Border-sensitive learning in generalized learning vector quantization: an alternative to support vector machines

Learning vector quantization (LVQ) algorithms as powerful classifier models for class discrimination of vectorial data belong to the family of prototype-based classifiers with a learning scheme based on Hebbian learning as a widely accepted neuronal learning paradigm. Those classifier approaches estimate the class distribution and generate from this a class decision for vectors to be classified. The estimation can be done by the determination of class-typical sensitive prototypes inside the class distribution area like in LVQ or by detection of the class borders for class discrimination as preferred by support vector machines (SVMs). Both strategies provide advantages and disadvantages depending on the given classification task. Whereas LVQs are very intuitive and usually process the data during learning in the data space, frequently equipped with variants of the Euclidean metric, SVMs implicitly map the data into a high-dimensional kernel-induced feature space for better separation. In this Hilbert space, the inner product is compliant to the kernel. However, this implicit mapping makes a vivid interpretation more difficult. As an alternative, we propose in this paper two modifications of LVQ to make it comparable to SVM: first border-sensitive learning is introduced to achieve border-responsible prototypes comparable with support vectors in SVM. Second, kernel distances for differentiable kernels are considered, such that prototype learning takes place in a metric space isomorphic to the feature mapping space of SVM. Combination of both features gives a powerful prototype-based classifier while keeping the easy interpretation and the intuitive Hebbian learning scheme of LVQ.