A Note on the Generalization Performance of Kernel Classifiers with Margin

We present distribution independent bounds on the generalization misclassification performance of a family of kernel classifiers with margin. Support Vector Machine classifiers (SVM) stem out of this class of machines. The bounds are derived through computations of the $V_gamma$ dimension of a family of loss functions where the SVM one belongs to. Bounds that use functions of margin distributions (i.e. functions of the slack variables of SVM) are derived.

Generalization over contrast and mirror reversal, but not figure-ground reversal, in an "edge-based

Baylis & Driver (Nature Neuroscience, 2001) have recently presented data on the response of neurons in macaque inferotemporal cortex (IT) to various stimulus transformations. They report that neurons can generalize over contrast and mirror reversal, but not over figure-ground reversal. This finding is taken to demonstrate that ``the selectivity of IT neurons is not determined simply by the distinctive contours in a display, contrary to simple edge-based models of shape recognition'', citing our recently presented model of object recognition in cortex (Riesenhuber & Poggio, Nature Neuroscience, 1999). In this memo, I show that the main effects of the experiment can be obtained by performing the appropriate simulations in our simple feedforward model. This suggests for IT cell tuning that the possible contributions of explicit edge assignment processes postulated in (Baylis & Driver, 2001) might be smaller than expected.