The joint clustering of multimodal remote sensing (RS) data represents a multiobjective optimization challenge involving conflicting modality-specific objectives and diverse regularization objectives. Current approaches to multiview subspace clustering (MVSC) often oversimplify this task by transforming it into a weighted single-objective optimization problem, neglecting the intricate interactions between objectives and leading to suboptimal subspace representations. The presence of quadratic decision variables in MVSC renders direct application on large-scale RS data impracticable using multiobjective evolutionary algorithms (MOEAs). To overcome this challenge, we propose a novel MVSC method termed multiobjective multiview attributed graph learning (MMAGL). Instead of optimizing every self-representation coefficient individually, our method transforms MVSC into a link prediction task over a sparse attributed graph that fuses different modalities. We incorporate superpixel-based sample reduction and proximity-based population coding, leveraging spatial and structural priors, respectively. This results in a significantly compressed decision space, enabling optimization with MOEAs. To fully exploit node attributes and the graph structure, we redefine self-representation using contrastive learning and introduce an efficient graph filtering (GF) through a generalized spectral graph convolution, enhancing clustering discriminability. The proposed MMAGL constitutes a hybrid and versatile framework, adaptable to any MOEA. Extensive experimental evaluations demonstrate that our MMAGL method surpasses the current state-of-the-art on multimodal RS benchmarks (e.g., with nearly 2% gain on Trento and 3% on Houston) on overall accuracy.

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.

This article presents FLGC, a simple yet effective fully linear graph convolutional network for semi-supervised and unsupervised learning. Instead of using gradient descent, we train FLGC based on computing a global optimal closed-form solution with a decoupled procedure, resulting in a generalized linear framework and making it easier to implement, train, and apply. We show that (1) FLGC is powerful to deal with both graph-structured data and regular data, (2) training graph convolutional models with closed-form solutions improve computational efficiency without degrading performance, and (3) FLGC acts as a natural generalization of classic linear models in the non-Euclidean domain (e.g., ridge regression and subspace clustering). Furthermore, we implement a semi-supervised FLGC and an unsupervised FLGC by introducing an initial residual strategy, enabling FLGC to aggregate long-range neighborhoods and alleviate over-smoothing. We compare our semi-supervised and unsupervised FLGCs against many state-of-the-art methods on a variety of classification and clustering benchmarks, demonstrating that the proposed FLGC models consistently outperform previous methods in terms of accuracy, robustness, and learning efficiency. The core code of our FLGC is released at https://github.com/AngryCai/FLGC .

Deep neural networks have gained increasing interest in hyperspectral image (HSI) processing. However, prior arts often neglect the high-order correlation among data points, failing to capture intraclass variations. In this letter, we present a unified neural network framework, termed as hypergraph-structured autoencoder (HyperAE), to leverage the high-order relationship among data and learn robust deep representation for downstream tasks. Technically, the proposed method adopts a deep autoencoder regularized by hypergraph structure as the backbone network, which is jointly trained with a task-specific branch, resulting in a multitask architecture. We separately combine the subspace clustering model and the softmax classifier into the HyperAE to deal with HSI unsupervised and semisupervised classification problems. Benefiting from the hypergraph, HyperAE endows traditional networks with the capacity of preserving the high-order structured information. We evaluate the proposed methods on three benchmarking HSI data sets, demonstrating that the proposed HyperAE dramatically outperforms many existing methods with significant margins in both unsupervised and semisupervised HSI classification problems.

Deep subspace clustering has achieved remarkable performances in the unsupervised classification of hyperspectral images. However, previous models based on pixel-level self-expressiveness of data suffer from the exponential growth of computational complexity and access memory requirements with increasing number of samples, thus leading to poor applicability to large hyperspectral images. This paper presents a Neighborhood Contrastive Subspace Clustering network (NCSC), a scalable and robust deep subspace clustering approach, for unsupervised classification of large hyperspectral images. Instead of using a conventional autoencoder, we devise a novel superpixel pooling autoencoder to learn the superpixel-level latent representation and subspace, allowing a contracted self-expressive layer. To encourage a robust subspace representation, we propose a novel neighborhood contrastive regularization to maximize the agreement between positive samples in subspace. We jointly train the resulting model in an end-to-end fashion by optimizing an adaptively weighted multi-task loss. Extensive experiments on three hyperspectral benchmarks demonstrate the effectiveness of the proposed approach and its substantial advancement of state-of-the-art approaches.

Randomized neural networks (NNs), such as random vector functional link (RVFL) and extreme learning machine (ELM), have been widely applied in various classification problems owing to their computational efficiency and universal approximation capability. However, such approaches are designed for regular Euclidean data and lack the ability to generalize to complex structured data. Moreover, their randomly generated parameters often lead to a suboptimal decision boundary with a growing requirement of hidden neurons. In this article, we first propose a plain framework, termed randomized graph convolutional networks (RGCNs), to generalize the classic randomized NNs to the non-Euclidean domain. Then, a hybrid framework called evolution-driven RGCN (EvoRGCN) is presented by using adaptive differential evolution with novelty search strategy to seek the globally optimal graph embedding for the plain RGCN. Finally, we recast the classic ELM and RVFL under the proposed frameworks, resulting in four novel semi-supervised models, including the plain models [i.e., graph convolutional extreme learning machines (GCELMs) and graph convolutional RVFL (GCRVFL)] and the optimized models (i.e., O-GCELM and O-GCRVFL). We show that our approaches are the natural generalization of the traditional randomized NNs in the non-Euclidean domain. Furthermore, our approaches not only retain the advantages of the classic approaches but also enable them to handle graph data. We compare our approaches against many existing methods across regular datasets and graph benchmarks, demonstrating that the proposed approaches dramatically outperform the compared methods with better generalization ability and robustness. Particularly, we quantitatively show the performance ranking of different randomized NNs, i.e., O-GCRVFL$> $O-GCELM$\approx $GCRVFL$> $GCELM$\approx $RVFL$> $ELM.

Hyperspectral image (HSI) clustering is a challenging task due to the high complexity of HSI data. Subspace clustering has been proven to be powerful for exploiting the intrinsic relationship between data points. Despite the impressive performance in the HSI clustering, traditional subspace clustering methods often ignore the inherent structural information among data. In this article, we revisit the subspace clustering with graph convolution and present a novel subspace clustering framework called graph convolutional subspace clustering (GCSC) for robust HSI clustering. Specifically, the framework recasts the self-expressiveness property of the data into the non-Euclidean domain, which results in a more robust graph embedding dictionary. We show that traditional subspace clustering models are the special forms of our framework with the Euclidean data. On the basis of the framework, we further propose two novel subspace clustering models by using the Frobenius norm, namely efficient GCSC (EGCSC) and efficient kernel GCSC (EKGCSC). Each model has a globally optimal closed-form solution, making it easier to implement, train, and apply in practice. Extensive experiments strongly evidence that EGCSC and EKGCSC dramatically outperform current models on three popular HSI data sets consistently.

Extreme Learning Machine (ELM) has gained lots of research interest due to its universal approximation capability and fast learning speed. However, traditional ELMs are devised for regular Euclidean data, such as 2D grid and 1D sequence, and thus don't apply to non-Euclidean data, e.g., graph-structured data. To overcome this shortcoming, this paper presents a Graph Convolutional Extreme Learning Machine (termed as GCELM) for semi-supervised classification. Technically, a random graph convolutional layer is introduced to replace the random projection of original ELM, which endues ELM with the capability of dealing with graph-structured data directly. To generate a robust graph from the raw dataset, a self-representation model is adopted to construct a weighted graph. Extensive experiments on 27 UCI datasets demonstrate that GCELM outperforms many popular semi-supervised methods, and with faster learning speed. To the best of our knowledge, this is the first work that combines graph convolution with ELM.