Multi-agent cooperation is essential for tasks that require collaboration to achieve optimal performance or cannot be completed by individual agents alone. These tasks often necessitate a divide-and-conquer strategy, where subgoals are allocated to individual agents or groups. By integrating coalition formation concepts from cooperative game theory, we demonstrate the implicit learning of coalition formation and task assignments, resulting in emergent cooperative behavior. We propose a novel COaLition LABeling technique for Multi-Agent Reinforcement Learning (COLLAB-MARL) to encourage coalition formation and introduce a structural entropy measure to detect the emergence of coalitions and cooperative behavior. Compared to classical MARL methods, COLLAB-MARL is more effective, explainable, and easier to implement. Experiments on state-of-the-art cooperative MARL benchmarks show that our method’s mean return outperforms the strongest baselines by 8.4% on average. Additionally, visualization and structural entropy analysis reveal that COLLAB-MARL effectively learns meaningful cooperative behavior. The source code is available at https://github.com/SELGroup/collab.

Superpixel segmentation is a foundation for many higher-level computer vision tasks, such as image segmentation, object recognition, and scene understanding. Existing graph-based superpixel segmentation methods typically concentrate on the relationships between a given pixel and its directly adjacent pixels while overlooking the influence of non-adjacent pixels. These approaches do not fully leverage the global information in the graph, leading to suboptimal segmentation quality. To address this limitation, we present SIT-HSS, a hierarchical superpixel segmentation method based on structural information theory. Specifically, we first design a novel graph construction strategy that incrementally explores the pixel neighborhood to add edges based on 1-dimensional structural entropy (1D SE). This strategy maximizes the retention of graph information while avoiding an overly complex graph structure. Then, we design a new 2D SE-guided hierarchical graph partitioning method, which iteratively merges pixel clusters layer by layer to reduce the graph’s 2D SE until a predefined segmentation scale is achieved. Experimental results on three benchmark datasets demonstrate that the SIT-HSS performs better than state-of-the-art unsupervised superpixel segmentation algorithms. The source code is available at https://github.com/SELGroup/SIT-HSS.

Semi-supervised clustering leverages prior information in the form of constraints to achieve higher-quality clustering outcomes. However, most existing methods struggle with large-scale datasets owing to their high time and space complexity. Moreover, they encounter the challenge of seamlessly integrating various constraints, thereby limiting their applicability. In this paper, we presentScalableSemi-supervised clustering viaStructuralEntropy (SSSE), a novel method that tackles scalable datasets with different types of constraints from diverse sources to perform both semi-supervised partitioning and hierarchical clustering, which is fully explainable compared to deep learning-based methods. Specifically, we design objectives based on structural entropy, integrating constraints for semi-supervised partitioning and hierarchical clustering. To achieve scalability on data size, we develop efficient algorithms based on graph sampling to reduce the time and space complexity. To achieve generalization on constraint types, we formulate a uniform view for widely used pairwise and label constraints. Extensive experiments on real-world clustering datasets at different scales demonstrate the superiority of SSSE in clustering accuracy and scalability with different constraints. Additionally, Cell clustering experiments on single-cell RNA-seq datasets demonstrate the functionality of SSSE for biological data analysis.

Semi-supervised clustering techniques have emerged as valuable tools for leveraging prior information in the form of constraints to improve the quality of clustering outcomes. Despite the proliferation of such methods, the ability to seamlessly integrate various types of constraints remains limited. While structural entropy has proven to be a powerful clustering approach with wide-ranging applications, it has lacked a variant capable of accommodating these constraints. In this work, we present Semi-supervised clustering via Structural Entropy (SSE), a novel method that can incorporate different types of constraints from diverse sources to perform both partitioning and hierarchical clustering. Specifically, we formulate a uniform view for the commonly used pairwise and label constraints for both types of clustering. Then, we design objectives that incorporate these constraints into structural entropy and develop tailored algorithms for their optimization. We evaluate SSE on nine clustering datasets and compare it with eleven semi-supervised partitioning and hierarchical clustering methods. Experimental results demonstrate the superiority of SSE on clustering accuracy with different types of constraints. Additionally, the functionality of SSE for biological data analysis is demonstrated by cell clustering experiments conducted on four single-cell RNA-seq datasets.

Skin lesion segmentation is a fundamental task in dermoscopic image analysis. The complex features of pixels in the lesion region impede the lesion segmentation accuracy, and existing deep learning-based methods often lack interpretability to this problem. In this work, we propose a novel unsupervised Skin Lesion sEgmentation framework based on structural entropy and isolation forest outlier Detection, namely SLED. Specifically, skin lesions are segmented by minimizing the structural entropy of a superpixel graph constructed from the dermoscopic image. Then, we characterize the consistency of healthy skin features and devise a novel multi-scale segmentation mechanism by outlier detection, which enhances the segmentation accuracy by leveraging the superpixel features from multiple scales. We conduct experiments on four skin lesion benchmarks and compare SLED with nine representative unsupervised segmentation methods. Experimental results demonstrate the superiority of the proposed framework. Additionally, some case studies are analyzed to demonstrate the effectiveness of SLED.