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Multi-scale Dynamic Graph Convolutional Network for Hyperspectral Image Classification

Sheng Wan, Chen Gong, Ping Zhong, Bo Du, Lefei Zhang, Jian Yang

arXiv:1905.06133v1eess.IVcs.LGstat.ML

TL;DR

Traditional CNNs use fixed regular grids, while conventional GCNs use fixed graphs that may misrepresent irregular hyperspectral regions. MDGCN dynamically refines graphs during convolution, combines multiple neighborhood scales, and uses superpixels; experiments on three datasets report better performance than state-of-the-art methods.

  • Problem

    Fixed-grid CNNs cannot adapt universally to irregular local regions, and fixed-graph GCNs may degrade classification when their input graph is inaccurate.

  • Method

    MDGCN alternates graph updating and feature embedding, constructs graphs at multiple neighborhood scales, and uses SLIC superpixels to reduce training complexity.

  • Results

    Experiments on three widely used hyperspectral image datasets show that MDGCN achieves better performance than compared state-of-the-art methods, while dynamic graphs outperform fixed-graph multi-scale convolution in ablation results.

  • Takeaways & Limitations

    Dynamic graph refinement and multi-scale graph convolution provide a framework for representing hyperspectral image regions and exploiting spatial context at multiple scales.

Abstract

from arXiv · show

Convolutional Neural Network (CNN) has demonstrated impressive ability to represent hyperspectral images and to achieve promising results in hyperspectral image classification. However, traditional CNN models can only operate convolution on regular square image regions with fixed size and weights, so they cannot universally adapt to the distinct local regions with various object distributions and geometric appearances. Therefore, their classification performances are still to be improved, especially in class boundaries. To alleviate this shortcoming, we consider employing the recently proposed Graph Convolutional Network (GCN) for hyperspectral image classification, as it can conduct the convolution on arbitrarily structured non-Euclidean data and is applicable to the irregular image regions represented by graph topological information. Different from the commonly used GCN models which work on a fixed graph, we enable the graph to be dynamically updated along with the graph convolution process, so that these two steps can be benefited from each other to gradually produce the discriminative embedded features as well as a refined graph. Moreover, to comprehensively deploy the multi-scale information inherited by hyperspectral images, we establish multiple input graphs with different neighborhood scales to extensively exploit the diversified spectral-spatial correlations at multiple scales. Therefore, our method is termed 'Multi-scale Dynamic Graph Convolutional Network' (MDGCN). The experimental results on three typical benchmark datasets firmly demonstrate the superiority of the proposed MDGCN to other state-of-the-art methods in both qualitative and quantitative aspects.

I. INTRODUCTION

Hyperspectral image classification has progressed from handcrafted and conventional methods toward deep learning, but CNNs and fixed-graph approaches remain limited in adapting to irregular spatial structure and evolving pixel relationships. MDGCN addresses these issues with dynamically refined, multi-scale graphs and reports state-of-the-art performance on three benchmark datasets.

  • Hyperspectral images contain hundreds of contiguous bands and support applications including target detection, vegetation monitoring, and disaster prevention.
  • Conventional methods rely on handcrafted spectral-spatial features that depend heavily on professional expertise and are empirical.
  • CNN-based approaches can learn representations, but spectral-only models neglect spatial details and regular-grid convolution cannot universally adapt to varied local regions and class boundaries.
  • GCN aggregates neighboring node features on arbitrary graph structures, encoding node features and local graph structure while preserving irregular class boundaries.
  • Traditional GCN remains inadequate because noisy hyperspectral data can produce inaccurate graphs, while pixel-scale processing omits spatial context and can be computationally costly.
  • MDGCN alternates graph updating and feature embedding, constructs multiple neighborhood-scale graphs, uses superpixels to reduce training complexity, and achieves state-of-the-art performance on three datasets.

B. Graph Convolutional Network

The method converts a hyperspectral image into a multi-scale graph representation over SLIC superpixels, then applies graph convolutions that aggregate spectral-spatial information while refining the graphs.

  • Prior GNN and GCN methods operate on graph-structured non-Euclidean data, but prior hyperspectral GCN work uses a fixed graph and limited neighborhood size.
  • Graphs are constructed over superpixels at different spatial scales, and convolutions simultaneously aggregate multi-scale spectral-spatial features and refine input graphs.
  • A. Superpixel Segmentation: SLIC segments the image into compact, homogeneous superpixels, each treated as a graph node with an average spectral signature.
  • A. Superpixel Segmentation: Replacing pixels with superpixels significantly reduces graph-node count and improves computational efficiency for graph convolution and classification.
  • A. Superpixel Segmentation: Nearby pixels with high spatial consistency are likely to share land-cover labels, supporting superpixel-based local structural preservation.

B. Graph Convolutional Network

The GCN backbone performs localized spectral graph filtering and stacks nonlinear graph-convolution layers to generate node embeddings from neighborhood information.

  • B. Graph Convolutional Network: GCN generates node embeddings by progressively fusing features from neighboring nodes on a graph.
  • B. Graph Convolutional Network: Graph spectral filtering uses the normalized Laplacian, whose eigendecomposition defines filters as functions of graph-Laplacian eigenvalues.
  • B. Graph Convolutional Network: Chebyshev-polynomial expansion approximates spectral filters without explicitly computing the eigenvector decomposition.
  • B. Graph Convolutional Network: A Kth-order polynomial filter depends only on nodes at most K steps away; this work uses first-order neighborhoods with K = 1.
  • B. Graph Convolutional Network: Multiple graph-convolutional layers followed by softplus nonlinearities produce diverse filter functions through layer stacking.

2 AD−1 2 )x (6)

The GCN formulation applies a renormalized adjacency-based propagation operator to transform node features through trainable weights and a nonlinear activation.

  • Renormalization addresses numerical instability and exploding or vanishing gradients caused by repeatedly applying the unnormalized propagation operator.
  • The convolutional layer maps input features through the graph propagation operator, trainable weight matrix, and activation function to produce an embedding output.

C. Dynamic Graph Evolution

MDGCN dynamically refines the graph during convolution by combining the previous adjacency structure with similarities from current embeddings. An additional projection preserves the initial graph structure when embeddings are not yet sufficiently accurate.

  • Dynamic graph refinement: Dynamic GCN alternates graph updating and feature embedding so each progressively improves the other.The refined graph is intended to produce more discriminative embeddings, while improved embeddings support a more accurate graph.
  • Dynamic graph refinement: The embedding kernel KE = H(l)H(l)⊤ encodes pairwise similarity between embeddings generated at layer l.A(l) denotes the adjacency matrix in the lth layer.
  • Kernel fusion: The fused kernel combines the previous adjacency matrix A(l) and embedding kernel KE through a weighted linear combination.α controls the weight assigned to KE.
  • Kernel fusion: Embedding-based fusion can degrade performance when embeddings do not yet characterize intrinsic similarity accurately.The method therefore re-emphasizes structure carried by the initial adjacency matrix through a subsequent projection.
  • Graph update: The updated graph A(l+1) is initialized from the original adjacency matrix at the first graph-convolution layer and then dynamically updated across layers.The update is derived from the marginal Gaussian covariance of the next-layer representation.
  • Graph update: The update assigns greater similarity to nodes that share many common neighbors.This provides a structural interpretation of the dynamically refined adjacency.

D. Multi-Scale Manipulation

MDGCN captures spectral-spatial context at multiple neighborhood scales by constructing separate graphs over superpixels. These scale-specific convolutions share the input features and produce a combined network output while dynamically updating the graphs.

  • Multi-scale graph construction: Different neighborhood scales capture contextual information from diverse geometric appearances and local image properties.At scale s, each superpixel xi connects to its s-hop neighbors.
  • Multi-scale convolution: MDGCN computes graph-convolution outputs for each scale while updating the corresponding adjacency matrices after every layer.Algorithm 1 alternates layer-output calculation and graph updates before producing the final network output.
  • Multi-scale convolution: The input feature matrix H(0) is shared across scales, while each scale has its own adjacency, output, and trainable weight matrices.The shared input enables parallel scale-specific processing from common initial features.
  • Multi-scale convolution: The outputs from the shared-depth scale branches are combined into O, the MDGCN output, and trained with cross-entropy on labeled examples.All superpixels are used for full-batch gradient descent.

IV. EXPERIMENTAL RESULTS

The experiments evaluate MDGCN on three publicly available hyperspectral datasets using classification accuracy and efficiency analyses. They also test the contributions of multi-scale processing and dynamic graph updating.

  • Experimental design: MDGCN is compared with state-of-the-art methods on three publicly available hyperspectral datasets using per-class accuracy, OA, AA, and kappa.The study additionally analyzes the effects of multi-scale manipulation, dynamic graphs, and computational time.
  • Experimental design: The experimental procedure trains the model after SLIC segmentation, initial multi-scale graph construction, and repeated dynamic convolution.The listed configuration uses T = 5000 iterations, η = 0.0005, S = 3 scales, and L = 2 graph-convolution layers.
  • Qualitative evaluation: The visual comparison on Indian Pines includes classification maps from different methods alongside the ground-truth map.The passage identifies the figure as a qualitative comparison.

A. Datasets

The evaluation uses three hyperspectral image datasets: Indian Pines, the University of Pavia, and the Kennedy Space Center.

  • Evaluation datasets: The three evaluation datasets are Indian Pines, the University of Pavia, and the Kennedy Space Center.They are introduced as the datasets used to evaluate MDGCN.

1) Indian Pines:

The paper evaluates MDGCN on three benchmark hyperspectral datasets and uses dataset-specific labeled and unlabeled pixels for classification experiments. Its architecture employs three neighborhood scales across all datasets.

  • Indian Pines contains 145 × 145 pixels, 200 retained spectral bands, and 16 land-cover classes after removing noisy and water-absorption bands.
  • The University of Pavia dataset contains 610×340 pixels, 103 spectral channels, and 9 land-cover classes.
  • The Kennedy Space Center dataset contains 614 × 512 pixels, 176 retained bands, and 13 land-cover classes after removing noisy and water-absorption bands.
  • Training usually selects 30 labeled pixels per class, or 15 when a class has fewer than 30 examples, then splits labeled examples into training and validation sets.
  • MDGCN uses three neighborhood scales, s = 1, s = 2, and s = 3, with two graph convolutional layers per scale.

C. Classification Results

MDGCN is compared with CNN- and GCN-based baselines using quantitative tables and classification maps. Across Indian Pines and University of Pavia, it achieves the strongest reported results and produces smoother, less misclassified maps.

  • Results on the Indian Pines Dataset: On Indian Pines, MDGCN achieves top-level performance for OA, AA, and Kappa, with small standard deviations.
  • Results on the Indian Pines Dataset: GCN-based methods outperform R-2D-CNN and DR-CNN on Indian Pines by adaptively aggregating features over irregular non-Euclidean regions.
  • Results on the Indian Pines Dataset: On Indian Pines, MDGCN produces a smoother classification map with fewer misclassifications than the compared methods.
  • Results on the University of Pavia Dataset: On University of Pavia, MDGCN ranks first and outperforms the compared methods by a substantial margin, while GCN and S2GCN are excluded for scalability reasons.
  • Results on the University of Pavia Dataset: Because University of Pavia classes are widely scattered, DR-CNN and MDGCN outperform HiFi, JSDF, and other baseline methods.
  • Results on the University of Pavia Dataset: The University of Pavia map for MDGCN shows stronger spatial correlation and fewer misclassifications than DR-CNN and other competitors.

3) Results on the Kennedy Space Center Dataset:

On Kennedy Space Center, MDGCN performs competitively against strong baselines and produces precise classifications in small, difficult regions. Its evaluation also examines robustness to labeled-example counts and the contributions of multi-scale and dynamic graph operations.

  • HiFi achieves the highest OA among baseline methods, while only slight OA gaps separate it from MDGCN.
  • MDGCN misclassifies pixels only in the sixth class, “Hardwood,” on the Kennedy Space Center dataset.
  • Enlarged classification maps show that MDGCN produces precise results in small and difficult Kennedy Space Center regions.
  • Increasing labeled examples per class from 5 to 30 improves the overall accuracy of all evaluated methods on Indian Pines.
  • Ablation Study: MDGCN consistently outperforms single-scale settings s = 1, s = 2, and s = 3 in OA, AA, and Kappa coefficient.
  • Ablation Study: Compared with fixed-graph MGCN, MDGCN improves OA, AA, and Kappa coefficient, indicating the usefulness of dynamically updated graphs.

F. Classification Performance in the Boundary Region

MDGCN is designed to preserve class-boundary information by applying graph convolution to irregular regions, while dynamic multi-scale graphs refine representations and spatial context. Boundary-region maps show more compact and accurate MDGCN classifications than competing methods.

  • Traditional CNNs use identical kernel weights over image patches, which may cause misclassifications in boundary regions.
  • MDGCN applies graph convolution flexibly to irregular image patches, reducing boundary erasure during convolution.
  • In the Indian Pines boundary region, GCN, S2GCN, R-2D-CNN, DR-CNN, MDA, HiFi, and JSDF produce confusing and inaccurate results near class boundaries.
  • MDGCN produces a more compact and accurate classification map than the other compared methods in the investigated boundary region.
  • Dynamic graphs are refined during convolution to encode intrinsic similarities and support accurate region representations.
  • Multiple graphs with different neighborhood scales exploit spatial context carried by different scales.
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