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C$^3$DG: Conditional Domain Generalization for Hyperspectral Imagery Classification with Convergence and Constrained-risk Theories

Zhe Gao, Bin Pan, Zhenwei Shi

TL;DR

This work tackles hyperspectral monospectra by developing C$^3$DG, a conditional domain generalization framework that relies on spectral information alone. Central to the approach is the Conditional Revising Inference Block (CRIB), which uses a shared encoder and multiple decoders to capture conditional distributions and disentangle domain factors from semantic content. The authors provide theoretical support, including a convergence corollary and a risk upper bound linked to test-time revision, strengthening the method's reliability. Empirically, C$^3$DG demonstrates superior or competitive performance across three HSIs benchmarks (Houston, Pavia, Hyrank) compared with ERM and various DG baselines, while avoiding spatial-feature leakage and offering adaptive, domain-aware outputs at inference time.

Abstract

Hyperspectral imagery (HSI) classification may suffer the challenge of hyperspectral-monospectra, where different classes present similar spectra. Joint spatial-spectral feature extraction is a popular solution for the problem, but this strategy tends to inflate accuracy since test pixels may exist in training patches. Domain generalization methods show promising potential, but they still fail to distinguish similar spectra across varying domains, in addition, the theoretical support is usually ignored. In this paper, we only rely on spectral information to solve the hyperspectral-monospectra problem, and propose a Convergence and Error-Constrained Conditional Domain Generalization method for Hyperspectral Imagery Classification (C$^3$DG). The major contributions of this paper include two aspects: the Conditional Revising Inference Block (CRIB), and the corresponding theories for model convergence and generalization errors. CRIB is the kernel structure of the proposed method, which employs a shared encoder and multi-branch decoders to fully leverage the conditional distribution during training, achieving a decoupling that aligns with the generation mechanisms of HSI. Moreover, to ensure model convergence and maintain controllable error, we propose the optimization convergence theorem and risk upper bound theorem. In the optimization convergence theorem, we ensure the model convergence by demonstrating that the gradients of the loss terms are not contradictory. In the risk upper bound theorem, our theoretical analysis explores the relationship between test-time training and recent related work to establish a concrete bound for error. Experimental results on three benchmark datasets indicate the superiority of C$^3$DG.

C$^3$DG: Conditional Domain Generalization for Hyperspectral Imagery Classification with Convergence and Constrained-risk Theories

TL;DR

This work tackles hyperspectral monospectra by developing CDG, a conditional domain generalization framework that relies on spectral information alone. Central to the approach is the Conditional Revising Inference Block (CRIB), which uses a shared encoder and multiple decoders to capture conditional distributions and disentangle domain factors from semantic content. The authors provide theoretical support, including a convergence corollary and a risk upper bound linked to test-time revision, strengthening the method's reliability. Empirically, CDG demonstrates superior or competitive performance across three HSIs benchmarks (Houston, Pavia, Hyrank) compared with ERM and various DG baselines, while avoiding spatial-feature leakage and offering adaptive, domain-aware outputs at inference time.

Abstract

Hyperspectral imagery (HSI) classification may suffer the challenge of hyperspectral-monospectra, where different classes present similar spectra. Joint spatial-spectral feature extraction is a popular solution for the problem, but this strategy tends to inflate accuracy since test pixels may exist in training patches. Domain generalization methods show promising potential, but they still fail to distinguish similar spectra across varying domains, in addition, the theoretical support is usually ignored. In this paper, we only rely on spectral information to solve the hyperspectral-monospectra problem, and propose a Convergence and Error-Constrained Conditional Domain Generalization method for Hyperspectral Imagery Classification (CDG). The major contributions of this paper include two aspects: the Conditional Revising Inference Block (CRIB), and the corresponding theories for model convergence and generalization errors. CRIB is the kernel structure of the proposed method, which employs a shared encoder and multi-branch decoders to fully leverage the conditional distribution during training, achieving a decoupling that aligns with the generation mechanisms of HSI. Moreover, to ensure model convergence and maintain controllable error, we propose the optimization convergence theorem and risk upper bound theorem. In the optimization convergence theorem, we ensure the model convergence by demonstrating that the gradients of the loss terms are not contradictory. In the risk upper bound theorem, our theoretical analysis explores the relationship between test-time training and recent related work to establish a concrete bound for error. Experimental results on three benchmark datasets indicate the superiority of CDG.
Paper Structure (15 sections, 4 theorems, 26 equations, 8 figures, 5 tables, 2 algorithms)

This paper contains 15 sections, 4 theorems, 26 equations, 8 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Backgrounds
  4. The Overall Framework
  5. Conditional Revising Inference Block
  6. Architectures of CRIB
  7. Optimization for CRIB
  8. Theoretical Analysis for Convergence
  9. Theoretical Analysis for Upper Bound
  10. Experiments
  11. dataset
  12. Implementation Details
  13. Comparative Experiments
  14. Ablation experiment
  15. Conclusion

Key Result

Theorem 1

(The Convergency Theorem) The backward gradient mutual information suppress loss is not contradict to the gradient of the backbone predictor, i.e. $\langle \frac{\partial\sum CE(\hat{h}_d(z_{d},z_{s}),d_i))}{\partial w_j},\frac{\partial\sum CE(\hat{h}_d(z_{d},z_{s}),d_i))}{\partial w_j} - \frac{\par

Figures (8)

  • Figure 1: The framework of proposed C$^3$DG architecture. The context encoder in the CRIB consists of C branches that handle different conditional distributions, sharing the same encoder. Specifically, C forward networks, named Reverse Dualnet, act as decoders to output the final revision features.
  • Figure 2: Causal map of HSI generating. left is from previous work and right is our finer considerated map.
  • Figure 3: (a) is the false-color image of the source domain Houston 2013, which we divided into four source domains along the white dashed lines. (b) is the false-color image of the target domain Houston 2018. (c) is the ground truth image of Houston 2018.
  • Figure 4: (a) is the false-color image of the source domain Pavia City, which we divided into four source domains along the white dashed lines. (b) is the false-color image of the target domain Pavia University. (c) is the ground truth image of Pavia University.
  • Figure 5: (a) is the false-color image of the source domain Dioni, which we divided into four source domains along the white dashed lines. (b) is the false-color image of the target domain Loukia. (c) is the ground truth image of Loukia.
  • ...and 3 more figures

Theorems & Definitions (8)

  • Definition 1
  • Theorem 1
  • Proof 1
  • Definition 2
  • Lemma 1
  • Lemma 2
  • Theorem 2
  • Proof 2