text: Inverted file and asymmetric distance computation (IVFADC) have been successfully applied to approximate nearest neighbor search and subsequently maximum inner product search. In such a framework, vector quantization is used for coarse partitioning while product quantization is used for quantizing residuals. In the original IVFADC as well as all of its variants, after residuals are computed, the second production quantization step is completely independent of the first vector quantization step. In this work, we seek to exploit the connection between these two steps when we perform non-exhaustive search. More specifically, we decompose a residual vector locally into two orthogonal components and perform uniform quantization and multiscale quantization to each component respectively. The proposed method, called local orthogonal decomposition, combined with multiscale quantization consistently achieves higher recall than previous methods under the same bitrates. We conduct comprehensive experiments on large scale datasets as well as detailed ablation tests, demonstrating effectiveness of our method.
  @cite_19: This paper introduces a product quantization-based approach for approximate nearest neighbor search. The idea is to decompose the space into a Cartesian product of low-dimensional subspaces and to quantize each subspace separately. A vector is represented by a short code composed of its subspace quantization indices. The euclidean distance between two vectors can be efficiently estimated from their codes. An asymmetric version increases precision, as it computes the approximate distance between a vector and a code. Experimental results show that our approach searches for nearest neighbors efficiently, in particular in combination with an inverted file system. Results for SIFT and GIST image descriptors show excellent search accuracy, outperforming three state-of-the-art approaches. The scalability of our approach is validated on a data set of two billion vectors.
  @cite_16: Similarity search finds application in specialized database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles the problem of better utilizing GPUs for this task. While GPUs excel at data-parallel tasks, prior approaches are bottlenecked by algorithms that expose less parallelism, such as k-min selection, or make poor use of the memory hierarchy. We propose a design for k-selection that operates at up to 55 of theoretical peak performance, enabling a nearest neighbor implementation that is 8.5x faster than prior GPU state of the art. We apply it in different similarity search scenarios, by proposing optimized design for brute-force, approximate and compressed-domain search based on product quantization. In all these setups, we outperform the state of the art by large margins. Our implementation enables the construction of a high accuracy k-NN graph on 95 million images from the Yfcc100M dataset in 35 minutes, and of a graph connecting 1 billion vectors in less than 12 hours on 4 Maxwell Titan X GPUs. We have open-sourced our approach for the sake of comparison and reproducibility.
  @cite_13: 
  @cite_26: Nearest Neighbor (NN) search in high dimension is an important feature in many applications (e.g., image retrieval, multimedia databases). Product Quantization (PQ) is a widely used solution which offers high performance, i.e., low response time while preserving a high accuracy. PQ represents high-dimensional vectors (e.g., image descriptors) by compact codes. Hence, very large databases can be stored in memory, allowing NN queries without resorting to slow I O operations. PQ computes distances to neighbors using cache-resident lookup tables, thus its performance remains limited by (i) the many cache accesses that the algorithm requires, and (ii) its inability to leverage SIMD instructions available on modern CPUs. In this paper, we advocate that cache locality is not sufficient for efficiency. To address these limitations, we design a novel algorithm, PQ Fast Scan, that transforms the cache-resident lookup tables into small tables, sized to fit SIMD registers. This transformation allows (i) in-register lookups in place of cache accesses and (ii) an efficient SIMD implementation. PQ Fast Scan has the exact same accuracy as PQ, while having 4 to 6 times lower response time (e.g., for 25 million vectors, scan time is reduced from 74ms to 13ms).
summary: . ADC transforms inner product computations into a lookup table based operation, which can be implemented in different ways. The original ADC paper @cite_19 used L1 cache based lookup table. @cite_16 used an GPU implementation for ADC lookup. A SIMD based approach was also developed by @cite_26 @cite_13 . Again, this is orthogonal to the local decomposition idea of this work, as any ADC implementation can be used in this work.