Robust Quantization for General Similarity Search

The recent years have witnessed the emerging of vector quantization (VQ) techniques for efficient similarity search. VQ partitions the feature space into a set of codewords and encodes data points as integer indices using the codewords. Then the distance between data points can be efficiently approximated by simple memory lookup operations. By the compact quantization, the storage cost, and searching complexity are significantly reduced, thereby facilitating efficient largescale similarity search. However, the performance of several celebrated VQ approaches degrades significantly when dealing with noisy data. In addition, it can barely facilitate a wide range of applications as the distortion measurement only limits to l(2) norm. To address the shortcomings of the squared Euclidean (l(2,2) norm) loss function employed by the VQ approaches, in this paper, we propose a novel robust and general VQ framework, named RGVQ, to enhance both robustness and generalization of VQ approaches. Specifically, a l(p,q)-norm loss function is proposed to conduct the l(p)-norm similarity search, rather than the l(2) norm search, and the q-th order loss is used to enhance the robustness. Despite the fact that changing the loss function to l(p,q) norm makes VQ approaches more robust and generic, it brings us a challenge that a non-smooth and non-convex orthogonality constrained l(p,q)-norm function has to be minimized. To solve this problem, we propose a novel and efficient optimization scheme and specify it to VQ approaches and theoretically prove its convergence. Extensive experiments on benchmark data sets demonstrate that the proposed RGVQ is better than the original VQ for several approaches, especially when searching similarity in noisy data.