Enclosing Machine Learning for Class Description

A novel machine learning paradigm, i.e. enclosing machine learning based on regular geometric shapes was proposed. It adopted regular minimum volume enclosing and bounding geometric shapes (sphere, ellipsoid, and box) or their unions and so on to obtain one class description model and thus imitate the human "Cognizing" process. A point detection and assignment algorithm based on the one class description model was presented to imitate the human "Recognizing" process. To illustrate the concept and algorithm, a minimum volume enclosing ellipsoid (MVEE) strategy for enclosing machine learning was investigated in detail. A regularized minimum volume enclosing ellipsoid problem and dual form were presented due to probable existence of zero eigenvalues in regular MVEE problem. To solve the high dimensional one class description problem, the MVEE in kernel defined feature space was presented. A corresponding dual form and kernelized Mahalanobis distance formula was presented. We investigated the performance of the enclosing learning machine via benchmark datasets and compared with support vector machines (SVM).