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SLCGC: A lightweight Self-supervised Low-pass Contrastive Graph Clustering Network for Hyperspectral Images

Yao Ding, Zhili Zhang, Aitao Yang, Yaoming Cai, Xiongwu Xiao, Danfeng Hong, Junsong Yuan

arXiv:2502.03497v2eess.IV

TL;DR

HSI clustering lacks labels while requiring representations that capture complex spatial-spectral structure, and existing methods face limitations in accuracy, discriminability, efficiency, and noise robustness. SLCGC combines homogeneous-region graph construction, low-pass denoising, dual-branch contrastive learning, and K-means clustering. Experiments report strong clustering performance, computational efficiency, and robustness, including gains on the Salinas image.

  • Problem

    HSI clustering must learn spatial-spectral structure without manually labeled data, while existing methods have limitations in accuracy, feature discriminability, computational efficiency, and noise robustness.

  • Method

    SLCGC aggregates pixels into homogeneous regions, applies low-pass graph denoising, generates augmented views with two MLP-based branches, uses cross-view contrastive learning, and clusters latent features with K-means.

  • Results

    85.48% OA, 83.77% κ, 88.81% ARI, and 86.01% Purity were achieved on Salinas, improving over second-best performances by 6.67%, 7.75%, 16.98%, and 2.44%, respectively.

  • Takeaways & Limitations

    The reported experiments support SLCGC as an efficient self-supervised HSI clustering method with strong clustering performance and robustness to noise interference.

Abstract

from arXiv · show

Self-supervised hyperspectral image (HSI) clustering remains a fundamental yet challenging task due to the absence of labeled data and the inherent complexity of spatial-spectral interactions. While recent advancements have explored innovative approaches, existing methods face critical limitations in clustering accuracy, feature discriminability, computational efficiency, and robustness to noise, hindering their practical deployment. In this paper, a self-supervised efficient low-pass contrastive graph clustering (SLCGC) is introduced for HSIs. Our approach begins with homogeneous region generation, which aggregates pixels into spectrally consistent regions to preserve local spatial-spectral coherence while drastically reducing graph complexity. We then construct a structural graph using an adjacency matrix A and introduce a low-pass graph denoising mechanism to suppress high-frequency noise in the graph topology, ensuring stable feature propagation. A dual-branch graph contrastive learning module is developed, where Gaussian noise perturbations generate augmented views through two multilayer perceptrons (MLPs), and a cross-view contrastive loss enforces structural consistency between views to learn noise-invariant representations. Finally, latent embeddings optimized by this process are clustered via K-means. Extensive experiments and repeated comparative analysis have verified that our SLCGC contains high clustering accuracy, low computational complexity, and strong robustness. The code source will be available at https://github.com/DY-HYX.

I. INTRODUCTION

HSI clustering addresses the need to discover pixel groups without manually labeled data, while existing methods struggle to represent deep spatial structure. SLCGC reduces graph complexity, denoises graph features, and uses contrastive learning to improve structural consistency and discriminative representations.

  • HSI clustering is challenging because it lacks labeled samples and must capture rich spatial details and inherent relationships without supervision.
  • Traditional clustering methods remain limited by HSI spectral complexity and weak expression of deep structural information, affecting accuracy and robustness.
  • SLCGC transforms pixels into homogeneous regions with superpixel segmentation, preserving local spatial-spectral structure while reducing graph node count.
  • Low-pass graph denoising filters high-frequency noise and preserves smoothed node features during neighbor information aggregation.
  • Two MLP-based branches provide augmented views, while a cross-view contrastive loss enhances structural consistency and discriminative capability.
  • The method represents graph nodes, features, filters, augmented views, similarity, adjacency, and contrastive loss through the paper’s defined notation.

B. Graph Filter

The graph filter section connects Fourier-domain filtering with graph convolution and graph filtering, defining frequency responses over graph signals. These operations provide the basis for manipulating graph-node signals according to graph frequencies.

  • Fourier convolution represents a discrete signal through an input frequency-domain signal, an output time-domain signal, and a frequency response function.
  • Graph convolution replaces the continuous integral with a sum over graph frequencies and Fourier-basis components.
  • The graph filter is defined through a frequency response matrix that operates on graph-signal components.

C. Contrastive Learning

Contrastive learning learns representations by comparing similar and dissimilar samples. In SLCGC, this framework is organized around positive and negative relationships between samples and supports the broader clustering pipeline.

  • Contrastive learning extracts features by comparing similarities and differences between positive and negative sample pairs.
  • The learned mapping function is designed so each sample remains similar to a positive sample and dissimilar to a negative sample.
  • SLCGC’s method overview includes homogeneous-region generation, low-pass graph denoising, graph structural contrastive learning, and feature fusion and clustering.

A. Problem Definition and Overview of SLCGC

SLCGC transforms hyperspectral images from pixels into homogeneous superpixel graph nodes, preserving local spatial-spectral structure while reducing graph size. Its workflow then denoises the graph, learns structural representations, fuses features, and clusters them.

  • Homogeneous Region Generation: SLCGC uses homogeneous-region generation to transform HSI pixels into superpixel graph nodes while preserving local spatial-spectral structure and reducing node count.Superpixels are formed after dimensionality reduction and spatial clustering.
  • Overall Framework: The framework comprises homogeneous-region generation, low-pass graph denoising, graph structural contrastive learning, and feature fusion and clustering modules.These components are joined in an end-to-end network, with each portion interacting with the others.
  • Overall Workflow: The workflow constructs an adjacency-based structure graph, applies low-pass denoising, performs graph contrastive learning with two MLPs, and clusters latent features using K-means.The conceptual workflow presents these stages in sequence.
  • Graph Construction: Each superpixel becomes a graph node, with nearest-neighbor relationships defining the adjacency matrix and average spectral features defining node features.The number of graph nodes satisfies N ≪ h × w.
  • Pixel-to-Graph Projection: A correlation matrix maps pixels to superpixels, while normalized graph projection produces superpixel-level node features from the original HSI.The projection uses the SLIC-derived pixel-superpixel correspondence matrix.

C. Low-pass Graph Denoising

SLCGC applies graph Laplacian filtering to smooth node signals by suppressing high-frequency components while preserving low-frequency components. The resulting smoothed features are used to improve clustering performance, with filter depth trading off denoising against computational cost.

  • Denoising Mechanism: The low-pass graph denoising mechanism filters graph-structure noise and obtains a smoothed structure graph for efficient high-frequency noise removal.The mechanism is motivated by graph-filtering effects on graph convolution performance.
  • Signal Smoothness: A smaller Rayleigh quotient indicates a smoother graph signal because it measures similarity between node features across graph edges.The quotient is used to quantify graph-signal smoothness.
  • Frequency Filtering: Filtering high-frequency basis signals while preserving low-frequency basis signals produces a smoother graph signal.The stated condition is a nonnegative, nonincreasing frequency response for the graph filter.
  • Layered Filtering: The graph Laplacian filter is stacked for t layers, producing smoothed node features that preserve low-pass spectral information.X denotes the original node feature and X_t the smoothed node feature.

D. Graph Structural Contrastive Learning

The graph structural contrastive module encodes smoothed node features through two unshared MLP branches and creates augmented views with Gaussian noise. A cross-view loss compares these views to graph adjacency structure, after which fused representations are clustered with K-means.

  • Dual-Branch Encoding: Two parameter-unshared MLP encoders process smoothed node features without using a graph convolutional neural network.The learned node features are subsequently normalized with the ℓ2 norm.
  • Dual-Branch Encoding: The two unshared branches produce augmented views containing different semantic information during training.The branches are denoted l1 and l2.
  • View Augmentation: Random Gaussian noise perturbs one branch to generate two augmented representations and improve robustness to noise.The perturbation is introduced after the first branch representation is formed.
  • Feature Fusion and Clustering: The learned augmented views are fused linearly into clustering-oriented node features, and K-means produces the final clustering results.The algorithm applies K-means to the resulting feature representation.
  • Cross-View Contrastive Loss: A cross-view contrastive loss enhances structural consistency by comparing a similarity matrix between the two views with a self-looped adjacency matrix.The similarity matrix evaluates pairwise node-feature similarity across branches.
  • Contrastive Pairing: Cross-view neighbor nodes are treated as positive samples and nonneighbor nodes as negative samples during Adam-optimized training.The loss is minimized to update the network weights.

F. Computational Complexity Analysis

SLCGC’s complexity is expressed in terms of graph size, feature dimensions, MLP dimensions, and training iterations, and the analysis characterizes the resulting network as computationally efficient.

  • Component Complexity: The low-pass graph denoising mechanism has computational complexity O(Nd2), while graph structural contrastive learning has complexity O(2Ndd1 + 2Nd1d2).N is the graph dimension, d is the HSI dimension, and d1 and d2 are MLP dimensions.
  • Overall Complexity: With T training iterations, SLCGC has overall complexity O[(Nd2) + 2Nd1(d + d2)T].The expression combines denoising and contrastive-learning costs across training iterations.
  • Efficiency Conclusion: The complexity analysis concludes that the proposed network has high computational efficiency.

IV. EXPERIMENT

Experiments evaluate SLCGC on three HSI datasets against representative traditional, subspace, deep, and graph autoencoder clustering methods using repeated runs and multiple metrics.

  • Experiments use the Salinas, Pavia University, and Trento HSI datasets.
  • SLCGC is compared with K-means, FCM, SC, SSSC, NCSC, SDCN, EGAE, and AdaGAE.The baselines span traditional, subspace, deep clustering, and graph autoencoder methods.
  • All methods are executed ten times on an NVIDIA Titan RTX using PyTorch to reduce bias from random training-sample selection.
  • Evaluation reports OA, PA, κ, NMI, ARI, and Purity, alongside qualitative clustering maps.

C. Comparative Experimental Results and Analysis

Across Salinas, PU, and Trento, SLCGC achieves the strongest reported clustering performance and produces visually smoother maps with fewer misclassifications.

  • Salinas: On Salinas, SLCGC achieves OA=85.48%, κ=83.77%, ARI=88.81%, and Purity=86.01%.These improve over the second-best performances by 6.67%, 7.75%, 16.98%, and 2.44%, respectively.
  • Qualitative analysis: SLCGC produces smoother clustering maps and fewer misclassified pixels than competing methods on Salinas, PU, and Trento.The Trento comparison identifies SLCGC as having the best visual clustering result.
  • PU: On PU, SLCGC obtains OA=68.23%, κ=58.70%, NMI=63.92%, ARI=52.32%, and Purity=75.36%.The reported improvements over second-best results are 13.04%, 6.24%, 8.63%, 13.63%, and 5.24%, respectively.
  • Sensitivity analysis: The sensitivity study varies epochs T and learning rate L across Salinas, PU, and Trento.
  • Trento: On Trento, SLCGC improves over second-best results by 13.36% OA, 17.05% κ, 11.26% NMI, 18.31% ARI, and 2.59% Purity.

D. Ablation Studies

Ablation experiments show that removing any principal SLCGC component reduces clustering performance, while hyperparameter tests identify dataset-sensitive training and filtering choices.

  • Ablation variants: The default ablations define SLCGC-V1 without homogeneous-region generation, SLCGC-V2 without low-pass graph denoising, and SLCGC-V3 without graph structural contrastive learning.
  • Ablation results: Removing homogeneous-region generation, low-pass graph denoising, graph structural contrastive learning, or Gaussian noise decreases clustering accuracy.The ablation results report declines across all indicators for the simplified variants.
  • Ablation results: Each proposed SLCGC block contributes differently to clustering accuracy.
  • Training hyperparameters: OA is highest when T=400 and L=10^-3, while different combinations of epochs and learning rate substantially affect clustering results.
  • Filtering hyperparameters: A graph Laplacian filter layer count of t=2 balances high-frequency noise filtering against computational complexity.Larger t filters more high-frequency graph noise but increases computational complexity.

F. Hyper-parameter Study

The study examines feature distributions and computational practicality, reporting strong clustering behavior, low model complexity, and future interest in lighter contrastive-learning methods.

  • Feature visualization: t-SNE visualizations compare original graph-node distributions with distributions after SLCGC processing across three datasets.Different map colors denote different land covers.
  • Computational cost: SLCGC has lower training time, testing time, and FLOPs than the other investigated deep clustering methods.
  • Overall assessment: The reported results combine strong clustering performance with small model complexity, supporting SLCGC’s practical application prospects.
  • Future work: Future work will explore more lightweight graph contrastive-learning methods and reinforcement learning for HSI preprocessing.
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