Estimating the largest eigenvalues by the power and Lanczos algorithms with a random start
SIAM Journal on Matrix Analysis and Applications
Convex Optimization
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Distance metric learning with eigenvalue optimization
The Journal of Machine Learning Research
Optimizing over the growing spectrahedron
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Distance metric learning revisited
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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We propose an algorithm for approximately maximizing a concave function over the bounded semi-definite cone, which produces sparse solutions. Sparsity for SDP corresponds to low rank matrices, and is a important property for both computational as well as learning theoretic reasons. As an application, building on Aaronson's recent work, we derive a linear time algorithm for Quantum State Tomography.