On intrinsic generalization of low dimensional representations of images for recognition

Low dimensional representations of images impose equivalence relations in the image space; the induced equivalence class of an image is named as its intrinsic generalization. The intrinsic generalization of a representation provides a novel way to measure its generalization and leads to more fundamental insights than the commonly used recognition performance, which is heavily influenced by the choice of training and test data. We demonstrate the limitations of linear subspace representations by sampling their intrinsic generalization, and propose a nonlinear representation that overcomes these limitations. The proposed representation projects images nonlinearly into the marginal densities of their filter responses, followed by linear projections of the marginals. We have used experiments on large datasets to show that the representations that have better intrinsic generalization also lead to a better recognition performance.