Semi-supervised Bayesian deep clustering with uncertainty-guided representation and robustness

In real-world data, tackling missing data, noisy observations, and uncertainty at the same time is hard since the number of labelled data is limited. Current deep clustering algorithms have considered the imputation, noise, semi-supervision, and uncertainty problems separately, such as without modelling the uncertainty in the noise, or without modelling the missingness in the missing data. There is still a need to develop an end-to-end deep clustering algorithm that incorporates all these four factors.

To overcome the limitations, we propose to robust the semi-supervised Bayesian Deep Clustering (RBDC), which involves four parts, namely: The Student-t decoder does not explicitly impute for missing features and yields a robust reconstruction for heavy-tailed noise. Label-guided Gaussian mixture priors provide partial class label guidance in the learning process within the latent space, which is positioned between supervised and unsupervised learning. An uncertainty-weighted Evidence Lower Bound (ELBO) scales the contribution of each sample by the posterior uncertainty, effectively being noisy or contaminated. Sytems with Hybrid EM + SGD optimisation strategy. The mixture is trained using the hybrid EM + SGD optimisation strategies. The latent uncertainty is used in the mixture updates. The framework is tested on University of California, Irvine (UCI) Adult Income and Gym Members Fitness datasets, and the results are compared against strong deep clustering baselines.

Results show that RBDC outperforms baseline methods in calibration, discrimination/predictive ability and clustering quality in the low supervision regime. Ablation studies suggest the benefit of label informed priors and uncertainty weighting in enabling stable and interpretable clustering. Results also highlight the complementary benefits of semi-supervision and modelling of uncertainty.

Our results show that RBDC offers a strong and label-efficient calibration-aware framework to clustering of noisy, incomplete and partially labelled tabular data. RBDC attempts to model in a single generative framework the missingness, noise, uncertainty and weak supervision in the data, with a possible benefit to downstream applications in decision support such as risk stratification, anomaly detection and predictive modelling. Hence RBDC provides a conceptually integrated approach to semi-supervised deep clustering for challenging real-world datasets.