### Abstract

This paper considers the problem of canonical- correlation analysis, and more broadly, the generalized eigenvector problem for a pair of symmetric matrices. We consider the setting of finding top-A- canonical/eigen subspace, and solve these problems through a general framework that simply requires black box access to an approximate linear system solver. Instantiating this framework with acceleratcd gradient descent we obtain a running time of O log(l/) log (∗ κ/p)) where z is the total number of nonzero entries, κ is the condition number and p is the relative eigenvalue gap of the appropriate matrices. Our algorithm is linear in the input size and the number of components κup to a iog( κ) factor, which is essential for handling large-scale matrices that appear in practice. To the best of our knowledge this is the first such algorithm with global linear convergence. We hope that our results prompt further research improving the practical running time for performing these important data analysis procedures on large-scale data sets.

Original language | English (US) |
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Title of host publication | 33rd International Conference on Machine Learning, ICML 2016 |

Editors | Kilian Q. Weinberger, Maria Florina Balcan |

Publisher | International Machine Learning Society (IMLS) |

Pages | 4009-4026 |

Number of pages | 18 |

ISBN (Electronic) | 9781510829008 |

State | Published - Jan 1 2016 |

Externally published | Yes |

Event | 33rd International Conference on Machine Learning, ICML 2016 - New York City, United States Duration: Jun 19 2016 → Jun 24 2016 |

### Publication series

Name | 33rd International Conference on Machine Learning, ICML 2016 |
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Volume | 6 |

### Other

Other | 33rd International Conference on Machine Learning, ICML 2016 |
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Country | United States |

City | New York City |

Period | 6/19/16 → 6/24/16 |

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Software
- Computer Networks and Communications

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## Cite this

*33rd International Conference on Machine Learning, ICML 2016*(pp. 4009-4026). (33rd International Conference on Machine Learning, ICML 2016; Vol. 6). International Machine Learning Society (IMLS).