Multi-class Classification Using Hypersphere Support Vector Machines

In this article, we explore the implementation of multi-class classification using hypersphere support vector machines (SVMs). The core concept involves constructing multiple hyperspheres, each designed to encapsulate data points belonging to a specific class. Implementation typically begins by defining two key parameters for each hypersphere: the center coordinates and the radius. Computational methods leverage kernel functions—such as radial basis function (RBF) or polynomial kernels—to transform input data into higher-dimensional space where linear separation becomes feasible. Optimization algorithms like sequential minimal optimization (SMO) are employed to minimize the sphere volume while ensuring most training samples remain within their class-specific hypersphere. During inference, new data points are classified by determining which hypersphere's boundary they fall inside, often calculated using distance metrics in the kernel-induced feature space. This approach excels at handling complex decision boundaries and overlapping class distributions, as each hypersphere can adapt non-linearly to data geometry through kernel trick implementations.