Sparse Convex Biclustering

Biclustering is an essential unsupervised machine learning technique for simultaneously clustering rows and columns of a data matrix, with widespread applications in genomics, transcriptomics, and other high-dimensional omics data. Despite its importance, existing biclustering methods struggle to meet the demands of modern large-scale datasets. The challenges stem from the accumulation of noise in high-dimensional features, the limitations of non-convex optimization formulations, and the computational complexity of identifying meaningful biclusters. These issues often result in reduced accuracy and stability as the size of the dataset increases. To overcome these challenges, we propose Sparse Convex Biclustering (SpaCoBi), a novel method that penalizes noise during the biclustering process to improve both accuracy and robustness. By adopting a convex optimization framework and introducing a stability-based tuning criterion, SpaCoBi achieves an optimal balance between cluster fidelity and sparsity. Comprehensive numerical studies, including simulations and an application to mouse olfactory bulb data, demonstrate that SpaCoBi significantly outperforms state-of-the-art methods in accuracy. These results highlight SpaCoBi as a robust and efficient solution for biclustering in high-dimensional and large-scale datasets.

HDNet: A Hierarchically Decoupled Network for Crowd Counting

Recently, density map regression-based methods have dominated in crowd counting owing to their excellent fitting ability on density distribution. However, further improvement tends to saturate mainly because of the confusing background noise and the large density variation. In this paper, we propose a Hierarchically Decoupled Network (HDNet) to solve the above two problems within a unified framework. Specifically, a background classification sub-task is decomposed from the density map prediction task, which is then assigned to a Density Decoupling Module (DDM) to exploit its highly discriminative ability. For the remaining foreground prediction sub-task, it is further hierarchically decomposed to several density-specific sub-tasks by the DDM, which are then solved by the regression-based experts in a Foreground Density Estimation Module (FDEM). Although the proposed strategy effectively reduces the hypothesis space so as to relieve the optimization for those task-specific experts, the high correlation of these sub-tasks are ignored. Therefore, we introduce three types of interaction strategies to unify the whole framework, which are Feature Interaction, Gradient Interaction, and Scale Interaction. Integrated with the above spirits, HDNet achieves state-of-the-art performance on several popular counting benchmarks.