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Improved Consistent Weighted Sampling

As datasets become larger and more high-dimensional, it becomes increasingly important to find data representations that allow compact storage and efficient distance computation and retrieval. Improved Consistent Weighted Sampling(ICWS, ICDM, 2010) is the state-of-the-art of the sampling methods in weighted sets. There are some variants of ICWS which decreases the time of sampling or increase the quality of samples.

This repository implements ICWS and its variants.

Build Instruction

$ git clone git@github.com:yuuun/Consistent-Weighted-Sampling.git
$ cd Consistent-Weighted-Sampling
$ pip3 install -r requirements.txt
$ mkdir dataset

After Downloading datasets to 'dataset/' file, you can run the file by the following command

$ python3 main.py

Datasets

  • Datasets can be downloaded in LIBSVM

Input File Data Formats

[label1] [idx1_1]:[weight1_1] [idx1_2]:[weight1_2] ...
[label2] [idx2_1]:[weight2_1] [idx2_2]:[weight2_2] ...
[label3] [idx3_1]:[weight3_1] [idx3_2]:[weight3_2] ...

Example

1 1:5 3:7 10:9
2 2:6 3:1 8:10

Models

  • ICWS
    • state of the CWS method that improves the effectiveness and efficiency
  • 0-bit CWS
    • improves the space efficiency and GJS estimation time
  • CCWS
    • improves the time efficiency of ICWS by removing the cacluation of logarithm
  • PCWS
    • replace one of the two gamma distributions with uniform distribution which improves both time and space complexities in ICWS
  • I2CWS
    • hashes yk and zk separately which makes k' and yk' dependent
  • BCWS
    • applies OPH on CWS and increased the time efficiency dramatically

Experiments

The classification accuracy of Generalized Jaccard Similarity

Classification Accuracy
Mnist 93.6%

Evaluation

  • Hashing Time

  • Classification Accuracy

  • Precision(the criteria of Jaccard Similarity)

  • The experiments will be depicted as follows,

[Name of Method] | [Dataset]([Number of Samples])

Time

Method Mnist(100) Mnist(500)
ICWS 175.4s 869.6s
0-bit CWS 169.3s 842.1s
CCWS 129.2s 647.4s
PCWS 154.4s 767.0s
I2CWS 162.3s 805.7s
BCWS 6.3s 17.9s

Accuracy

Method Mnist(100) Mnist(500)
ICWS 88.7% 92.6%
0-bit CWS 90.7% 94.1%
CCWS 79.3% 81.8%
PCWS 90.6% 93.2%
I2CWS 89.7% 92.5%
BCWS 84.3% 84.4%

Precision@10

Method Mnist(100) Mnist(500)
ICWS 59.9% 80.4%
0-bit CWS 61.6% 80.5%
CCWS 35.43% 40.8%
PCWS 60.9% 79.5%
I2CWS 59.2% 78.8%
BCWS 46.4% 46.4%

Precision@100

Method Mnist(100) Mnist(500)
ICWS 71.1% 86.8%
0-bit CWS 71.8% 86.3%
CCWS 48.7% 54.8%
PCWS 70.5% 85.8%
I2CWS 69.9% 84.8%
BCWS 57.5% 52.8%

References