Ordinal Constraint Binary Coding for Approximate Nearest Neighbor Search

Binary code learning, a.k.a. hashing, has been successfully applied to the approximate nearest neighbor search in large-scale image collections. The key challenge lies in reducing the quantization error from the original real-valued feature space to a discrete Hamming space. Recent advances in unsup...

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Vydáno v:IEEE transactions on pattern analysis and machine intelligence Ročník 41; číslo 4; s. 941 - 955
Hlavní autoři: Liu, Hong, Ji, Rongrong, Wang, Jingdong, Shen, Chunhua
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.04.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Anchors
Binary code learning
Binary codes
Binary system
Codes
Data points
discrete optimization
Encoding
Hash based algorithms
hashing
image retrieval
Learning
Manifolds
Manifolds (mathematics)
Measurement
Optimization
ordinal preserving
Permutations
Preservation
Quantization (signal)
Ranking
Tensile stress
tensor graph
Tensors
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
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Popis
Shrnutí:Binary code learning, a.k.a. hashing, has been successfully applied to the approximate nearest neighbor search in large-scale image collections. The key challenge lies in reducing the quantization error from the original real-valued feature space to a discrete Hamming space. Recent advances in unsupervised hashing advocate the preservation of ranking information, which is achieved by constraining the binary code learning to be correlated with pairwise similarity. However, few unsupervised methods consider the preservation of ordinal relations in the learning process, which serves as a more basic cue to learn optimal binary codes. In this paper, we propose a novel hashing scheme, termed Ordinal Constraint Hashing (OCH), which embeds the ordinal relation among data points to preserve ranking into binary codes. The core idea is to construct an ordinal graph via tensor product, and then train the hash function over this graph to preserve the permutation relations among data points in the Hamming space. Subsequently, an in-depth acceleration scheme, termed Ordinal Constraint Projection (OCP), is introduced, which approximates the <inline-formula><tex-math notation="LaTeX">n</tex-math> <inline-graphic xlink:href="ji-ieq1-2819978.gif"/> </inline-formula>-pair ordinal graph by <inline-formula><tex-math notation="LaTeX">L</tex-math> <inline-graphic xlink:href="ji-ieq2-2819978.gif"/> </inline-formula>-pair anchor-based ordinal graph, and reduce the corresponding complexity from <inline-formula><tex-math notation="LaTeX">O(n^4)</tex-math> <inline-graphic xlink:href="ji-ieq3-2819978.gif"/> </inline-formula> to <inline-formula><tex-math notation="LaTeX">O(L^3)</tex-math> <inline-graphic xlink:href="ji-ieq4-2819978.gif"/> </inline-formula> (<inline-formula><tex-math notation="LaTeX">L\ll n</tex-math> <inline-graphic xlink:href="ji-ieq5-2819978.gif"/> </inline-formula>). Finally, to make the optimization tractable, we further relax the discrete constrains and design a customized stochastic gradient decent algorithm on the Stiefel manifold. Experimental results on serval large-scale benchmarks demonstrate that the proposed OCH method can achieve superior performance over the state-of-the-art approaches.
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2018.2819978