Hypersphere Support Vector Machine

In machine learning, Support Vector Machines (SVMs) represent one of the most common classification algorithms. Among these, Hypersphere Support Vector Machine (HSVM) is a specialized one-class SVM variant that constructs classifiers using hypersphere boundaries. Unlike traditional binary SVMs that require labeled data from two classes, HSVM only needs labeled data from a single target class, making it particularly suitable for one-class classification problems such as anomaly detection and novelty recognition. The algorithm implementation typically involves solving an optimization problem to find the smallest hypersphere that encloses most of the target class data points in the feature space. Key computational steps include: - Mapping input data to high-dimensional feature space using kernel functions (RBF kernel is commonly used) - Formulating the quadratic programming problem to minimize sphere volume while capturing data distribution - Calculating decision function based on distance to sphere center for classification In practical applications, HSVM has been widely adopted across various domains including image processing (for defect detection), medical diagnosis (identifying rare diseases), and industrial quality control (detecting manufacturing anomalies). The implementation often leverages libraries like scikit-learn's OneClassSVM with appropriate kernel selection and parameter tuning for optimal performance.