Non-linear feature space transformations

Linear methods are strongly preferred in statistical pattern recognition, but problems in perception require nonlinear analysis and operators. Even the most successful linear methods lack robustness, especially when the normal variation in the data reveals new structure. An alternative to computing complex features or devising a complex decision rule is to transform the feature space so that the structure of the density is simplified. Simple nonlinear operations such as folding, applying gauge coordinate transformations, and nonlinear diffusion have been explored. The ultimate objective is to derive the appropriate nonlinear transformations from training data or from a verbal description of the classification task in terms of the variances, equivariances, and invariances of the problem.