Doubly Accelerated Methods for Faster CCA and Generalized Eigendecomposition

Zeyuan Allen-Zhu; Yuanzhi Li

Doubly Accelerated Methods for Faster CCA and Generalized Eigendecomposition

Optimization and Control 2017-01-24 v2 Data Structures and Algorithms Machine Learning Machine Learning

Authors: Zeyuan Allen-Zhu , Yuanzhi Li

Abstract

We study $k$ -GenEV, the problem of finding the top $k$ generalized eigenvectors, and $k$ -CCA, the problem of finding the top $k$ vectors in canonical-correlation analysis. We propose algorithms $\mathtt{LazyEV}$ and $\mathtt{LazyCCA}$ to solve the two problems with running times linearly dependent on the input size and on $k$ . Furthermore, our algorithms are DOUBLY-ACCELERATED: our running times depend only on the square root of the matrix condition number, and on the square root of the eigengap. This is the first such result for both $k$ -GenEV or $k$ -CCA. We also provide the first gap-free results, which provide running times that depend on $1/\sqrt{\varepsilon}$ rather than the eigengap.

Cite

@article{arxiv.1607.06017,
  title  = {Doubly Accelerated Methods for Faster CCA and Generalized Eigendecomposition},
  author = {Zeyuan Allen-Zhu and Yuanzhi Li},
  journal= {arXiv preprint arXiv:1607.06017},
  year   = {2017}
}

Comments

We have now stated more clearly why this paper has outperformed relevant previous results, and included discussions for doubly-stochastic methods. arXiv admin note: text overlap with arXiv:1607.03463

Doubly Accelerated Methods for Faster CCA and Generalized Eigendecomposition

Abstract

Cite

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