@saibaba2013randomized]. Statistically, the finite-sample second moment estimates can be inaccurate when the number of dimensions overwhelms the number of examples. The effect of this inaccuracy on the extracted eigenvectors needs further investigation. In particular, it might be unimportant for datasets encountered in practice, e.g., if the true class-conditional second moment matrices have low effective rank [@bunea2012].

Finally, our approach is simple to implement and well suited to the distributed setting. Although a distributed implementation is out of the scope of this paper, we do note that aspects of Algorithm \[alg:gem\] were motivated by the desire for efficient distributed implementation. The recent success of non-convex learning systems has sparked renewed interest in non-convex representation learning. However, generic distributed non-convex optimization is extremely challenging. Our approach first decomposes the problem into tractable non-convex subproblems and then subsequently composes with convex techniques. Ultimately we hope that judicious application of convenient non-convex objectives, coupled with convex optimization techniques, will yield competitive and scalable learning algorithms.

Conclusion
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We have shown a method for creating discriminative features via solving generalized eigenvalue problems, and demonstrated empirical efficacy via multiple experiments. The method has multiple computational and statistical desiderata. Computationally, generalized eigenvalue extraction is a mature numerical 