[Paper Review] A Weakly Supervised Learning Approach based on Spectral Graph-Theoretic Grouping

Tameem Adel, Alexander Wong+1 more|arXiv (Cornell University)|Aug 3, 2015

Face and Expression Recognition22 references3 citations

TL;DR

This paper proposes a weakly supervised learning method that uses spectral graph-theoretic grouping to infer weak labels for unlabelled data by leveraging similarity relationships between labelled and unlabelled instances. By constructing novel similarity graph models, the approach improves classification accuracy on EMG and benchmark datasets compared to fully supervised baselines, with logistic regression showing the most consistent gains.

ABSTRACT

In this study, a spectral graph-theoretic grouping strategy for weakly supervised classification is introduced, where a limited number of labelled samples and a larger set of unlabelled samples are used to construct a larger annotated training set composed of strongly labelled and weakly labelled samples. The inherent relationship between the set of strongly labelled samples and the set of unlabelled samples is established via spectral grouping, with the unlabelled samples subsequently weakly annotated based on the strongly labelled samples within the associated spectral groups. A number of similarity graph models for spectral grouping, including two new similarity graph models introduced in this study, are explored to investigate their performance in the context of weakly supervised classification in handling different types of data. Experimental results using benchmark datasets as well as real EMG datasets demonstrate that the proposed approach to weakly supervised classification can provide noticeable improvements in classification performance, and that the proposed similarity graph models can lead to ultimate learning results that are either better than or on a par with existing similarity graph models in the context of spectral grouping for weakly supervised classification.

Motivation & Objective

• Address the challenge of limited labelled data in medical signal classification, particularly for electromyographic (EMG) signals where only muscle-level labels are available.
• Improve classification performance by generating reliable weak labels for unlabelled instances using graph-based grouping strategies.
• Develop robust similarity graph models that adapt to varying data densities, enhancing spectral clustering performance in weakly supervised settings.
• Demonstrate that weakly annotated data, when combined with strongly labelled data, leads to superior classifier performance compared to fully supervised learning with naive label propagation.
• Validate the method on real EMG datasets and benchmark datasets to show generalization across data types.

Proposed method

• Construct a similarity graph where nodes represent data instances and edges encode pairwise similarities between strongly labelled and unlabelled instances.
• Apply spectral clustering to group unlabelled instances based on their similarity to strongly labelled instances, using the graph's eigenvectors to identify cohesive clusters.
• Introduce two novel similarity graph models designed to handle heterogeneous data densities, improving robustness in real-world data distributions.
• Assign weak labels to unlabelled instances based on the majority label of strongly labelled instances within the same spectral group.
• Train a classifier (logistic regression, k-NN, QDA) on the combined set of strongly and weakly labelled instances using leave-one-muscle-out cross-validation.
• Optimize hyperparameters such as K in k-NN and the number of clusters via cross-validation to ensure generalization.

Experimental results

Research questions

• RQ1 Can spectral graph-theoretic grouping effectively infer meaningful weak labels for unlabelled instances in weakly supervised learning?
• RQ2 Do the proposed similarity graph models outperform or match existing models in terms of clustering quality and downstream classification accuracy?
• RQ3 Does combining weakly labelled instances with strongly labelled data lead to better classification performance than using only strongly labelled data?
• RQ4 How robust are the proposed graph models to variations in data density and distribution across different datasets?
• RQ5 Is the performance improvement consistent across different classification algorithms (e.g., logistic regression, k-NN, QDA)?

Key findings

• The weakly supervised classifier significantly outperforms the fully supervised baseline on both the Upper Leg and Lower Leg EMG datasets.
• Logistic regression achieved the highest classification accuracy among the three classifiers tested, indicating stable and effective learning from weakly annotated data.
• The proposed similarity graph models led to grouping results that were either better than or on par with existing models in spectral grouping for weakly supervised learning.
• The method improved classification performance by enabling the model to learn from a larger, more informative training set augmented with reliable weak labels.
• Leave-one-muscle-out cross-validation confirmed consistent performance gains, demonstrating the method’s robustness and generalization capability.
• The flexibility of the new graph models in adapting to varying data densities contributed to improved clustering and classification outcomes.