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Extreme Learning Machine (ELM) has been widely used for various classification problems. However, the traditional ELMs are typically based on the regular Euclidean data, thus ignoring the intrinsic structured information among data and resulting in poor robustness. In this paper, we present a novel semi-supervised learning framework, termed Graph Convolutional Extreme Learning Machines (GCELM), based on extending the traditional ELM to the non-Euclidean domain. Technically, we recast ELM layers into a randomized graph convolutional embedding layer followed by a graph convolutional regression layer, which endows ELM with the capability to handle graphs in the non-Euclidean domain. Benefiting from the diversity of the randomized graph convolution, we further propose an enhanced GCELM, i.e., Voting-based GCELM (V-GCELM), by using a simple voting ensemble strategy. The proposed methods preserve the advantages of ELMs, thus being more efficient than the gradient-based graph convolutional networks but without loss of graph learning ability. Extensive experiments on 36 benchmark datasets demonstrate that the proposed methods significantly outperform many previous semi-supervised classification methods. • Classic ELM is generalized into the non-Euclidean domain by using graph convolution. • An ensemble-based graph convolutional ELM is proposed for semi-supervised learning. • The proposed methods are benchmarked on 36 standard UCI datasets. • Our methods significantly outperform many existing methods by a large margin. [ABSTRACT FROM AUTHOR]

• MARP can perform excellent performance with low computational complexity. • Nodes impaction on classification is suppressed via proposed ARP mechanism. • LSTM is adopted to update nodes and preserve local convolutional feature. • Avoiding local optimization problem by multi-scale perception mechanism. In recent years, the applications of graph convolutional networks (GCNs) in hyperspectral image (HSI) classification have attracted much attention. However, hyperspectral classification faces problems such as complex noise effects, spectral variability, labelled training sample deficiency, and high spectral mixing between materials. Furthermore, the available GCN-based methods are computationally complex and cannot automatically adjust aggregate paths. To mitigate these issues, we propose a novel multiadaptive receptive field-based graph neural framework (MARP) for HSI classification. In our method, an adaptive receptive path aggregation (ARP) mechanism is proposed to suppress the impact of noise nodes on classification and automatically explore an adaptive receptive field, where a graph attention (GAT) neural network is introduced to learn the importance of different-sized neighbourhoods and a long short-term memory (LSTM) method is adopted to update the nodes and preserve the local convolutional features of the nodes. To address the problem that ARP may fall into a local optimum, we design a multiscale receptive mechanism. Extensive experimental results obtained on four public HSI datasets demonstrate that the proposed MARP method can mitigate oversmoothing and reduce computational complexity while achieving competitive performance when compared to several state-of-the-art methods. [ABSTRACT FROM AUTHOR]