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abstract: 'Representing examples in a way that is compatible with the underlying classifier can greatly enhance the performance of a learning system. In this paper we investigate scalable techniques for inducing discriminative features by taking advantage of simple second order structure in the data. We focus on multiclass classification and show that features extracted from the generalized eigenvectors of the class conditional second moments lead to classifiers with excellent empirical performance. Moreover, these features have attractive theoretical properties, such as inducing representations that are invariant to linear transformations of the input. We evaluate classifiers built from these features on three different tasks, obtaining state of the art results.'
bibliography:
- 'gev.bib'
---

Introduction {#intro}
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Supervised learning has been a great success story for machine learning, both in theory and in practice. In theory, we have a good understanding of the conditions under which supervised learning can succeed [@vapnik1998statistical]. In practice, supervised learning approaches are profitably employed in many domains, from movie recommendation to speech and image recognition [@koren2009matrix; @hinton2012deep; @krizhevsky2012imagenet]. The success of all of these systems crucially hinges on the compatibility between the model and the representation used to solve the problem.

For some problems, the kinds 