abstract
- This work introduces a sequential clustering algorithm that combines unsupervised and supervised learning methodologies using ellipsoidal calculus and recurrent neural networks (RNNs). The unsupervised clustering algorithm (ULCA) identifies ellipsoidal sets for the data by applying Lagrange multipliers. These sets are then optimized with gradient descent to adjust their volume and orientation. For time-dependent data, the optimized ellipsoidal sets are updated dynamically by an RNN, which refines their center, orientation, and axis sizes in response to changes in the data. The ULCA is compared to density-based spatial clustering (DBSCAN) and K-means algorithms, showing superior accuracy without the need for pre-determined cluster numbers. Additionally, the convergence of the ULCA and RNN algorithms, working sequentially, is formally proven using Lyapunov stability theory, ensuring continuous classification of data that evolves over time. This study demonstrates the advantages of the proposed hybrid method over traditional clustering algorithms. © 2025