Learning of Variability for Invariant Statistical Pattern Recognition

In many applications, modelling techniques are necessary which take into account the inherent variability of given data. In this paper, we present an approach to model class specific pattern variation based on tangent distance within a statistical framework for classification. The model is an effective means to explicitly incorporate invariance with respect to transformations that do not change class-membership like e.g. small affine transformations in the case of image objects. If no prior knowledge about the type of variability is available, it is desirable to learn the model parameters from the data. The probabilistic interpretation presented here allows us to view learning of the variational derivatives in terms of a maximum likelihood estimation problem. We present experimental results from two different real-world pattern recognition tasks, namely image object recognition and automatic speech recognition. On the US Postal Service handwritten digit recognition task, learning of variability achieves results well comparable to those obtained using specific domain knowledge. On the SieTill corpus for continuously spoken telephone line recorded German digit strings the method shows a significant improvement in comparison with a common mixture density approach using a comparable amount of parameters. The probabilistic model is well-suited to be used in the field of statistical pattern recognition and can be extended to other domains like cluster analysis.