Dual algorithms for orthogonal Procrustes rotations
SIAM Journal on Matrix Analysis and Applications
Approximating the cut-norm via Grothendieck's inequality
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization
ICML '06 Proceedings of the 23rd international conference on Machine learning
Sums of random symmetric matrices and quadratic optimization under orthogonality constraints
Mathematical Programming: Series A and B
Principal Component Analysis Based on L1-Norm Maximization
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Grothendieck Constant is Strictly Smaller than Krivine's Bound
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Moment inequalities for sums of random matrices and their applications in optimization
Mathematical Programming: Series A and B
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The classical Grothendieck inequality has applications to the design of approximation algorithms for NP-hard optimization problems. We show that an algorithmic interpretation may also be given for a noncommutative generalization of the Grothendieck inequality due to Pisier and Haagerup. Our main result, an efficient rounding procedure for this inequality, leads to a constant-factor polynomial time approximation algorithm for an optimization problem which generalizes the Cut Norm problem of Frieze and Kannan, and is shown here to have additional applications to robust principle component analysis and the orthogonal Procrustes problem.