Deep contrastive clustering has recently gained significant attention due to its advantageous ability to leverage the contrastive learning paradigm for joint representation learning and clustering. However, previous deep contrastive clustering approaches mostly focus on instance discrimination or cluster discrimination, which often overlook the rich semantic information latent in the vast intermediate levels of granularity between instances and clusters. Moreover, they are typically prone to utilizing relationships only within the same level of granularity, e.g., instance-instance relationships and cluster-cluster relationships, but frequently neglect the interactions between different granularity-levels that are ubiquitous in real-world scenarios. To tackle these issues, this paper presents a novel end-to-end deep contrastive clustering approach termed Deep Clustering with Hybrid-Grained Contrastive and Discriminative Learning (DCHL). Particularly, the instance-level contrastive learning and cluster-level contrastive learning are first formulated, where the cluster-level contrastive learning is further split into fine-grained and coarse-grained branches. To capture the global dependencies, the cluster-level contrastiveness is explored on the coarse-grained cluster branch. Meanwhile, to capture the hybrid-grained relationships, the dual-level instance-group discrimination learning is enforced between the instance branch and the fine-grained cluster branch, where the self instance-group discrimination and the cross instance-group discrimination are simultaneously optimized for enhancing the deep clustering performance. Experimental results on five challenging image datasets confirm the superiority of DCHL over state-of-the-art. Code available: https://github.com/dengxiaozhi/DCHL.

Aberrant activation of signaling pathways is frequently observed and reported to be associated with the progression and poor prognosis of prostate cancer (PCa). We aimed to identify key biological processes regulated by androgen receptor (AR) using gene co-expression network from single cell resolution. The bimodal index was used to evaluate whether two subpopulations exist among the single cells. Gene expression among single cells revealed averaging pitfalls and bimodality pattern. Weighted gene co-expression network analysis (WGCNA) was used to identify modules of highly correlated genes. Twenty-nine gene modules were identified and AR-regulated modules were screened by significantly overlapping reported androgen induced differentially expressed genes. The biological function “generation of precursor metabolites and energy” was significantly enriched by AR-regulated modules with bimodality, presenting differential androgen response among subpopulations. Integrating with public ChIP-seq data, two genes FECH, and CROT has AR binding sites. Public in vitro studies also show that androgen regulates FECH and CROT. After receiving androgen deprivation therapy, patients lowly express FECH and CROT. Further survival analysis indicates that FECH/CROT signature can predict PCa recurrence. We reveal the heterogeneous function of “generation of precursor metabolites and energy” upon androgen stimulation from the perspective of single cells. Inhibitors targeting this biological process will facilitate to prevent prostate cancer progression.

Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observations with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the methods using the TR model either require a preassigned TR rank or aggressively pursue the minimum TR rank, where the latter often leads to biased solutions in the presence of noise. To tackle these bottlenecks, a Bayesian robust TR decomposition (BRTR) method is proposed to give a more accurate solution for the RTC problem, which can avoid exquisite selection of the TR rank and penalty parameters. A variational Bayesian (VB) algorithm is developed to infer the probability distribution of posteriors. During the learning process, BRTR can prune off zero components of core tensors, resulting in automatic TR rank determination. Extensive experiments show that BRTR can achieve significantly improved performance than other state-of-the-art methods.