The book describes the development and performance of proximal classifiers, a class of kernel-based regularized mean square error type classifier that learns within the penalized modeling paradigm. The name proximal classifier indicates the fact of classification of a test pattern by its proximity either to a hyperplane or to a class centroid. The basic idea of the nonparallel plane classifier is to model each class of data by fitting separate hyperplane through it. A computationally efficient binary Nonparallel Plane Proximal Classifier (NPPC) is described in detail along with its nonlinear extension. NPPC is also extended to classify multiclass data. A new approach of multiclass data classification through vector-valued regression technique by the proximity to a class centroid is described in detail. These classifiers are applied to discriminate cancerous tissue samples from gene microarray data. The book provides a complete literature survey in the field of Support Vector Machine (SVM). It includes mathematical models, detailed solution procedures and algorithms of the different proximal classifiers with hands-on examples and well-documented MATLAB programs.