Information geometry of topology preserving adaptation

We consider adaptation by topologically smooth transformations with applications to environment and speaker adaptation for robust speech recognition. Specifically, the tradeoff between global affine transformations that fail to capture local variation but preserve topology and local class dependent bias transformations that have more resolution but may destroy the topology of the reference model is addressed. We cast the problem of topology preservation of the reference model in an information divergence geometry framework and derive a class of alternating minimization algorithms that aims to preserve topology explicitly during adaptation.