Spectral Hashing

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 eigenvectors 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 datapoint. Taken together, both learning the code and applying it to a novel point are extremely simple. Our experiments show that our codes outperform the state-of-the art.

• Type: Conference
• Year: 2008
• Where: NIPS
• Authors: Yair Weiss, Antonio Torralba, Robert Fergus
• Keywords: Compact Binary Codes, Graph Laplacian, Graph Laplacian Eigenvectors, Information Technology, NIPS 2008