Regularized discriminant analysis for transformation-invariant object recognition

We present a novel method for incorporating prior knowledge about invariances in object recognition for discriminant analysis. In contrast to conventional isotropic regularization approaches, our approach shows how to incorporate known transformation invariances in the geometry of the problem to better regularize discriminant analysis. In particular, we show how to incorporate group invariance and tangent vector structure with multiple parameters and derive special covariance terms that are used to regularize discriminant analysis. We apply this method to Fisher discriminant analysis, as well as its kernelized version, and show that this invariant regularization improves recognition performance over conventional regularization techniques.