Unsupervised binary hashing method using locality preservation and quantisation error minimisation

Abstract

An unsupervised binary hashing (UBH) method is proposed. To preserve the local and Euclidean metric structures in the reduced feature space, it performs the dimensionality reduction (DR) by using the orthogonal locality-preserving projection. In addition, it minimises the error between the generated binary hash codes and low-dimensional feature vectors that are obtained in DR. To minimise the quantisation error, the binary hash codes are generated using the optimal rotation and offset. Experimental results show that the proposed UBH method has better performance than other existing methods in terms of the mean average precision and recall-precision curve.Introduction: Recently, similarity analysis of images has attracted increasing attention in the computer vision field. To measure the similarity between images, the conventional nearest neighbour (NN) search compares a query feature vector with all the feature vectors in the database by using some distance metric such as Euclidean, Hamming or Mahalanobis distance metrics. However, the computational load of the NN search is high, because it uses the full search. Binary hash is used to reduce the computation time spent on calculating the distance between the query feature vector and every feature vector. There are various existing methods that are used to reduce the computational cost of the NN search. The locality sensitive hashing (LSH) [1] measures the similarity between two vectors using the inner product operation. The hashing function of LSH projects the raw features into hyperplanes the coefficients of which are drawn from the multivariate normal distribution. The element of the projected feature vector is mapped into +1, if it is positive, otherwise, mapped into −1. The shift-invariant kernel LSH (SKLSH) [2] measures the similarity of two vectors using the inner product of outputs of the shift-invariant kernel. Then, the hashing function is defined similar to the LSH. The spectral hashing (SH) [3] finds the best codes for given feature vectors by solving the optimisation problem, which is expressed by the sum of weighted differences between raw feature vectors. Spectral relaxation is used to solve this NP-hard optimisation problem. The key idea of iterative quantisation (ITQ) [4] is simply rotating the data to minimise the error that is defined by the difference between the binary hashing code and the low-dimensional vector acquired in dimensionality reduction (DR). Existing methods such as LSH, SKLSH, SH and ITQ assume that input features are zero-centred. However, this assumption does not hold when input feature vectors are degraded by noise. The proposed unsupervised binary hashing (UBH) method considers the preservation of local and Euclidean metric structures in DR by using the orthogonal locality preserving projection (OLPP) [5]. In addition, it minimises the error between the binary hash code and lowdimensional vector acquired in DR by using the optimal rotation and offset. The zero-centred assumption can be satisfied by introducing the optimal offset.

Comprehensive analysis and evaluation to unsupervised binary hashing method in image similarity measurement

“…This paper is an extended version of the work initially published [18]. This paper has four contributions with respect to our previous work [18]. First, the detailed mathematical analysis of the proposed and other existing methods is described.…”