Fast multi-view clustering via tensor hyperbolic tangent-p norm minimization

Tensor-based multi-view clustering methods have gained significant attention due to their ability to directly capture high-order information, often outperforming matrix-based approaches. However, these methods face challenges in efficiently processing large-scale datasets due to their high computational complexity. Moreover, most existing tensor-based approaches rely on the tensor nuclear norm (TNN) to approximate the tensor rank function. However, TNN penalizes larger singular values, which are essential for preserving critical structural information, thus constraining the extraction of multi-view information. To address these challenges, we propose a novel fast multi-view clustering method via tensor hyperbolic tangent-$p$ norm minimization. First, we incorporate an efficient anchor selection strategy and construct tensors from anchor-based representations, significantly reducing the computational burden of tensor-based approaches for large-scale datasets. Second, we introduce the tensor hyperbolic tangent-$p$ norm (THT${}_p$N), a more robust and accurate approximation of the tensor rank function, enabling improved extraction of multi-view consistency and complementarity. Extensive experiments on eight real-world datasets show that our proposed model not only surpasses tensor-based methods in clustering performance but also outperforms matrix-based methods in computational efficiency, establishing a new benchmark for fast multi-view clustering. Code is available at https://github.com/usualheart/FTHMC.