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Locality and Structure Regularized Low Rank Representation for Hyperspectral Image Classification

Qi Wang, Xiange He, Xuelong Li

arXiv:1905.02488v1cs.CVeess.IV

TL;DR

HSI classification is challenging for LRR because local geometry is neglected and the learned representation may not separate classes sufficiently. LSLRR addresses these issues with a spatial-spectral locality constraint and a structure constraint that encourages near block-diagonal representations. Experiments on three HSI datasets report that LSLRR outperforms other state-of-the-art methods.

  • Problem

    LRR captures global HSI structure but neglects local geometry and provides insufficiently discriminative representations for separating classes.

  • Method

    LSLRR improves LRR with LCC based on a spatial-spectral distance metric and SPS encouraging class-wise block-diagonal representations.

  • Results

    LSLRR achieves the best classification results among comparison methods and improves over classical LRR by more than 20% in one reported comparison.

  • Takeaways & Limitations

    The learned representation can be used directly to determine HSI classification labels.

Abstract

from arXiv · show

Hyperspectral image (HSI) classification, which aims to assign an accurate label for hyperspectral pixels, has drawn great interest in recent years. Although low rank representation (LRR) has been used to classify HSI, its ability to segment each class from the whole HSI data has not been exploited fully yet. LRR has a good capacity to capture the underlying lowdimensional subspaces embedded in original data. However, there are still two drawbacks for LRR. First, LRR does not consider the local geometric structure within data, which makes the local correlation among neighboring data easily ignored. Second, the representation obtained by solving LRR is not discriminative enough to separate different data. In this paper, a novel locality and structure regularized low rank representation (LSLRR) model is proposed for HSI classification. To overcome the above limitations, we present locality constraint criterion (LCC) and structure preserving strategy (SPS) to improve the classical LRR. Specifically, we introduce a new distance metric, which combines both spatial and spectral features, to explore the local similarity of pixels. Thus, the global and local structures of HSI data can be exploited sufficiently. Besides, we propose a structure constraint to make the representation have a near block-diagonal structure. This helps to determine the final classification labels directly. Extensive experiments have been conducted on three popular HSI datasets. And the experimental results demonstrate that the proposed LSLRR outperforms other state-of-the-art methods.

I. INTRODUCTION

HSI classification benefits from rich spectral and spatial information but remains difficult because of high dimensionality and limited labeled samples. The paper proposes LSLRR, combining locality and structure constraints to improve LRR-based classification.

  • HSIs contain hundreds of continuous spectral bands that provide discriminative information about land-surface materials.
  • High dimensionality and limited training samples are major challenges for HSI classification.
  • LRR captures global low-dimensional subspace structure but neglects local geometry and neighboring-pixel relationships.
  • LSLRR improves LRR with a spatial-spectral distance metric and locality constraint criterion to characterize global and local HSI structures.
  • A structure preserving strategy learns more discriminative representations with class-wise block-diagonal structure, enabling direct classification of testing data.

B. LRR-based Methods

LRR-based HSI methods exploit low-rank structure in data from multiple subspaces, while dictionary selection and noise remain important considerations. The paper develops LSLRR with locality, structure, dictionary-learning, and optimization components.

  • The proposed LSLRR section combines regularization terms with dictionary learning and derives an optimization algorithm for the objective.
  • LRR seeks low-rank representations for data modeled as samples from a union of low-dimensional subspaces.
  • The original LRR formulation represents data using a dictionary and sparse noise component while balancing rank and reconstruction terms.
  • Unlike sparse representation, LRR captures global data structure by seeking low-rank rather than sparsest representations.
  • Convex relaxation replaces rank and ℓ0 terms with nuclear and ℓ1 norms, while the ℓ2,1 norm encourages entire noise columns to be zero.

B. Locality Constraint Criterion (LCC) for LSLRR

The locality constraint criterion incorporates neighboring-pixel information into LRR. It uses a spatial-spectral similarity metric so representations preserve local structure while distinguishing pixels with larger distances.

  • Neighboring HSI pixels have a high probability of sharing the same class, making spatial context useful for classification.
  • LCC addresses LRR’s neglected local manifold structure by using both spectral and spatial similarity.
  • The proposed distance metric combines spectral pixel vectors with spatial position coordinates to measure pixel distances.
  • The hyper-parameter m controls the relative weight of spectral and spatial distance and can be increased for datasets with more compact classes.
  • LCC penalizes dissimilar pixel pairs through M ◦ Z, while nonnegative Z treats the representation as an affinity matrix.

C. Structure Preserving Strategy (SPS) for LSLRR

SPS encourages training and testing representations to approximate class-wise block-diagonal structure. It constructs a structured auxiliary matrix using labeled training classes and distance-based sparsity for testing samples.

  • HSI data is split into training and testing samples, with training samples rearranged according to class.
  • Using the training data as dictionary, LRR produces representations for both training and testing samples.
  • Class-ordered data has an ideal representation matrix with class-wise block-diagonal structure.
  • SPS constrains the representation toward a structured auxiliary matrix Q, whose training component is built from class-specific representations.
  • For testing samples, large training-testing distances produce zero entries in Q, encouraging a sparse testing representation.
  • Figure 1 uses colored, white, and gray blocks to depict non-zero, zero, and near-zero representation values in a simplified two-class example.

D. Dictionary Learning for LSLRR

LSLRR learns a discriminative dictionary from corrupted HSI data rather than fixing randomly selected atoms, while encouraging block-diagonal representations.

  • The method learns a discriminative dictionary from corrupted HSI data because a polluted or unrepresentative fixed dictionary can make the representation useless.
  • Dictionary learning is integrated into LSLRR instead of fixing randomly selected dictionary atoms from the HSI pixels.
  • LSLRR jointly learns a discriminative dictionary and requires the representation to have a block-diagonal structure.
  • The training representation is block-diagonal, whereas the testing representation is approximately block-diagonal under the learned dictionary.

E. HSI Classification via LSLRR

LSLRR uses low-rank representation to connect HSI training and testing pixels, with optimization variables and constraints designed for structured classification. Its representation directly supports label assignment through similarity values.

  • LSLRR exploits HSI low-rank subspaces to segment classes using both global and local structure, with larger representation values indicating greater same-class similarity.
  • Auxiliary variables H and J convert the LSLRR problem into an equivalent form that is easier to solve.
  • The alternating optimization updates H, J, Z, E, and D separately, using SVD and soft-thresholding for parts of the solution.
  • The dictionary is initialized with randomly selected HSI pixels and then iteratively updated alongside the other variables using IALM.
  • The Indian Pines classification map reports 95.63% for LSLRR, compared with 70.47% for LRR and 94.52% for LGIDL.

V. EXPERIMENTS AND ANALYSES

The experiments evaluate LSLRR against multiple state-of-the-art HSI classification methods on three popular hyperspectral datasets, followed by detailed analyses.

  • The evaluation uses three popular hyperspectral datasets and compares LSLRR with many state-of-the-art classification algorithms.

A. Dataset Descriptions

The study evaluates HSI classification across Indian Pines, Pavia University, and Salinas, which differ in sensors, spatial dimensions, spectral bands, and class counts.

  • Indian Pines contains 145 × 145 pixels, 200 usable spectral bands after removing noise and water-absorption bands, and 16 classes.
  • Pavia University retains 103 spectral bands, has 610 × 340 bands at 1.3 meters per pixel, and includes nine ground-cover categories.
  • The experiments use data acquired by AVIRIS for Indian Pines and Salinas and by ROSIS for Pavia University.
  • The Pavia University classification maps compare SVM, SVMCK, JRSRC, cdSRC, LRR, LGIDL, and LSLRR against ground truth.
  • Salinas has 512 lines, 217 samples, 204 spectral bands after discarding polluted bands, 3.7-meter spatial resolution, and 16 ground categories.

B. Experimental Setups

The experiments compare LSLRR with SVM-, SR-, and LRR-based HSI classification methods using repeated evaluation, cross-validated parameters, and standard accuracy metrics.

  • Comparison Algorithms: Six state-of-the-art comparison methods comprise SVM, SVMCK, JRSRC, cdSRC, LRR, and LGIDL.The competitors span SVM-based, SR-based, and LRR-based methods.
  • Parameter Settings: Each method is repeated ten times to reduce bias from random sampling.
  • Visualization: Salinas classification maps compare ground truth with six competitors and LSLRR, whose displayed OA is 97.77%.The maps also report LRR at 86.81% and LGIDL at 96.58%.
  • Parameter Settings: Free parameters are selected by cross validation using training data only.SVM uses an RBF kernel with C and γ tuned by grid search.
  • Evaluation Indexes: Overall accuracy, average accuracy, and kappa coefficient evaluate classification performance.OA measures correctly classified HSI pixels, while AA averages per-class accuracy.

C. Experimental Results and Analyses

Experiments on Indian Pines, Pavia University, and Salinas show that LSLRR consistently improves HSI classification, including under limited training data. Results also indicate that its locality and structure regularizers are important to performance.

  • Indian Pines: LSLRR achieves the best overall classification performance among the compared methods on Indian Pines, with OA improving more than 20% over classical LRR.The improvement is attributed to LCC capturing local features and SPS producing a near block-diagonal representation.
  • Training-sample analysis: Across Indian Pines, Pavia University, and Salinas, LSLRR has the highest overall-accuracy curve as the percentage of training samples varies.The comparison is reported in Fig. 5 for the three datasets.
  • Pavia University: With 5% training pixels, LSLRR attains the highest classification performance on Pavia University and improves nearly 12% in OA and more than 16% in kappa over LRR.LSLRR also achieves the best result for eight of the nine classes and an OA of 99.9% for the sixth class.
  • Salinas: On Salinas, most classes exceed 99% accuracy, all OA values are at least 94%, and LSLRR remains best when only a small training set is used.The experiment uses 5% of pixels for training and 95% for testing.
  • Parameter and component analysis: The optimal spatial-information parameter m is 25, 15, and 40 for Indian Pines, Pavia University, and Salinas, respectively.The paper states that larger m is more reasonable for datasets whose classes are more compact.
  • Parameter and component analysis: Removing LCC causes Indian Pines OA to decrease by more than 12%, while setting β = 0 produces very low accuracy, demonstrating the importance of LCC and SPS.Optimal α values are 0.8, 0.3, and 1.0; optimal β values are 0.6, 1.2, and 0.4 for the three datasets, respectively.

D. Comparison of Running Time

The running-time comparison evaluates computational complexity alongside classification accuracy on the Indian Pines dataset. LSLRR is reported as computationally acceptable while achieving the highest classification accuracy.

  • D. Comparison of Running Time: The comparison uses running time to assess the computational complexity of HSI classification algorithms.Experiments use Indian Pines with 10% of each class’s labeled pixels for training, implemented in MATLAB R2015a.
  • D. Comparison of Running Time: SVM and SVMCK require the least time, but their classification accuracy is not high enough compared with several competing methods.The comparison includes JRSRC, cdSRC, LGIDL, and LSLRR.
  • D. Comparison of Running Time: JRSRC and LGIDL provide promising classification performance, but their running time is too long.
  • D. Comparison of Running Time: LSLRR is computationally acceptable and achieves the highest classification accuracy in the comparison.
  • D. Comparison of Running Time: Table IV reports OA, AA, kappa coefficient, and running time for each HSI classification method.

VI. CONCLUSION

The conclusion presents LSLRR as an HSI classification method that addresses limitations of traditional LRR through locality and structure regularization. Experiments on three public datasets show that it outperforms the state-of-the-art comparison methods.

  • VI. CONCLUSION: LSLRR improves traditional LRR for HSI classification using locality constraint criterion and structure preserving strategy.
  • VI. CONCLUSION: A spatial-spectral similarity metric and LCC help capture local structure by assigning small similarity to pixels with large distance.
  • VI. CONCLUSION: SPS makes the LSLRR solution close to a class-wise block-diagonal matrix.
  • VI. CONCLUSION: LSLRR classification results can be obtained directly without complex classifiers.
  • VI. CONCLUSION: Experiments on three public HSI datasets show that LSLRR outperforms other state-of-the-art comparison methods.
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