Chengliang Song

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, Chengliang Song, Weidong Jiang et al.

High-dimensional data, particularly in the form of high-order tensors, presents a major challenge in self-supervised learning. While MLP-based autoencoders (AE) are commonly employed, their dependence on flattening operations exacerbates the curse of dimensionality, leading to excessively large model sizes, high computational overhead, and challenging optimization for deep structural feature capture. Although existing tensor networks alleviate computational burdens through tensor decomposition techniques, most exhibit limited capability in learning non-linear relationships. To overcome these limitations, we introduce the Mode-Aware Non-linear Tucker Autoencoder (MA-NTAE). MA-NTAE generalized classical Tucker decomposition to a non-linear framework and employs a Pick-and-Unfold strategy, facilitating flexible per-mode encoding of high-order tensors via recursive unfold-encode-fold operations, effectively integrating tensor structural priors. Notably, MA-NTAE exhibits linear growth in computational complexity with tensor order and proportional growth with mode dimensions. Extensive experiments demonstrate MA-NTAE's performance advantages over standard AE and current tensor networks in compression and clustering tasks, which become increasingly pronounced for higher-order, higher-dimensional tensors.