This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity constraints. Our approach accommodates both linear and logistic regression formulations for diverse response variables while addressing the structural heterogeneity inherent in multidimensional tensor data. We integrate fused LASSO, total variation, and ridge regularizers — each tailored to specific tensor modes — and develop an efficient alternating direction method of multipliers (ADMM)-based algorithm for parameter estimation. Comprehensive experiments on synthetic signals and real hyperspectral datasets demonstrate that NS-KTR consistently outperforms conventional tensor regression methods. The framework’s ability to preserve distinct structural characteristics across tensor dimensions while ensuring physical interpretability makes it especially suitable for applications in signal processing and hyperspectral image analysis. • NS-KTR: nonnegative structured Kruskal tensor regression with hybrid regularization. • Mode-specific regularization: LASSO, total variation, and ridge across tensor modes. • Unified framework supports linear and logistic regression for diverse responses. • ADMM-based optimization achieves superior accuracy with significant speedups.

We propose a robust activity detection for grant free random access using greedy covariance-learning-based matching pursuit (RCL-MP) algorithm. The method incorporates a robust loss function into the Gaussian negative log-likelihood function, and uses matching pursuit framework for greedily selecting the indices of active users. This algorithm employs a flexible loss function effectively recovering sparse support under non-Gaussian noise conditions. Furthermore, we numerically demonstrate the robustness of RCL-MP across various conditions in massive access scenarios.

Detecting social communities in large social networks provides an effective way to analyze the social media users' behaviors and activities. It has drawn extensive attention from both academia and industry. One essential aspect of communities in social networks is outer influence which is the capability to spread internal information of communities to external users. Detecting the communities of high outer influence has particular interest in a wide range of applications, e.g., Ads trending analytics, social opinion mining and news propagation pattern discovery. However, the existing detection techniques largely ignore the outer influence of the communities. To fill the gap, this work investigates the Most Influential Community Search problem to disclose the communities with the highest outer influences. We firstly propose a new community model, maximal kr-Clique community, which has desirable properties, i.e., society, cohesiveness, connectivity, and maximum. Then, we design a novel tree-based index structure, denoted as C-Tree, to maintain the offline computed r-cliques. To efficiently search the most influential communities, we also develop four advanced index-based algorithms which improve the search performance of non-indexed solution by about 200 times. The efficiency and effectiveness of our solution have been extensively verified using six real datasets and a small case study.