DDCL: Deep Dual Competitive Learning: A Differentiable End-to-End Framework for Unsupervised Prototype-Based Representation Learning

Learning discriminative representations is a central goal of supervised deep learning. While cross-entropy (CE) remains the dominant objective for classification, it does not explicitly enforce desirable geometric properties in the embedding space, such as intra-class compactness and inter-class separation. Existing metric learning approaches, including supervised contrastive learning (SupCon) and proxy-based methods, address this limitation by operating on pairwise or proxy-based relationships, but often increase computational cost and complexity. In this work, we introduce Soft Silhouette Loss, a novel differentiable objective inspired by the classical silhouette coefficient from clustering analysis. Unlike pairwise objectives, our formulation evaluates each sample against all classes in the batch, providing a batch-level notion of global structure. The proposed loss directly encourages samples to be closer to their own class than to competing classes, while remaining lightweight. Soft Silhouette Loss can be seamlessly combined with cross-entropy, and is also complementary to supervised contrastive learning. We propose a hybrid objective that integrates them, jointly optimizing local pairwise consistency and global cluster structure. Extensive experiments on seven diverse datasets demonstrate that: (i) augmenting CE with Soft Silhouette Loss consistently improves over CE and other metric learning baselines; (ii) the hybrid formulation outperforms SupCon alone; and (iii) the combined method achieves the best performance, improving average top-1 accuracy from 36.71% (CE) and 37.85% (SupCon2) to 39.08%, while incurring substantially lower computational overhead. These results suggest that classical clustering principles can be reinterpreted as differentiable objectives for deep learning, enabling efficient optimization of both local and global structure in representation spaces.

An unsupervised framework for hyperspectral image (HSI) clustering is proposed that incorporates masked deep representation learning with diffusion-based clustering, extending the Spatially-Regularized Superpixel-based Diffusion Learning ($S^2DL$) algorithm. Initially, a denoised latent representation of the original HSI is learned via an unsupervised masked autoencoder (UMAE) model with a Vision Transformer backbone. The UMAE takes spatial context and long-range spectral correlations into account and incorporates an efficient pretraining process via masking that utilizes only a small subset of training pixels. In the next stage, the entropy rate superpixel (ERS) algorithm is used to segment the image into superpixels, and a spatially regularized diffusion graph is constructed using Euclidean and diffusion distances within the compressed latent space instead of the HSI space. The proposed algorithm, Deep Spatially-Regularized Superpixel-based Diffusion Learning ($DS^2DL$), leverages more faithful diffusion distances and subsequent diffusion graph construction that better reflect the intrinsic geometry of the underlying data manifold, improving labeling accuracy and clustering quality. Experiments on Botswana and KSC datasets demonstrate the efficacy of $DS^2DL$.

Clustering is an unsupervised learning technique that partitions unlabeled data into groups. Most existing methods require user-specified parameters, such as the number of clusters or neighborhood size. Conversely, we propose automatic depth-based local center clustering (A-DLCC), a fully data-driven method that eliminates numerical parameter tuning. A-DLCC uses the $β$-integrated local depth to identify stable exemplars, points consistently central across multiple locality levels, termed local centers, which are ranked by their representativeness. Each local center induces a group of similar points, with group-level similarity measured by a proposed nonparametric metric called group-level local similarity. To guide merging, we incorporate the bottleneck path idea from graph theory, which forms the basis of our adaptive merging criterion. Based on this criterion, we design a single agglomeration rule in which a group is either absorbed by a neighbor it reaches better than itself or bonded to a neighbor that both sides find more reachable than their own background, every merge being additionally required to be carried by a contact stronger than a configuration-model null expects. The rule automatically estimates the number of clusters and decides when to stop merging. Experiments on synthetic and real data show that A-DLCC produces interpretable clustering results without parameter tuning.