UAI2023-OnMC: Online Similarity Matrix Correction

The source code for the UAI'2023 paper titled "Online Estimation of Similarity Matrices with Incomplete Data".

Introduction

This Github repository contains the implementation of our proposed Online Simlarity Matrix Correction algorithms, designed to enhance the estimation of similarity matrices in online scenarios, especially when dealing with incomplete observations. The algorithms are built leveraging the positive semi-definiteness (PSD) of the similarity matrix, ensuring a solid theoretical performance guarantee and an excellent potential for parallel execution on large-scale data.

Method

Traditional solution: to impute the online incomplete data by $y \rightarrow \hat{y}$

• Cons: highly relies on data assumptions without a guarantee on similarities

Proposed method: to correct the online similarity vector by $v \rightarrow \hat{v}$

• Pros: has a theoretical guarantee on the quality of the corrected similarity matrix

Folders and files

./                              - Top directory.
./README.md                     - This readme file.
./example_main.m                - Demo of online scenario with incomplete data.
./example_scale.m               - Demo of scalability analysis.
./demo_data.mat                 - A demo dataset. 
./similarity.m                  - Similarity matrix approximation on incomplete data. 

|Baseline/                      - Some imputation baseline methods.
|Our_Method/                    - Our proposed similarity matrix correction methods.
   ./correct_offmc.m            - Offline similarity matrix correction method.
   ./correct_onmc_s.m           - Online similarity matrix correction for sequential data.
   ./correct_onmc_b.m           - Online similarity matrix correction for batch data.
   ./correct_onmc_l.m           - Online similarity matrix correction for large-scale data.

Citation

If you find this code useful for your research, please use the following BibTeX entry.

@inproceedings{yu2023online,
  title={Online estimation of similarity matrices with incomplete data},
  author={Yu, Fangchen and Zeng, Yicheng and Mao, Jianfeng and Li, Wenye},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={2454--2464},
  year={2023},
  organization={PMLR}
}

Contact

If you have any problems or questions, please contact the author: Fangchen Yu (email: fangchenyu@link.cuhk.edu.cn)