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SuperPCA: A Superpixelwise PCA Approach for Unsupervised Feature Extraction of Hyperspectral Imagery

Junjun Jiang, Jiayi Ma, Chen Chen, Zhongyuan Wang, Zhihua Cai, Lizhe Wang

arXiv:1806.09807v2cs.CV

TL;DR

HSI dimensionality reduction traditionally uses a unified projection despite diverse spectral features across regions. SuperPCA learns region-specific low-dimensional features through superpixel segmentation, while MSuperPCA fuses multiscale decisions; experiments on three standard datasets report competitive or superior classification performance, including under limited labels.

  • Problem

    Unified projections overlook diverse spectral features across HSI regions, while high dimensionality increases storage and transmission burdens and creates curse-of-dimensionality challenges.

  • Method

    SuperPCA segments an HSI into homogeneous regions and performs superpixelwise PCA, while MSuperPCA fuses classification decisions from multiple segmentation scales.

  • Results

    SuperPCA and MSuperPCA outperform existing state-of-the-art feature extraction methods on three standard HSI datasets, with MSuperPCA exceeding supervised methods on University of Pavia and Salinas.

  • Takeaways & Limitations

    With few labeled samples, SuperPCA and MSuperPCA can achieve better classification accuracies than state-of-the-art supervised feature extraction techniques.

Abstract

from arXiv · show

As an unsupervised dimensionality reduction method, principal component analysis (PCA) has been widely considered as an efficient and effective preprocessing step for hyperspectral image (HSI) processing and analysis tasks. It takes each band as a whole and globally extracts the most representative bands. However, different homogeneous regions correspond to different objects, whose spectral features are diverse. It is obviously inappropriate to carry out dimensionality reduction through a unified projection for an entire HSI. In this paper, a simple but very effective superpixelwise PCA approach, called SuperPCA, is proposed to learn the intrinsic low-dimensional features of HSIs. In contrast to classical PCA models, SuperPCA has four main properties. (1) Unlike the traditional PCA method based on a whole image, SuperPCA takes into account the diversity in different homogeneous regions, that is, different regions should have different projections. (2) Most of the conventional feature extraction models cannot directly use the spatial information of HSIs, while SuperPCA is able to incorporate the spatial context information into the unsupervised dimensionality reduction by superpixel segmentation. (3) Since the regions obtained by superpixel segmentation have homogeneity, SuperPCA can extract potential low-dimensional features even under noise. (4) Although SuperPCA is an unsupervised method, it can achieve competitive performance when compared with supervised approaches. The resulting features are discriminative, compact, and noise resistant, leading to improved HSI classification performance. Experiments on three public datasets demonstrate that the SuperPCA model significantly outperforms the conventional PCA based dimensionality reduction baselines for HSI classification. The Matlab source code is available at https://github.com/junjun-jiang/SuperPCA

I. INTRODUCTION

HSI data offer rich spectral information but their high dimensionality creates storage, transmission, and classification challenges. Existing dimensionality-reduction methods include feature selection, feature extraction, unsupervised approaches such as PCA, and supervised approaches that use labels, while many methods do not directly incorporate spatial information.

  • HSIs record hundreds of thousands of spectral wavelengths per pixel, enabling material discrimination through subtle spectral signatures.
  • High dimensionality burdens data transmission and storage and can reduce classifier generalization and classification performance when labeled samples are limited.
  • Feature selection chooses representative existing bands, whereas feature extraction projects high-dimensional spectral features into a low-dimensional subspace.
  • PCA is a widely used unsupervised technique that finds orthogonal transformations maximizing projected data variance without label information.
  • Many feature-extraction methods use only pixelwise spectral signatures and cannot directly incorporate HSI spatial information, despite its value for representation and classification.

A. Motivation and Contributions

The paper addresses the mismatch between unified projections and region-specific spectral diversity by introducing SuperPCA, which performs PCA within superpixel-defined homogeneous regions. It further proposes MSuperPCA, which fuses classification decisions across segmentation scales to exploit multiscale spatial information.

  • A. Motivation and Contributions: Different HSI regions may represent different objects with diverse spectral features, motivating distinct projection matrices for different homogeneous regions.
  • A. Motivation and Contributions: SuperPCA segments an HSI into homogeneous regions, applies PCA to each region, and recombines the resulting low-dimensional matrices.
  • A. Motivation and Contributions: MSuperPCA obtains multiscale superpixel segmentations, applies SuperPCA at each scale, and fuses SVM predictions through majority voting.
  • A. Motivation and Contributions: SuperPCA and MSuperPCA are presented as the first superpixelwise unsupervised dimensionality-reduction and classification models for hyperspectral imagery.
  • A. Motivation and Contributions: With few labeled samples, including five samples per class, the proposed methods obtain better classification accuracies than state-of-the-art supervised feature-extraction techniques.

II. ENTROPY RATE SUPER-PIXEL SEGMENTATION (ERS)

The paper describes superpixel segmentation requirements and ERS optimization before introducing HSI and PCA formulations. Its motivation is that global PCA can overlook differences among homogeneous regions, motivating regionwise projections.

  • II. ENTROPY RATE SUPER-PIXEL SEGMENTATION (ERS): Superpixels should adhere to object boundaries while remaining computationally inexpensive as a preprocessing step.
  • II. ENTROPY RATE SUPER-PIXEL SEGMENTATION (ERS): NCuts can be computationally expensive because it constructs a large pixel-similarity graph and performs eigenvalue decomposition.
  • II. ENTROPY RATE SUPER-PIXEL SEGMENTATION (ERS): ERS partitions the graph into connected components by selecting an edge subset A ⊆ E and optimizes entropy-rate and balancing terms.
  • II. ENTROPY RATE SUPER-PIXEL SEGMENTATION (ERS): ERS favors homogeneous, compact clusters and similar cluster sizes, with α balancing the entropy-rate and balancing terms.
  • III. SUPERPIXELWISE PRINCIPAL COMPONENT ANALYSIS (SUPERPCA): An HSI cube is reshaped into X ∈ R^L×P, where each column is a pixel spectrum and P = MN.
  • III. SUPERPIXELWISE PRINCIPAL COMPONENT ANALYSIS (SUPERPCA): PCA maps L-dimensional spectra to a d-dimensional representation by maximizing variance through a linear transformation yi = W^Txi, with d < L.
  • III. SUPERPIXELWISE PRINCIPAL COMPONENT ANALYSIS (SUPERPCA): Global PCA may ignore differences among homogeneous regions, motivating unsupervised PCA performed separately for each region.

A. Generation of Homogeneous Regions

SuperPCA partitions an HSI into homogeneous regions and applies PCA separately to each region, enabling region-specific low-dimensional projections.

  • A. Generation of Homogeneous Regions: SuperPCA uses a divide-and-conquer strategy that applies PCA independently to each homogeneous region.The reduced regions are combined to form the dimensionality-reduced HSI.
  • A. Generation of Homogeneous Regions: Superpixel segmentation exhaustively partitions the image into homogeneous regions that provide spatial structures for spectral-spatial analysis.
  • A. Generation of Homogeneous Regions: Fig. 4 compares spectral-band correlation matrices for the entire University of Pavia image and its different homogeneous regions.
  • A. Generation of Homogeneous Regions: The method adopts ERS superpixel segmentation, while S denotes the number of generated superpixels.The first principal component is used to reduce the computational cost of segmentation.

B. Multiscale Extension of SuperPCA

MSuperPCA extends SuperPCA across multiple superpixel scales and fuses the resulting classification decisions to integrate spatial information at different region sizes.

  • B. Multiscale Extension of SuperPCA: Multiscale segmentation addresses the difficulty of selecting one superpixel size by combining classification results from multiple scales.The paper uses 2C + 1 scales derived from the first principal component image.
  • B. Multiscale Extension of SuperPCA: The c-th scale uses a superpixel count determined from the fundamental number Sf and scale index c.The resulting count is rounded and bounded between 1 and the total number of pixels P.
  • B. Multiscale Extension of SuperPCA: Fig. 5 displays λ1/λ2 for global PCA and homogeneous regions produced by SuperPCA across three datasets and logarithmic ratio axes.The blue horizontal line denotes the average regional ratio.
  • B. Multiscale Extension of SuperPCA: At each scale, SuperPCA performs PCA within every homogeneous region, combines the reduced regions, and classifies the resulting HSI.SVM classification is applied separately to each scale before fusion.
  • B. Multiscale Extension of SuperPCA: Majority voting fuses the 2C + 1 scale-specific predictions using equal voting strength for all classifiers.The voting rule selects the class receiving the most predictions.

C. Analysis of the Proposed SuperPCA

The analysis argues that region-specific PCA produces more representative projections than global PCA, while experiments compare spatially aware and spatially unaware divide-and-conquer strategies.

  • C. Analysis of the Proposed SuperPCA: SuperPCA obtains larger first-to-second eigenvalue ratios than global PCA across the analyzed HSI datasets.The paper interprets larger ratios as indicating more representative and discriminant primary projected features.
  • C. Analysis of the Proposed SuperPCA: Smaller superpixels improve regional consistency but do not necessarily improve classification because each region may contain too few samples.
  • C. Analysis of the Proposed SuperPCA: Table I reports Indian Pines overall accuracy for ClusterPCA, SquarePCA, and SuperPCA using SVM and nearest-neighbor classifiers.
  • C. Analysis of the Proposed SuperPCA: ClusterPCA and global PCA show similar results, whereas SquarePCA and SuperPCA benefit from using spatial information in patches or superpixel regions.
  • C. Analysis of the Proposed SuperPCA: Under AWGN with variance σ = 10, ClusterPCA performance drops drastically, while SquarePCA and SuperPCA retain a comparative advantage.

IV. EXPERIMENTAL RESULTS AND ANALYSIS

The experiments use three HSI datasets to study SuperPCA parameters and compare its classification performance with state-of-the-art dimensionality-reduction methods.

  • IV. EXPERIMENTAL RESULTS AND ANALYSIS: Experiments evaluate the impact of superpixel number and reduced dimension on SuperPCA classification performance.
  • IV. EXPERIMENTAL RESULTS AND ANALYSIS: The study uses three HSI datasets and presents comparisons with state-of-the-art dimensionality-reduction approaches.
  • IV. EXPERIMENTAL RESULTS AND ANALYSIS: For classes with relatively small sample sizes, at most half of the total samples are selected for training.

A. Datasets and Experimental Procedure

The experiments use three public HSI datasets and compare SuperPCA with raw spectral features, PCA, unsupervised and supervised feature-extraction methods. Classification is evaluated with varying training sizes and overall accuracy.

  • Datasets: Experiments use the Indian Pines, University of Pavia, and Salinas Scene HSI datasets.The datasets are publicly available; Indian Pines contains 16 land-cover classes and uses 200 bands after removing 20 low-SNR bands.
  • Comparison methods: The comparison includes raw spectral features, PCA, five unsupervised methods, and two supervised methods.The supervised methods are LDA and LFDA; the unsupervised methods include PCA, ICA, LPP, NPE, and LPNPE.
  • Experimental procedure: All methods extract features first and then use a supervised SVM classifier to test classification performance.The comparison pipeline applies a 5×5 weighted mean filter before SVM classification.
  • Experimental procedure: Figure 6 reports SuperPCA overall accuracy across superpixel counts, datasets, and training sizes of 5, 10, 20, and 30 samples per class.Columns correspond to Indian Pines, University of Pavia, and Salinas Scene; rows correspond to the four training sizes.

B. Parameter Tuning

Parameter tuning shows that SuperPCA benefits from an intermediate superpixel count, while multiscale fusion is evaluated through the scale parameter C. The selected fundamental counts are dataset-dependent, and multiscale fusion improves single-scale performance.

  • Superpixel number: SuperPCA accuracy first increases and then decreases as the number of superpixels grows.Too many superpixels over-segment regions and reduce PCA stability, whereas too few under-segment regions and mix different homogeneous areas.
  • Superpixel number: Proper superpixel counts outperform the single-superpixel setting, which corresponds to traditional global PCA.The selected fundamental counts are 100 for Indian Pines, 20 for University of Pavia, and 100 for Salinas Scene.
  • Multiscale fusion: SuperPCA achieves its best overall performance at the fundamental scale but not necessarily the best performance for every class.This motivates decision fusion across multiple segmentation scales.
  • Multiscale fusion: The best multiscale scale numbers C are 4, 6, and 4 for Indian Pines, University of Pavia, and Salinas Scene, respectively.Figure 7 reports overall accuracy according to C for the three datasets.
  • Multiscale fusion: Multiscale fusion improves single-scale SuperPCA by 0.65%, 4.38%, and 0.30% on Indian Pines, University of Pavia, and Salinas Scene, respectively.The improvement is largest on University of Pavia, which has richer and more complex texture information.

C. Comparison Results with State-of-the-arts

Across the classification comparisons, SuperPCA and MSuperPCA are competitive with or better than state-of-the-art dimensionality-reduction methods, including supervised approaches. MSuperPCA consistently improves on SuperPCA, especially for University of Pavia.

  • Classification maps: SuperPCA and MSuperPCA are clearly better than previous methods on the Indian Pines and University of Pavia classification maps.On University of Pavia, they produce better results for large regions such as Bare soil and Meadows than LDA and LFDA.
  • Limited-label setting: With limited training samples, the proposed method achieves good classification performance while using no label information.The comparison varies the training set from T = 5 to 30 samples per class.
  • Multiscale comparison: MSuperPCA outperforms SuperPCA across all datasets and training-sample numbers, with an improvement over 4% on University of Pavia.The method fuses decisions from different segmentation scales to use additional spatial information.
  • Large-label setting: With T = 200, MSuperPCA surpasses LDA and LFDA on the University of Pavia and Salinas datasets.The supervised methods improve with more labeled data, yet the unsupervised multiscale approach remains competitive and exceeds them on these datasets.

D. Running Times

Runtime measurements include SuperPCA segmentation and dimensionality reduction and compare feature-extraction algorithms across three datasets and four training sizes. PCA, LDA, and LFDA are fastest, while graph-based methods are more computationally demanding.

  • Evaluation setup: Runtime tests cover Indian Pines, University of Pavia, and Salinas Scene with T = 5, 10, 20, and 30 training samples per class.For SuperPCA, the reported time includes both segmentation and dimensionality reduction of all superpixels.
  • Runtime comparison: PCA, LDA, and LFDA show the fastest runtime among the compared methods.Supervised-method runtimes increase with the number of training samples, whereas several other methods do not change with training number.
  • Runtime comparison: LPP and NPE require relatively high computational complexity because they construct and decompose large similarity graphs.The decomposition uses SVD according to the reported runtime discussion.

E. Discussions

The discussion highlights segmentation-parameter selection as an open issue while presenting SuperPCA and MSuperPCA as effective region-wise feature-extraction approaches. It also documents classification-map and runtime comparisons on hyperspectral datasets.

  • Discussion: Selecting the ERS superpixel number and segmentation scales remains a crucial open problem, so the paper sets them experimentally for best performance.These parameters jointly determine the minimum and maximum homogeneous regions.
  • Discussion: Figure 9 compares Pavia classification maps for raw pixels, PCA, ICA, manifold methods, supervised methods, SuperPCA, and MSuperPCA.The figure includes the first principal component and ground truth as reference maps.
  • Discussion: Table VII reports feature-extraction running times for the proposed approach and comparison algorithms across three datasets and different training numbers.
  • Discussion: Edge detection is proposed as a direct way to estimate homogeneous-region sizes and guide segmentation-scale selection.The paper names Canny and Sobel as example edge detectors.
  • Discussion: SuperPCA and MSuperPCA outperform existing unsupervised and supervised feature-extraction methods, especially with limited training samples.With relatively large training sets, they remain competitive with supervised methods.
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