs in classical RS. • We introduce the concept of local knowledge distance(LKD), which takes into account the uncertainty induced by the discrepancy between provided lower and upper approximations. Besides, some related propositions, theorems, corollaries, and a novel GM are presented based on LKD. • The improved LRAMs are constructed by integrating LRAMs with the proposed GM. It demonstrates that the improved LRAMs maintain monotonic with the subdivision of the granularity. • The improved LRAMs is designed as a heuristic forward greedy algorithm, which is applied to the feature selection. The experiments validate that this algorithm is relatively reasonable from different sides. As the significant expansion of classical rough sets, local rough sets(LRS) is an effective model for processing large-scale datasets with finite labels. However, the process of establishing a category of monotonic uncertainty measure with strong distinguishing ability for LRS remains ambiguous. To construct this model, both the monotonicity of local lower approximation set and the local structure of granularity should be considered. First, the monotonicity of local rough approximation measure(LRAM) is established by the local lower and upper approximation sets. Subsequently, the local knowledge distance(LKD) is proposed to measure the uncertainty derived from the disparities between local upper and lower approximation sets. The more rational uncertainty measure associated LRAM with LKD is designed as a feature selection algorithm. Eventually, the experiments reflect the feasibility of the developed uncertainty measure. [ABSTRACT FROM AUTHOR]

As part of cognitive intelligence, concept cognition aims to view a concept from a comprehensive perspective and clearly grasp the concept intension (i.e., the typical attributes of the things referred to by the concept). Since knowledge graphs contain many entities that are beneficial for concept cognition, concept cognition for knowledge graphs is a promising research branch of concept cognition. Unlike general concept cognition, which selects all the attributes belonging to the concept and simultaneously eliminates other attributes, concept cognition for knowledge graphs focuses on determining the significance of concept-relevant attributes. Therefore, we propose a method of processing concept cognition for knowledge graphs that utilizes the hierarchical quotient space to determine attribute significance. Specifically, 1) this is the first study to propose and address concept cognition for knowledge graphs. 2) We propose a method of building a hierarchical quotient space for a concept in a knowledge graph that fully considers the characteristics of the concept-relevant attributes in the knowledge graph. 3) We propose using the distance between two hierarchical quotient spaces with and without a certain attribute to determine the significance of the concept-relevant attributes. Finally, the performance of our solution is measured from multiple aspects. [ABSTRACT FROM AUTHOR]

Strongly connected components (SCCs) are an important kind of subgraphs in digraphs. It can be viewed as a kind of knowledge in the viewpoint of knowledge discovery. In our previous work, a knowledge discovery algorithm called RSCC was proposed for finding SCCs of simple digraphs based on two operators, k -step R -related set and k -step upper approximation, of rough set theory (RST). RSCC algorithm can find SCCs more efficiently than Tarjan algorithm of linear complexity. However, on the one hand, as the theoretical basis of RST applied to SCCs discovery of digraphs, the theoretical relationships between RST and graph theory investigated in previous work only include four equivalences between fundamental RST and graph concepts relating to SCCs. The reasonability of using the two RST operators to find SCCs still need to be investigated. On the other hand, it is found that there are three SCCs correlations between vertices after we use three RST concepts, R -related set, lower and upper approximation sets, to analyze SCCs. RSCC algorithm ignores these SCCs correlations so that the efficiency of RSCC is affected negatively. For the above two issues, firstly, we explore the equivalence between the two RST operators and Breadth-First Search (BFS) which is one of the most basic graph search algorithms and the most direct way to find SCCs. These equivalences explain the reasonability of using the two RST operators to find SCCs, and enrich the content of the theoretical relationships between RST and graph theory. Secondly, we design a granulation strategy according to these three SCCs correlations. Then an algorithm called GRSCC for finding SCCs of simple digraphs based on granulation strategy is proposed. Experimental results show that GRSCC provides better performance to RSCC. [ABSTRACT FROM AUTHOR]

Molecular property prediction is an important task in drug discovery, especially the characterization of relationships between molecular substructures and their property. It is usually implemented by deep learning methods. However, deep model is a black-box that would lead to the prediction process and results are unbelievable and unreliable. To address these issues, researchers have begun to work on investigating explainable or substitute models for deep model. In this paper, an explainable framework of molecular property prediction with their multi-granularity representation (MgR) is proposed to characterize the contribution of substructures to prediction, called MgRX for short ('X' comes from 'eXplainable'). Specifically, the MgRX is constructed to denote the substructures' contribution of different granularity, in which each substructure is progressively finer from top to bottom. The finest substructures' contribution to target is implemented by the deep learning model with SHAP. Besides, several experiments are executed to analyze the effectiveness of the multi-granularity framework to molecular property. Based on above discussions, we develop a basic framework of quantitative characterization on substructures' contribution to property via multi-granularity. [ABSTRACT FROM AUTHOR]