Unsupervised Regression for Graph-Free and Discrete Clustering

Through optimizing discrete labels directly, discrete clustering technique enables to address potential information loss issue in spectral clustering caused by multi-stage label processing. However, existingmethods typically depend on graph proximity in the original feature space and often neglect the intrinsic mapping between data and labels in low-dimensional latent space, restricting the improvement of clustering performance on high-dimensional data. To this end, we draw the inspiration from unsupervised regression learning and design a novel trace maximization discrete clustering model, termed Unsupervised Regression for Graph-Free and Discrete Clustering (UR-GFDC). This model dynamically learns reliable discrete labels guided by regression information embedded in latent subspace. Furthermore, it decouples from graph dependence to prevent low-quality graphs from degrading clustering outcomes. To solve the designed discrete model, we develop a new optimization scheme that incorporates coordinate descent strategy into iteratively re-weighted algorithm, thus simplifying the quadratic optimization problem into a more tractable iteratively linear optimization problem. Systematic experiments illuminate the clustering efficacy and superiority of UR-GFDC.