The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods. We show how PCA could be reduced to solving a small number of well-conditioned convexâ€¦ (More)

The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. Aâ€¦ (More)

Computing the leading eigenvector of a symmetric real matrix is a fundamental primitive of numerical linear algebra with numerous applications. We consider a natural online extension of the leadingâ€¦ (More)

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example ofâ€¦ (More)

We give faster algorithms and improved sample complexities for the fundamental problem of estimating the top eigenvector. Given an explicit matrix A âˆˆ RnÃ—d, we show how to compute an approximate topâ€¦ (More)

We consider the online version of the well known Principal Component Analysis (PCA) problem. In standard PCA, the input to the problem is a set of ddimensional vectors X = [x1, . . . ,xn] and aâ€¦ (More)

In recent years semidefinite optimization has become a tool of major importance in various optimization and machine learning problems. In many of these problems the amount of data in practice is soâ€¦ (More)

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient basedâ€¦ (More)

Linear optimization is many times algorithmically simpler than nonlinear convex optimization. Linear optimization over matroid polytopes, matching polytopes, and path polytopes are examples ofâ€¦ (More)