Learning optimal features for visual pattern recognition

The optimal coding hypothesis proposes that the human visual system has adapted to the statistical properties of the environment by the use of relatively simple optimality criteria. We here (i) discuss how the properties of different models of image coding, i.e. sparseness, decorrelation, and statistical independence are related to each other (ii) propose to evaluate the different models by verifiable performance measures (iii) analyse the classification performance on images of handwritten digits (MNIST data base). We first employ the SPARSENET algorithm (Olshausen, 1998) to derive a local filter basis (on 13 × 13 pixels windows). We then filter the images in the database (28 × 28 pixels images of digits) and reduce the dimensionality of the resulting feature space by selecting the locally maximal filter responses. We then train a support vector machine on a training set to classify the digits and report results obtained on a separate test set. Currently, the best state-of-the-art result on the MNIST data base has an error rate of 0,4%. This result, however, has been obtained by using explicit knowledge that is specific to the data (elastic distortion model for digits). We here obtain an error rate of 0,55% which is second best but does not use explicit data specific knowledge. In particular it outperforms by far all methods that do not use data-specific knowledge.