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Partial Label Clustering

Yutong Xie, Fuchao Yang, Yuheng Jia

TL;DR

Partial Label Clustering (PLC) tackles clustering with partial supervision by jointly learning a feature-space weight matrix, disambiguating ground-truth labels, and propagating pairwise constraints through an adversarial dual-graph framework. The method alternates between weight construction, label confidence refinement, and constraint propagation, then applies spectral clustering on the learned weight matrix. Theoretical analysis shows that better label disambiguation tightens the bound on the deviation of the learned weight matrix from the ground-truth, thereby improving clustering. Empirically, PLC consistently surpasses constrained clustering, PLL, and semi-supervised PLL baselines on synthetic and real-world datasets, especially when partial labels are scarce.

Abstract

Partial label learning (PLL) is a significant weakly supervised learning framework, where each training example corresponds to a set of candidate labels and only one label is the ground-truth label. For the first time, this paper investigates the partial label clustering problem, which takes advantage of the limited available partial labels to improve the clustering performance. Specifically, we first construct a weight matrix of examples based on their relationships in the feature space and disambiguate the candidate labels to estimate the ground-truth label based on the weight matrix. Then, we construct a set of must-link and cannot-link constraints based on the disambiguation results. Moreover, we propagate the initial must-link and cannot-link constraints based on an adversarial prior promoted dual-graph learning approach. Finally, we integrate weight matrix construction, label disambiguation, and pairwise constraints propagation into a joint model to achieve mutual enhancement. We also theoretically prove that a better disambiguated label matrix can help improve clustering performance. Comprehensive experiments demonstrate our method realizes superior performance when comparing with state-of-the-art constrained clustering methods, and outperforms PLL and semi-supervised PLL methods when only limited samples are annotated. The code is publicly available at https://github.com/xyt-ml/PLC.

Partial Label Clustering

TL;DR

Partial Label Clustering (PLC) tackles clustering with partial supervision by jointly learning a feature-space weight matrix, disambiguating ground-truth labels, and propagating pairwise constraints through an adversarial dual-graph framework. The method alternates between weight construction, label confidence refinement, and constraint propagation, then applies spectral clustering on the learned weight matrix. Theoretical analysis shows that better label disambiguation tightens the bound on the deviation of the learned weight matrix from the ground-truth, thereby improving clustering. Empirically, PLC consistently surpasses constrained clustering, PLL, and semi-supervised PLL baselines on synthetic and real-world datasets, especially when partial labels are scarce.

Abstract

Partial label learning (PLL) is a significant weakly supervised learning framework, where each training example corresponds to a set of candidate labels and only one label is the ground-truth label. For the first time, this paper investigates the partial label clustering problem, which takes advantage of the limited available partial labels to improve the clustering performance. Specifically, we first construct a weight matrix of examples based on their relationships in the feature space and disambiguate the candidate labels to estimate the ground-truth label based on the weight matrix. Then, we construct a set of must-link and cannot-link constraints based on the disambiguation results. Moreover, we propagate the initial must-link and cannot-link constraints based on an adversarial prior promoted dual-graph learning approach. Finally, we integrate weight matrix construction, label disambiguation, and pairwise constraints propagation into a joint model to achieve mutual enhancement. We also theoretically prove that a better disambiguated label matrix can help improve clustering performance. Comprehensive experiments demonstrate our method realizes superior performance when comparing with state-of-the-art constrained clustering methods, and outperforms PLL and semi-supervised PLL methods when only limited samples are annotated. The code is publicly available at https://github.com/xyt-ml/PLC.
Paper Structure (26 sections, 2 theorems, 25 equations, 4 figures, 7 tables, 1 algorithm)

This paper contains 26 sections, 2 theorems, 25 equations, 4 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. The Proposed Method
  4. Notations
  5. Constructing Weight Matrix
  6. Label Disambiguation
  7. Pairwise Constraint Propagation
  8. Overall Model
  9. Alternating Optimization
  10. Theoretical Analysis
  11. Experiments
  12. Experimental Setup
  13. Experimental Results
  14. Comparison with Constrained Clustering Methods
  15. Comparison with PLL & Semi-supervised PLL Methods
  16. ...and 11 more sections

Key Result

Theorem 1

Denote $\textbf{F}\in[0, 1]^{n\times q}$ and $\textbf{W}\in[0, 1]^{n\times n}$ as the label confidence matrix and the weight matrix to be optimized. Let $\textbf{F}_G$ and $\textbf{W}_G$ be the ground-truth label matrix and the optimal weight matrix under the ground-truth labels. We assume that $\te

Figures (4)

  • Figure 1: ACCs and NMIs when compared with constrained clustering methods under different proportions of partial label training examples on synthetic UCI datasets.
  • Figure 2: Parameter sensitivity analysis for PLC. (a) ACCs of PLC on Lost and MSRCv2 by varying $\alpha$; (b) ACCs of PLC on Lost and MSRCv2 by varying $\beta$; (c) ACCs of PLC on Lost and MSRCv2 by varying $k$;
  • Figure 3: ACCs and NMIs when compared with constrained clustering methods under different proportions of partial label training samples on the datasets Ecoli $r=3$ and Coil20 $r=3$.
  • Figure 4: ACCs when compared with PLL and semi-supervised PLL methods under different proportions of partial label training samples on synthetic UCI datasets.

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1
  • proof
  • proof