Spatial–Spectral Bipartite Graph Clustering With Low-Frequency Tensor Regularization for Hyperspectral and LiDAR Data

The increasing complexity of remote sensing (RS) applications necessitates multimodal data fusion to overcome the inherent limitations of single-source data. In particular, the integration of hyperspectral images (HSIs) and light detection and ranging (LiDAR) data captures complementary spectral and spatial features, significantly enhancing object discrimination. Unlike supervised methods requiring costly expert annotations, unsupervised clustering eliminates labeling needs, thereby offering an efficient solution for complex scene analysis with reduced deployment costs. However, existing unsupervised clustering methods still face several challenges, including insufficient utilization of spatial information, high data dimensionality, and interference from high-frequency noise, which collectively hinder their further development and practical application. To address these issues, this article proposes a novel method called spatial–spectral bipartite graph clustering with low-frequency tensor (SSBC-LFT) regularization for hyperspectral and LiDAR data. The proposed method first focuses on modeling clustering structures, innovatively constructing spatially informed bipartite graphs for each modality to enrich spatial details while reducing computational complexity. Additionally, an adaptive spectral band selection mechanism dynamically assigns higher weights to discriminative bands during clustering while suppressing redundant ones. Finally, through proposed low-frequency tensor nuclear norm (LFTNN) regularization, high-frequency noise is effectively filtered in the frequency domain, extracting stable and consistent cross-modal structural information from the low-rank space to further enhance clustering robustness and accuracy. Extensive experiments on real-world multimodal RS datasets demonstrate the superior performance of the SSBC-LFT model, offering a robust and effective solution for unsupervised clustering in complex scenarios.