Transfer learning in classification based on manifolc. models and its relation to tangent metric learning

The paper deals with realizations of transfer learning for classification, i. e. the adaptation of a classifier model to a changed data distribution. This change could be a data drift or a more complex transformation. We propose to model those data changes by manifolds describing continuous transformations of the data. This description can be seen as a generalization of function based transfer models considered so far. The manifold description of the transfer function allows either to adjust the classifier model to the changed data distribution or a back-transformation of those data to the original data space. To get the approach feasible, the manifold is approximated by the affine part of the Taylor expansion of the manifold structure. Moreover, the affine approximation shows mathematical correspondences to tangent metric leaning, which was developed for handling of data with drifts in classification methods. The paper provides the mathematical background for manifold based transfer data learning. Further, the approach is exemplarily applied for the generalized learning vector quantization classifier. This classifier is a prominent method which frequently achieves a high performance and a robust behavior while the classifier complexity is low compared to more sophisticated approaches like deep learning architectures or support vector machines. Moreover, the good interpretability of learning vector quantization classifiers also contributes to an intuitive practical understanding of transfer learning.