The success of product quantization (PQ) for fast nearest neighbor search depends on the exponentially reduced complexities of both storage and computation with respect to the codebook size. Recent efforts have been focused on employing sophisticated optimization strategies, or seeking more effective models. Residual quantization (RQ) is such an alternative that holds the same property as PQ in terms of the aforementioned complexities. In addition to being a direct replacement of PQ, hybrids of PQ and RQ can yield more gains for approximate nearest neighbor search. This motivated us to propose a novel approach to optimizing RQ and the related hybrid models. With an observation of the general randomness increase in a residual space, we propose a new strategy that jointly learns a local transformation per residual cluster with an ultimate goal to reduce overall quantization errors. We have shown that our approach can achieve significantly better accuracy on nearest neighbor search than both the original and the optimized PQ on several very large scale benchmarks.
Different from PQ, RQ works by performing quantization to the whole feature space, and then recursively apply VQ models to the residuals of the previous quantization level, which is a stacked quantization model. In particular, it performs a @math -means clustering to the original feature vectors, and construct @math clusters. For points in each cluster, it computes the residuals between points and the cluster centers. In the next level, it aggregates all the residual vectors for all points, and performs another clustering to these residual vectors. This process is recursively applied (stacked) for several levels. In this way, RQ produces sequential-product codebooks. A comprehensive survey of earlier RQ models can be found in @cite_14 . Recent works have shown the effectiveness of RQ to perform both indexing @cite_39 and data compression @cite_29 tasks in ANN search problems.
@cite_29 @cite_14 @cite_39
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Product quantization (PQ) is an effective vector quantization method. A product quantizer can generate an exponentially large codebook at very low memory time cost. The essence of PQ is to decompose the high-dimensional vector space into the Cartesian product of subspaces and then quantize these subspaces separately. The optimal space decomposition is important for the PQ performance, but still remains an unaddressed issue. In this paper, we optimize PQ by minimizing quantization distortions w.r.t the space decomposition and the quantization codebooks. We present two novel solutions to this challenging optimization problem. The first solution iteratively solves two simpler sub-problems. The second solution is based on a Gaussian assumption and provides theoretical analysis of the optimality. We evaluate our optimized product quantizers in three applications: (i) compact encoding for exhaustive ranking [1], (ii) building inverted multi-indexing for non-exhaustive search [2], and (iii) compacting image representations for image retrieval [3]. In all applications our optimized product quantizers outperform existing solutions. 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 large-scale 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 @math norm . To address the shortcomings of the squared Euclidean ( @math 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 @math -norm loss function is proposed to conduct the @math -norm similarity search, rather than the @math norm search, and the @math -th order loss is used to enhance the robustness. Despite the fact that changing the loss function to @math norm makes VQ approaches more robust and generic, it brings us a challenge that a non-smooth and non-convex orthogonality constrained @math - 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. We present a simple vector quantizer that combines low distortion with fast search and apply it to approximate nearest neighbor (ANN) search in high dimensional spaces. Leveraging the very same data structure that is used to provide non-exhaustive search, i.e., inverted lists or a multi-index, the idea is to locally optimize an individual product quantizer (PQ) per cell and use it to encode residuals. Local optimization is over rotation and space decomposition, interestingly, we apply a parametric solution that assumes a normal distribution and is extremely fast to train. With a reasonable space and time overhead that is constant in the data size, we set a new state-of-the-art on several public datasets, including a billion-scale one. We present a new approach for efficient approximate nearest neighbor (ANN) search in high dimensional spaces, extending the idea of Product Quantization. We propose a two level product and vector quantization tree that reduces the number of vector comparisons required during tree traversal. Our approach also includes a novel highly parallelizable re-ranking method for candidate vectors by efficiently reusing already computed intermediate values. Due to its small memory footprint during traversal the method lends itself to an efficient, parallel GPU implementation. This Product Quantization Tree (PQT) approach significantly outperforms recent state of the art methods for high dimensional nearest neighbor queries on standard reference datasets. Ours is the first work that demonstrates GPU performance superior to CPU performance on high dimensional, large scale ANN problems in time-critical real-world applications, like loop-closing in videos.