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The joint clustering of multimodal remote sensing (RS) data poses a critical and challenging task in Earth observation. Although recent advances in multiview subspace clustering have shown remarkable success, existing methods become computationally prohibitive when dealing with large-scale RS datasets. Moreover, they neglect intrinsic nonlinear and spatial interdependencies among heterogeneous RS data and lack generalization ability for out-of-sample data, thereby restricting their applicability. This article introduces a novel unified framework called anchor-based multiview kernel subspace clustering with spatial regularization (AMKSC). It learns a scalable anchor graph in the kernel space, leveraging contributions from each modality instead of seeking a consensus full graph in the feature space. To ensure spatial consistency, we incorporate a spatial smoothing operation into the formulation. The method is efficiently solved using an alternating optimization strategy, and we provide theoretical evidence of its scalability with linear computational complexity. Furthermore, an out-of-sample extension of AMKSC based on multiview collaborative representation-based classification is introduced, enabling the handling of larger datasets and unseen instances. Extensive experiments on three real heterogeneous RS datasets confirm the superiority of our proposed approach over state-of-the-art methods in terms of clustering performance and time efficiency. The source code is available at https://github.com/AngryCai/AMKSC.