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Adaptive Homophily Clustering: Structure Homophily Graph Learning with Adaptive Filter for Hyperspectral Image

Yao Ding, Weijie Kang, Aitao Yang, Zhili Zhang, Junyang Zhao, Jie Feng, Danfeng Hong, Qinhe Zheng

arXiv:2501.01595v2cs.CV

TL;DR

HSI clustering lacks labels and is limited by insufficient structural information, feature presentation, and graph updating. AHSGC combines adaptive graph filtering, self-training, homophily-enhanced structure learning, and joint optimization. Experiments report high clustering accuracy, low computational complexity, and strong robustness, including improvements over comparison methods on PU.

  • Problem

    HSI clustering without training labels is limited by insufficient structural information utilization, poor feature presentation, and weak graph updating.

  • Method

    AHSGC constructs a superpixel graph, adaptively captures high- and low-frequency features, generates pseudo-labels for self-training, dynamically updates edges, and jointly optimizes the network.

  • Results

    AHSGC performs best among investigated clustering methods on PU, improving over the best comparison results by 3.55% OA, 1.83% κ, and 0.77% ARI.

  • Takeaways & Limitations

    The reported experiments support AHSGC as a clustering method with high accuracy, low computational complexity, and strong robustness.

Abstract

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Hyperspectral image (HSI) clustering has been a fundamental but challenging task with zero training labels. Currently, some deep graph clustering methods have been successfully explored for HSI due to their outstanding performance in effective spatial structural information encoding. Nevertheless, insufficient structural information utilization, poor feature presentation ability, and weak graph update capability limit their performance. Thus, in this paper, a homophily structure graph learning with an adaptive filter clustering method (AHSGC) for HSI is proposed. Specifically, homogeneous region generation is first developed for HSI processing and constructing the original graph. Afterward, an adaptive filter graph encoder is designed to adaptively capture the high and low frequency features on the graph for subsequence processing. Then, a graph embedding clustering self-training decoder is developed with KL Divergence, with which the pseudo-label is generated for network training. Meanwhile, homophily-enhanced structure learning is introduced to update the graph according to the clustering task, in which the orient correlation estimation is adopted to estimate the node connection, and graph edge sparsification is designed to adjust the edges in the graph dynamically. Finally, a joint network optimization is introduced to achieve network self-training and update the graph. The K-means is adopted to express the latent features. Extensive experiments and repeated comparative analysis have verified that our AHSGC 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 is challenged by high-dimensional, redundant data and graph methods that use fixed filters and graphs. AHSGC addresses these issues with adaptive filtering, homophily-enhanced graph learning, and joint optimization.

  • HSI analysis is difficult because hyperspectral data are high-dimensional, redundant, and computationally complex.
  • Traditional clustering methods rely on prototypical features, limiting dimension reduction, noise handling, optimization, and clustering accuracy.
  • Existing graph networks use invariant filters and fixed graphs, limiting feature processing and correction of erroneous edge connections.
  • Joint network optimization integrates self-training and graph updating, while K-means expresses the latent features.
  • AHSGC adaptively extracts high- and low-frequency graph components and dynamically adjusts graph structure for different clustering tasks.
  • AHSGC combines graph construction, adaptive filtering, clustering self-training, homophily-enhanced learning, and graph edge sparsification.

B. Homophily-enhanced Graph Learning

Graph clustering assigns nodes to classes using node features and seeks graph homogeneity through connections among same-class nodes.

  • Edge homogeneity is defined as the ratio of same-class edges to the total number of graph edges.
  • Graph clustering assigns each node to a specific cluster using its spatial-spectral information and cluster features.

III. PROPOSED METHODOLOGY

AHSGC is an end-to-end HSI clustering network composed of five interacting modules. Its modules jointly process graph features, self-training, graph structure, and latent representations.

  • AHSGC contains adaptive filtering, clustering self-training, homophily-enhanced structure learning, joint optimization, and HSI graph-construction modules.
  • The adaptive graph filter extracts low- and high-frequency graph features through neighbor information aggregation.
  • Self-training uses an auxiliary distribution, while K-means implements clustering on the learned representations.
  • Homophily-enhanced learning removes inter-cluster edges and recovers intra-cluster edges to adjust graph structure for clustering tasks.
  • Superpixel preprocessing preserves local spatial-spectral structure while reducing the graph’s node number.
  • The five modules form an end-to-end network in which each component interacts with the others.

B. Adaptive Filter Graph Encoder

Graph signals contain both smooth and non-smooth information relevant to clustering. AHSGC therefore uses adaptive graph filtering to capture and balance low- and high-frequency representations.

  • Low-pass filters capture smoother graph information, whereas high-pass filters capture contrasting high-frequency information.
  • Both low-pass and high-pass signals affect downstream clustering, motivating their comprehensive use.
  • The randomly wandering normalized affine matrix and its Laplacian provide graph operators for filtering node signals.
  • Eigenvalue settings determine whether graph-signal differences are amplified for non-smooth representations or reduced for smoother representations.
  • The adaptive graph filter balances high-pass and low-pass information using a learnable parameter μ > 0.
  • Stacked adaptive graph-filter layers capture high-pass and low-pass presentations of the constructed graph.

C. Graph Embedding Clustering Self-Training Decoder

The decoder learns clustering-oriented graph embeddings and uses self-training with KL divergence to refine node assignments. An auxiliary distribution sharpens assignments and helps avoid collapse into one cluster.

  • Graph embedding: The graph encoder output Z combines adaptive graph filtering with a linear transformation of the initial node features X.The encoder output is defined from Z0 = X, adaptive filters, and a learnable weight matrix W.
  • Graph embedding: High-pass and low-pass graph presentations are learned to capture structural-semantic information for clustering.
  • Self-training clustering: The decoder measures node-to-center similarity with a Student’s t-distribution to produce soft clustering assignments q_ik.
  • Self-training clustering: KL divergence is minimized between the clustering assignment distribution Q and an auxiliary distribution P.
  • Self-training clustering: The auxiliary distribution raises Q to the second power, sharpening assignments and avoiding collapse into a single cluster.

D. Homophily-enhanced Structure Learning

Homophily-enhanced structure learning estimates reliable node connections from confident cluster members and latent embeddings, then dynamically modifies graph edges. The process recovers strong intra-cluster links and removes unnecessary inter-cluster links.

  • Orient Correlation Estimation: The method selects the top γ percentage of nodes in each cluster by assignment confidence to form a high-confidence subset Γ_k.
  • Orient Correlation Estimation: Similarity is estimated from latent embeddings rather than clustering space to reduce the impact of confident but incorrect segments.
  • Orient Correlation Estimation: The node similarity matrix S is computed with dot products of node embeddings within each high-confidence cluster subset Γ_k.
  • Orient Correlation Estimation: Embedding similarity and soft assignments jointly identify incorrect or missing edges, improving graph structure learning reliability.
  • Graph Edge Sparsification: Graph edge sparsification adds highly similar intra-cluster connections and removes unnecessary inter-cluster connections during graph learning.The stated goal is tighter within-cluster connectivity and sparser between-cluster connectivity.

3) Homophily-enhanced Structure Learning:

AHSGC jointly optimizes self-training clustering and graph reconstruction while repeatedly updating the graph and network parameters. Final clustering applies K-means to the learned graph embeddings.

  • Joint network optimization: The updated adjacency matrix subtracts removed-edge connections and adds recovered intra-cluster connections.
  • Joint network optimization: The overall objective combines the self-training clustering loss L_c with the graph reconstruction loss L_g.
  • Joint network optimization: AHSGC treats the auxiliary distribution p_ik as ground truth and minimizes the overall objective for T iterations.
  • Optimization procedure: K-means is applied to the learned graph embeddings Z to obtain the final clustering results Q.
  • Optimization procedure: Each iteration encodes the graph, computes clustering loss, performs homophily-enhanced structure learning, updates adjacency, and evaluates graph reconstruction loss.

F. HSI Preprocessing and Initial Graph Construction

HSI preprocessing uses SLIC to create spatially connected superpixels and represents each superpixel with averaged spectral features. Pixel–superpixel projection then supports graph construction and feature transformation for clustering experiments on three datasets.

  • Initial graph construction: SLIC divides each HSI into spatially connected superpixels, whose node features are average spectral features of contained pixels.
  • Initial graph construction: The adjacency matrix is constructed from superpixel-level node features and their t-hop neighborhoods.
  • Pixel–superpixel projection: A correlation matrix Q records which superpixel contains each HSI pixel, enabling pixel-to-superpixel backprojection.
  • Pixel–superpixel projection: Graph projection maps pixel-level HSI features into superpixel-level node features through normalized matrix multiplication.
  • Experimental datasets: Experiments evaluate AHSGC on the Salina, Trento, and Pavia University datasets using quantitative and visual clustering comparisons.

B. Experimental Setup

The experiments evaluate AHSGC with five clustering metrics on three HSI datasets, compare it with nine baselines, and repeat runs to reduce random-selection bias. AHSGC reports the best SA performance and remains strongest on PU.

  • Evaluation metrics: OA, κ, NMI, ARI, and Purity are used to evaluate clustering performance.OA records overall clustering accuracy, while κ, NMI, ARI, and Purity assess consistency, similarity, agreement, and cluster purity.
  • Compared methods: AHSGC is compared with nine traditional, subspace, graph, and deep clustering baselines.The baselines include K-means, FCM, PCM, NCSC, DFCN, SDCN, EGAE, AdaGAE, and DAEGC.
  • Implementation: All methods are executed ten times to reduce bias from random training-sample selection.Experiments use an NVIDIA Titan RTX and PyTorch.
  • Quantitative comparison: On SA, AHSGC achieves the best reported results, including 83.60% OA, 81.62% Kappa, 77.42% NMI, and 83.68% ARI.The passage also reports a 0.11% improvement in Purity over the second-best result.
  • Quantitative comparison: On PU, AHSGC remains best among the investigated methods, improving over the best comparison results by 3.55% OA, 1.83% κ, and 0.77% ARI.The reported AHSGC OA is 63.65%.

2) Quantitative analysis of the PU dataset:

On Trento, AHSGC achieves strong quantitative and qualitative clustering results despite traditional methods’ limited feature extraction. Its adaptive filtering, graph updating, and relatively low computational cost support the reported performance.

  • Quantitative analysis: 86.03% OA is achieved by AHSGC on Trento, exceeding the second-best performance by 10.41%.Traditional K-means, FCM, and PCM obtain OAs of 63.01%, 51.32%, and 36.78%, respectively.
  • Quantitative analysis: AHSGC updates node connections through homophily-enhanced structure learning to estimate relationships between nodes and classes.The reported mechanism is linked to improved clustering accuracy on Trento.
  • Visual analysis: Visual comparisons show traditional methods with substantial salt-and-pepper noise, while deep methods produce smoother maps but can misclassify edge pixels.The figures compare K-means, FCM, PCM, NCSC, DFCN, SDCN, EGAE, AdaGAE, DAEGC, and AHSGC.
  • Visual analysis: AHSGC’s adaptive filter captures low- and high-frequency information while filtering excess high-frequency and low-frequency noise.The method is described as improving the perceptual representation of HSI topology through graph-connection updates.
  • Efficiency analysis: AHSGC has lower reported training time, testing time, and model complexity than the other investigated deep clustering methods.The method requires only 50 epochs to complete convergence.

F. Parameter Analysis

The analysis examines how graph-recovery, graph-removal, optimization, and iteration parameters affect clustering, alongside t-SNE, ablation, and conclusion-level evidence about AHSGC’s design. The paper identifies future exploration of additional spatial-spectral self-supervised graph-learning methods.

  • Parameter sensitivity: A grid search studies the effects of iteration number T, learning rate L, intra-cluster edge recovery ratio ξ, and inter-cluster edge removal ratio η.The reported plots show OA variation on SA, PU, and Trento across these parameter settings.
  • Feature visualization: t-SNE compares original graph-node distributions with node-feature distributions after AHSGC processing on SA, PU, and Trento.Different-colored nodes represent different land covers in the visualizations.
  • Ablation analysis: The ablation study evaluates the contributions of homogeneous-region generation, the adaptive filter graph encoder, and homophily-enhanced structure learning.AHSGC-V1, AHSGC-V2, and AHSGC-V3 remove corresponding modules for comparison.
  • Method summary: AHSGC combines homogeneous-region preprocessing, adaptive high- and low-frequency filtering, self-training, task-driven graph updating, and joint optimization.Orient correlation estimates node connections, while edge sparsification dynamically adjusts graph edges.
  • Future work: Future work will explore additional spatial-spectral self-supervised graph-learning methods and reinforcement learning for HSI preprocessing.The stated goal is to enhance clustering feature-extraction abilities.
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