A general framework of vector quantization with python.

Norm-Explicit Quantization: Improving Vector Quantization for Maximum Inner Product Search.

• Abstract

  Vector quantization (VQ) techniques are widely used in similarity search for data compression, fast metric computation and etc. Originally designed for Euclidean distance, existing VQ techniques (e.g., PQ, AQ) explicitly or implicitly minimize the quantization error. In this paper, we present a new angle to analyze the quantization error, which decomposes the quantization error into norm error and direction error. We show that quantization errors in norm have much higher influence on inner products than quantization errors in direction, and small quantization error does not necessarily lead to good performance in maximum inner product search (MIPS). Based on this observation, we propose norm-explicit quantization (NEQ) --- a general paradigm that improves existing VQ techniques for MIPS. NEQ quantizes the norms of items in a dataset explicitly to reduce errors in norm, which is crucial for MIPS. For the direction vectors, NEQ can simply reuse an existing VQ technique to quantize them without modification. We conducted extensive experiments on a variety of datasets and parameter configurations. The experimental results show that NEQ improves the performance of various VQ techniques for MIPS, including PQ, OPQ, RQ and AQ.

The netflix dataset is contained in this repository, you can download more datasets from here, then you can calculate the ground truth with the script

python run_ground_truth.py  --dataset netflix --topk 50 --metric product

python run_pq.py --dataset netflix --topk 20 --metric product --num_codebook 4 --Ks 256
python run_opq.py --dataset netflix --topk 20 --metric product --num_codebook 4 --Ks 256
python run_rq.py --dataset netflix --topk 20 --metric product --num_codebook 4 --Ks 256
python run_aq.py --dataset netflix --topk 20 --metric product --num_codebook 4 --Ks 256 # very slow

python run_norm_pq.py --dataset netflix --topk 20 --metric product --num_codebook 4 --Ks 256
python run_norm_opq.py --dataset netflix --topk 20 --metric product --num_codebook 4 --Ks 256
python run_norm_rq.py --dataset netflix --topk 20 --metric product --num_codebook 4 --Ks 256
python run_norm_aq.py --dataset netflix --topk 20 --metric product --num_codebook 4 --Ks 256 # very slow

If you use this code, please cite the following paper

@article{xinyandai,
  title={Norm-Explicit Quantization: Improving Vector Quantization for Maximum Inner Product Search},
  author={Dai, Xinyan and Yan, Xiao and Ng, Kelvin KW and Liu, Jie and Cheng, James},
  journal={arXiv preprint arXiv:1911.04654},
  year={2019}
}