Data-Dependent Hashing Based on p-Stable Distribution

• Published in: IEEE transactions on image processing Vol. 23; no. 12; pp. 5033 - 5046
• Main Authors: Bai, Xiao, Yang, Haichuan, Zhou, Jun, Ren, Peng, Cheng, Jian
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.12.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Binary codes; Educational institutions; Euclidean distance; Hash based algorithms; Image processing; Mathematical analysis; Methods; Preserves; Projection; Quantization (signal); Semantics; Similarity; Training; Vectors; Vectors (mathematics); hash retrieval; Image retrieval; p-stable distribution
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2014.2352458

The p-stable distribution is traditionally used for data-independent hashing. In this paper, we describe how to perform data-dependent hashing based on p-stable distribution. We commence by formulating the Euclidean distance preserving property in terms of variance estimation. Based on this property, we develop a projection method, which maps the original data to arbitrary dimensional vectors. Each projection vector is a linear combination of multiple random vectors subject to p-stable distribution, in which the weights for the linear combination are learned based on the training data. An orthogonal matrix is then learned data-dependently for minimizing the thresholding error in quantization. Combining the projection method and orthogonal matrix, we develop an unsupervised hashing scheme, which preserves the Euclidean distance. Compared with data-independent hashing methods, our method takes the data distribution into consideration and gives more accurate hashing results with compact hash codes. Different from many data-dependent hashing methods, our method accommodates multiple hash tables and is not restricted by the number of hash functions. To extend our method to a supervised scenario, we incorporate a supervised label propagation scheme into the proposed projection method. This results in a supervised hashing scheme, which preserves semantic similarity of data. Experimental results show that our methods have outperformed several state-of-the-art hashing approaches in both effectiveness and efficiency.