### Abstract

Semantic hashing[1] seeks compact binary codes of data-points so that the Hamming distance between codewords correlates with semantic similarity. In this paper, we show that the problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard. By relaxing the original problem, we obtain a spectral method whose solutions are simply a subset of thresholded eigen- vectors of the graph Laplacian. By utilizing recent results on convergence of graph Laplacian eigenvectors to the Laplace-Beltrami eigenfunctions of manifolds, we show how to efficiently calculate the code of a novel data- point. Taken together, both learning the code and applying it to a novel point are extremely simple. Our experiments show that our codes outper- form the state-of-the art.

Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference |

Pages | 1753-1760 |

Number of pages | 8 |

State | Published - 2009 |

Event | 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada Duration: Dec 8 2008 → Dec 11 2008 |

### Other

Other | 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 |
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Country | Canada |

City | Vancouver, BC |

Period | 12/8/08 → 12/11/08 |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems

### Cite this

*Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference*(pp. 1753-1760)

**Spectral hashing.** / Weiss, Yair; Torralba, Antonio; Fergus, Robert.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference.*pp. 1753-1760, 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008, Vancouver, BC, Canada, 12/8/08.

}

TY - GEN

T1 - Spectral hashing

AU - Weiss, Yair

AU - Torralba, Antonio

AU - Fergus, Robert

PY - 2009

Y1 - 2009

N2 - Semantic hashing[1] seeks compact binary codes of data-points so that the Hamming distance between codewords correlates with semantic similarity. In this paper, we show that the problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard. By relaxing the original problem, we obtain a spectral method whose solutions are simply a subset of thresholded eigen- vectors of the graph Laplacian. By utilizing recent results on convergence of graph Laplacian eigenvectors to the Laplace-Beltrami eigenfunctions of manifolds, we show how to efficiently calculate the code of a novel data- point. Taken together, both learning the code and applying it to a novel point are extremely simple. Our experiments show that our codes outper- form the state-of-the art.

AB - Semantic hashing[1] seeks compact binary codes of data-points so that the Hamming distance between codewords correlates with semantic similarity. In this paper, we show that the problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard. By relaxing the original problem, we obtain a spectral method whose solutions are simply a subset of thresholded eigen- vectors of the graph Laplacian. By utilizing recent results on convergence of graph Laplacian eigenvectors to the Laplace-Beltrami eigenfunctions of manifolds, we show how to efficiently calculate the code of a novel data- point. Taken together, both learning the code and applying it to a novel point are extremely simple. Our experiments show that our codes outper- form the state-of-the art.

UR - http://www.scopus.com/inward/record.url?scp=84858779327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858779327&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84858779327

SN - 9781605609492

SP - 1753

EP - 1760

BT - Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

ER -