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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.

    Source: §I · p. 2

  • 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.

    Source: §I · p. 2, A. Overall AHSGC Framework · p. 4, 1) Orient Correlation Estimation · p. 5

  • 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.

    Source: 2) Quantitative analysis of the PU… · p. 9

  • Takeaways & Limitations

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

    Source: §V · pp. 11–12

Abstract

from arXiv · show

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.Source: §I · p. 1
  • Traditional clustering methods rely on prototypical features, limiting dimension reduction, noise handling, optimization, and clustering accuracy.Source: §I · p. 1
  • Existing graph networks use invariant filters and fixed graphs, limiting feature processing and correction of erroneous edge connections.Source: §I · p. 2
  • Joint network optimization integrates self-training and graph updating, while K-means expresses the latent features.Source: §I · p. 2
  • AHSGC adaptively extracts high- and low-frequency graph components and dynamically adjusts graph structure for different clustering tasks.Source: §I · p. 2
  • AHSGC combines graph construction, adaptive filtering, clustering self-training, homophily-enhanced learning, and graph edge sparsification.Source: Figure 1 · p. 3

B. Homophily-enhanced Graph Learning

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

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.

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.

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

Self-training clustering

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

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.Source: 2) Graph Edge Sparsification · p. 6, Figure 3 · p. 6

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

Optimization procedure

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

Pixel–superpixel projection

Experimental datasets

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.Source: 1) Experiment Settings · pp. 7–8

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.Source: 1) Experiment Settings · p. 8

Implementation

  • All methods are executed ten times to reduce bias from random training-sample selection.Experiments use an NVIDIA Titan RTX and PyTorch.Source: 3) Implementation details · p. 8

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.Source: 1) Quantitative analysis of the SA… · p. 8
  • 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%.Source: 2) Quantitative analysis of the PU… · p. 9

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.Source: 3) Quantitative analysis of the Trento… · p. 9
  • 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.Source: 3) Quantitative analysis of the Trento… · p. 9

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.Source: D. Visual Clustering Results Analysis · p. 9, Figure 7 · p. 10
  • 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.Source: D. Visual Clustering Results Analysis · pp. 9–10

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.Source: E. Complexity Comparison · pp. 10–11

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

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.Source: G. Clustering Visualization · p. 11, Figure 8 · p. 11

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.Source: H. Ablation Experiment · p. 11, Figure 8 · p. 11

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.Source: §V · pp. 11–12

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.Source: §V · p. 12
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