Adaptive tangent distances in generalized learning vector quantization for transformation and distortion invariant classification learning

We propose a learning vector quantization algorithm variant for prototype-based classification learning with adaptive tangent distance learning. Tangent distances were developed to achieve dissimilarity measures invariant with respect to transformations and distortions like rotation, noise, etc.. Usually, these tangent distances are predefined in applications or are estimated in preprocessing. We introduce in this paper a generalized learning vector quantizer (GLVQ) with an online adaptation scheme for tangent distances. The adaptation takes place as a stochastic gradient descent learning accompanying the usual online prototype learning. In this way, class discriminative tangents are learned contributing to a better classification performance. Further, the resulting update schemes can be seen as a special type of local matrix learning in GLVQ. In this paper, we provide the full mathematical theory behind the derived tangent distance adaptation rule and demonstrate the classification ability of the resulting GLVQ model in comparison to state-of-the-art tangent distance based classifiers in the field.