Revisited Support Vector Machines: A Unified Joint Optimization Framework with Nyström Approximation for Scalable Adaptive Learning

Nassou Gongon Benjamin, Noulapeu Ngaffo, Patrick Njionou Sadjang

The theoretical elegance of Support Vector Machines (SVMs), grounded in statistical learning theory, establishes them as a reference for robust classification. However, in the era of Big Data, classical SVMs face two major bottlenecks: the prohibitive cubic complexity $\mathcal{O}(N^3)$ of training and the rigidity of static kernels. Traditional methodologies treat kernel selection as a discrete, "brute-force" GridSearch problem, effectively decoupling the learning of data representation from the optimization of the decision boundary. This paper proposes a paradigm shift with a so-called "Revisited SVM", a unified framework that recasts the learning process as a continuous %bi-level joint optimization problem. We derive a novel objective function $J(α, θ)$ that allows for the simultaneous optimization of dual Lagrange multipliers and kernel hyper-parameters. To solve this challenging non-convex problem efficiently, we introduce a hybrid Block Coordinate Ascent (BCA) algorithm, tightly integrated with Nyström-based low-rank approximation, which drastically reduces computational complexity to $\mathcal{O}(Nm)$. Extensive experiments conducted across four heterogeneous domains…