Ordinal Constraint Binary Coding for Approximate Nearest Neighbor Search.

Area of Science:

• Computer Science
• Machine Learning
• Data Science

Background:

• Binary code learning, or hashing, is crucial for approximate nearest neighbor search in large image datasets.
• Current unsupervised hashing methods focus on preserving pairwise similarity, overlooking ordinal relations.
• Quantization error reduction from real-valued to discrete Hamming space remains a key challenge.

Purpose of the Study:

• To introduce a novel unsupervised hashing scheme, Ordinal Constraint Hashing (OCH).
• To embed ordinal relations among data points into binary codes for improved ranking preservation.
• To develop an efficient acceleration scheme and a tractable optimization algorithm.

Main Methods:

• Constructing an ordinal graph via tensor product to capture permutation relations.
• Developing Ordinal Constraint Projection (OCP) to approximate the ordinal graph and reduce complexity from O(n^4) to O(L^3).
• Relaxing discrete constraints and employing a customized stochastic gradient descent on the Stiefel manifold for optimization.

Main Results:

• The proposed OCH method effectively embeds ordinal relations into binary codes.
• The OCP acceleration scheme significantly reduces computational complexity.
• Experimental results on large-scale benchmarks show superior performance compared to state-of-the-art methods.

Conclusions:

• OCH offers a novel and effective approach to unsupervised hashing by leveraging ordinal relations.
• The method achieves superior performance in approximate nearest neighbor search for large-scale image collections.
• OCH provides a promising direction for future research in binary code learning.