Non linear clustering optimization for scalable data mining in cloud and quantum computing environments
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Nonlinear optimization, clustering, cloud computing, quantum computing, scalable data mining, dynamical systemsAbstract
The article outlines an optimization model of nonlinear clustering that could strike a balance between the use of the complex mathematical models and scalability to the cloud and quantum computing systems. It is based on the classical clustering methodology, but utilizes nonlinear objective functions, graph, and manifold-sensitive regularization, and explicit resource constraints to find the subtle, non-Euclidean structures in heterogeneous data. The approach combines the dynamical systems analysis, PDE-based manifold models and quantum optimization mappings (QUBO/Ising), which ensure the theoretical soundness of the approach; specifically, the approach is coercive, has minimizers, and block-coordinate convergence guarantees. The system architecture makes use of the hybrid cloud-quantum orchestration, in which the workload clustering will dynamically relocate to distributed classical resources and quantum processors to optimize time, memory, power, and qubit usage. Evolutionary search also has adaptability, and neural feature embedding, as well as quantum solvers, are used to improve adaptability. Discrete assignment optimization under hardware-friendly penalties. These large-scale studies of synthetic manifolds, high-dimensional benchmarking, and real-world benchmarking reveal a much higher clustering accuracy, scaling, and resource efficiency than k-means, spectral clustering, and kernel methods, and density-based baselines. Ablation experiments prove the role of each nonlinear and quantum-inspired element and transparency protocols are made with regard to cloud and QPU systems. The findings make nonlinear analysis a fundamental component of unsupervised learning in the present day, and apply to the dynamical systems modelling, interpretable data mining, and resource-sensitive algorithm design. The model offers an intellectual roadmap to the future of cloud-quantum clustering systems that will take into account the needs of engineering, scientific, and industrial discovery.
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