Xiangfeng Qiu

Junjing Zheng, Xinyu Zhang, Xiangfeng Qiu et al.

Semi-supervised hierarchical clustering aims to learn a tree structure consistent with data patterns and user-provided supervision. Supervision is usually given as leaf-level relations, such as pairwise must-link/cannot-link constraints or triplet-wise must-link-before constraints. Although useful for regulating local sample relations, such supervision does not directly indicate which samples should form coherent subtrees. Consequently, the non-leaf structure of the learned tree may deviate from the hierarchical organization preferred by ground-truth labels. To address this limitation, we propose a semi-supervised hyperbolic hierarchical clustering method with set-level structural priors. The main contribution is to introduce sets as basic modeling units for hierarchy learning. Each set denotes samples expected to cohere within a subtree and is induced from leaf-level supervision together with a learned constraint-consistent similarity structure. These sets act as soft structural priors for subtree-level supervision, allowing supervision to guide non-leaf hierarchy formation beyond local leaf-level relations. Specifically, we first learn constraint-consistent embeddings to obtain a reliable set partition, then construct constraint-induced sets and estimate inter-set similarities to form set-level structural priors. Finally, these priors are incorporated into a hyperbolic hierarchy objective for continuous tree optimization. Experiments on eleven benchmark datasets and ablation studies show that the proposed method consistently improves label consistency over representative hierarchical clustering baselines while also enhancing similarity-based tree quality.

Junjing Zheng, Xinyu Zhang, Weidong Jiang et al.

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve the computation burden. However, while existing methods exploit TD to preserve the data tensor structure, they do not consider the influence of data orientation and thus have difficulty in handling orientation-specific data such as time series. To solve the above problem, we utilize the orientation-dependent tensor-tensor product from Tensor Singular Value Decomposition based on *M-product (T-SVDM) and extend the one-dimensional Sparse Principal Component Analysis (SPCA) to a tensor form. The proposed sparse tensor PCA model can constrain sparsity at the specified mode and yield sparse tensor principal components, enhancing flexibility and accuracy in learning feature relations. To ensure fast convergence and a flexible description of feature correlation, we develop a convex version specially designed for general UFS tasks and propose an efficient slice-by-slice algorithm that performs dual optimization in the transform domain. Experimental results on real-world datasets demonstrate the effectiveness and remarkable computational efficiency of the proposed method for tensor data of diverse structures over the state-of-the-art. When transform axes align with feature distribution patterns, our method is promising for various applications. The codes related to our proposed methods and the experiments are available at https://github.com/zjj20212035/STPCA.git.