Extended T: Learning with Mixed Closed-set and Open-set Noisy Labels

Xiaobo Xia, Bo Han, Nannan Wang*, Jiankang Deng, Jiatong Li, Yinian Mao, Tongliang Liu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


The noise transition matrix T, reflecting the probabilities that true labels flip into noisy ones, is of vital importance to model label noise and build statistically consistent classifiers. The traditional transition matrix is limited to model closed-set label noise, where noisy training data have true class labels within the noisy label set. It is unfitted to employ such a transition matrix to model open-set label noise, where some true class labels are outside the noisy label set. Therefore, when considering a more realistic situation, i.e., both closed-set and open-set label noises occur, prior works will give unbelievable solutions. Besides, the traditional transition matrix is mostly limited to model instance-independent label noise, which may not perform well in practice. In this paper, we focus on learning with the mixed closed-set and open-set noisy labels. We address the aforementioned issues by extending the traditional transition matrix to be able to model mixed label noise, and further to the cluster-dependent transition matrix to better combat the instance-dependent label noise in real-world applications. We term the proposed transition matrix as the cluster-dependent extended transition matrix. An unbiased estimator (i.e., extended T-estimator) has been designed to estimate the cluster-dependent extended transition matrix by only exploiting the noisy data. Comprehensive experiments validate that our method can better cope with realistic label noise, following its more robust performance than the prior state-of-the-art label-noise learning methods.

Original languageEnglish
Pages (from-to)3047-3058
Number of pages12
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number3
Early online date8 Jun 2022
Publication statusPublished - 1 Mar 2023

Scopus Subject Areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

User-Defined Keywords

  • deep clustering
  • instance-dependent label noise
  • mixed noisy labels
  • noise transition matrix
  • robustness


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