Invariances in Kernel Methods: From Samples to Objects

This paper presents a general method for incorporating prior knowledge into kernel methods such as Support Vector Machines. It applies when the prior knowledge can be formalized by the description of an object around each sample of the training set, assuming that all points in the given object share the same desired class. A~number of implementation techniques of this method, based on hard geometrical objects and soft objects based on distributions are considered. Tangent vectors are extensively used for object construction. Empirical results on one artificial dataset and two real datasets of Electro-Encephalogram signals and face images demonstrate the usefulness of the proposed method. The method could establish a foundation for an information retrieval and person identification systems.