Active clustering enhances traditional semi-supervised clustering by introducing machine-led interaction, where informative constraints are dynamically selected and posed to humans. This enables goal-driven interaction and reduces the number of required constraints for achieving high-quality clustering. In this paper, we propose a newly designed Active Clustering framework with Minimal Constraint Graph (ACMCG). ACMCG operates on two cooperating tailored sparse graphs: a tree-structured graph (clustering tree) representing the nested clustering result, and a minimal constraint graph that supports constraint deduction during iterative refinement. In each refinement round, (a) the most suspicious edge in the tree is identified for constraint verification; (b) if a cannot-link constraint is confirmed, a pruning-and-grafting approach is performed to refine the clustering tree, guided by our proposed constraint deduction strategies; (c) the constraint is either deduced from the minimal constraint graph using transitive and probabilistic deduction, or obtained via user interaction when deduction fails. Extensive experiments across diverse domains demonstrate that ACMCG consistently outperforms both classical and state-of-the-art methods in accuracy, while significantly reducing the number of user-provided constraints and maintaining low computational cost, highlighting its cost-effectiveness in real-world applications.

Active constraint-based clustering enhances semi-supervised clustering through a machine-led interaction process. This approach dynamically selects the most informative constraints to query, minimizing the number of human annotations required. Existing methods face three key challenges in real-world applications: scalability, timeliness, and robustness against user annotation errors. In this work, we propose a robust and high-efficiency Active Clustering framework with Multi-user Collaboration (ACMC). ACMC constructs a diffusion tree using the nearest-neighbor technique and employs a multi-user online collaboration framework to iteratively refine clustering results. In each iteration: (a) nodes with high uncertainty and representativeness are selected in batch; (b) well-designed multi-user asynchronous query categorizes selected nodes using neighborhood sets, reducing individual workloads and improving overall timeliness; (c) user-provided constraints and newly discovered categories are synchronized, with user confidences dynamically updated to enhance robustness against erroneous annotations; (d) categorized nodes, stored in neighborhood sets, serve as sources in the diffusion tree to refine the clusters. Experimental results demonstrate that ACMC outperforms baseline methods in terms of clustering quality, scalability, and robustness against user annotation errors.

Clustering is inherently subjective: without additional guidance, it cannot independently determine the most appropriate grouping. This limitation underscores the necessity of active constrained clustering, which integrates user preferences (expressed as constraints) into the clustering process. However, existing methods of active constrained clustering encounter significant challenges when processing large-scale datasets, thereby restricting their practical application. To address this issue, we introduce Cluster Skeleton Exploration (CSE), a novel clustering method that effectively scales to large datasets while maintaining high clustering quality. In CSE, the dataset is represented as a cluster skeleton, a directed sparse graph. Each weakly connected component within this skeleton corresponds to a cluster. Through iterative constraint queries posed by the user, CSE dynamically refines the cluster skeleton until the desired clustering structure is achieved. CSE demonstrates exceptional scalability, significantly outperforming state-of-the-art methods. Extensive experiments conducted on diverse real-world datasets validate its superior clustering quality.

Clustering is fundamentally a subjective task: a single dataset can be validly clustered in various ways, and without further information, clustering systems cannot determine the appropriate clustering to perform. This underscores the importance of integrating constraints into clustering, enabling users to convey their preferences to the system. Active constraint-based clustering approaches prioritize the identification of the most valuable constraints to inquire about, striving to achieve effective clustering with the minimal number of constraints needed. We propose an A ctive C lustering with D iffusion M odel (ACDM). ACDM applies the nearest-neighbor technique to construct a diffusion graph, and utilizes an online framework to refine the clustering result iteratively. In each iteration, (a) nodes with high uncertainty and representativeness are selected in batch mode, (b) then a novel neighborhood-set-based query is used for categorizing the selected nodes, using pairwise constraints, and (c) the categorized nodes are used as source nodes in the diffusion model for cluster refinement. We experimentally demonstrate that ACDM outperforms state-of-the-art methods in terms of clustering quality and scalability.

Computational models of musculoskeletal systems are essential tools for understanding how muscles, tendons, bones, and actuation signals generate motion. In particular, the OpenSim family of models has facilitated a wide range of studies on diverse human motions, clinical studies of gait, and even non-human locomotion. However, biological structures with many joints, such as fingers, necks, tails, and spines, have been a longstanding challenge to the OpenSim modeling community, especially because these structures comprise numerous bones and are frequently actuated by extrinsic muscles that span multiple joints-often more than three-and act through a complex network of branching tendons. Existing model building software, typically optimized for limb structures, makes it difficult to build OpenSim models that accurately reflect these intricacies. Here, we introduce ArborSim, customized software that efficiently creates musculoskeletal models of highly jointed structures and can build branched muscle-tendon architectures. We used ArborSim to construct toy models of articulated structures to determine which morphological features make a structure most sensitive to branching. By comparing the joint kinematics of models constructed with branched and parallel muscle-tendon units, we found that among various parameters-the number of tendon branches, the number of joints between branches, and the ratio of muscle fiber length to muscle tendon unit length-the number of tendon branches and the number of joints between branches are most sensitive to branching modeling method. Notably, the differences between these models showed no predictable pattern with increased complexity. As the proportion of muscle increased, the kinematic differences between branched and parallel models units also increased. Our findings suggest that stress and strain interactions between distal tendon branches and proximal tendon and muscle greatly affect the overall kinematics of a musculoskeletal system. By incorporating complex muscle-tendon branching into OpenSim models using ArborSim, we can gain deeper insight into the interactions between the axial and appendicular skeleton, model the evolution and function of diverse animal tails, and understand the mechanics of more complex motions and tasks.

Controlling soft robots with precision is a challenge due to the difficulty of constructing models that are amenable to model-based control design techniques. Koopman operator theory offers a way to construct explicit dynamical models of soft robots and to control them using established model-based control methods. This approach is data driven, yet yields an explicit control-oriented model rather than just a “black-box” input-output mapping. This work describes a Koopman-based system identification method and its application to model predictive control (MPC) design for soft robots. Three MPC controllers are developed for a pneumatic soft robot arm via the Koopman-based approach, and their performances are evaluated with respect to several real-world trajectory following tasks. In terms of average tracking error, these Koopman-based controllers are more than three times more accurate than a benchmark MPC controller based on a linear state-space model of the same system, demonstrating the utility of the Koopman approach in controlling real soft robots.