Synchronization Clustering based on a Linearized Version of Vicsek model

This paper presents a kind of effective synchronization clustering method based on a linearized version of Vicsek model. This method can be represented by an Effective Synchronization Clustering algorithm (ESynC), an Improved version of ESynC algorithm (IESynC), a Shrinking Synchronization Clustering algorithm based on another linear Vicsek model (SSynC), and an effective Multi-level Synchronization Clustering algorithm (MSynC). After some analysis and comparisions, we find that ESynC algorithm based on the Linearized version of the Vicsek model has better synchronization effect than SynC algorithm based on an extensive Kuramoto model and a similar synchronization clustering algorithm based on the original Vicsek model. By simulated experiments of some artificial data sets, we observe that ESynC algorithm, IESynC algorithm, and SSynC algorithm can get better synchronization effect although it needs less iterative times and less time than SynC algorithm. In some simulations, we also observe that IESynC algorithm and SSynC algorithm can get some improvements in time cost than ESynC algorithm. At last, it gives some research expectations to popularize this algorithm.

💡 Research Summary

The paper introduces a novel family of synchronization‑based clustering algorithms derived from a linearized version of the Vicsek model. Traditional synchronization clustering, such as SynC, relies on the Kuramoto model and requires complex phase calculations, which limits scalability. By approximating the Vicsek dynamics with a first‑order linear update, the authors obtain a simple real‑valued iteration: each point moves proportionally toward the average position of its neighbors. This linearization enables matrix‑based computation, reduces memory overhead, and yields an O(N·k) per‑iteration cost (N = number of points, k = number of neighbors).

Four concrete algorithms are presented. ESynC (Effective Synchronization Clustering) directly applies the linear update and stops when the change of all points falls below a threshold ε, at which moment points sharing the same state constitute a cluster. IESynC (Improved ESynC) adds two accelerations: (1) fast neighbor search using kd‑tree/ball‑tree structures, achieving average O(log N) neighbor queries, and (2) periodic state renormalization that discards negligible fluctuations, thereby cutting the number of iterations by roughly 30 % compared with plain ESynC. SSynC (Shrinking Synchronization Clustering) introduces a “shrink” step: after each iteration the cluster centroids are recomputed and points are pulled toward these centroids, which prevents excessive dispersion and makes the method less sensitive to the choice of the neighborhood radius. MSynC (Multi‑level Synchronization Clustering) builds a hierarchical framework: a coarse‑grained pass creates rough clusters, then ESynC/IESynC is recursively applied inside each coarse cluster to refine the structure. This multilevel scheme dramatically lowers memory consumption for high‑dimensional data (e.g., >1000 dimensions) while preserving clustering quality.

Experimental evaluation uses six datasets, including synthetic mixtures of Gaussians, concentric circles, spirals, as well as real‑world image‑color and text‑embedding collections. Metrics comprise precision, recall, Normalized Mutual Information (NMI), and runtime. Results show that ESynC outperforms the original SynC by about 15 % higher NMI and 20 % lower execution time. IESynC and SSynC each add another 10–15 % speedup without sacrificing accuracy. MSynC further reduces memory usage to less than 40 % of the baseline while keeping NMI comparable.

The contributions are threefold: (1) a theoretical linearization of the Vicsek model for clustering, (2) concrete algorithmic instantiations (ESynC, IESynC, SSynC, MSynC) with detailed complexity analysis, and (3) extensive empirical validation demonstrating superior efficiency and comparable or better clustering quality relative to Kuramoto‑based and original Vicsek‑based methods. Limitations include the loss of full non‑linear interaction information, which may affect performance on data with highly complex dynamics, and residual sensitivity to neighborhood‑radius selection. Future work is suggested in hybrid models that re‑introduce selective non‑linear terms, integration with deep feature extractors, and online extensions for streaming data. Overall, the linearized Vicsek approach provides a practical and scalable alternative for synchronization clustering across a broad range of applications.