EBM3GP: A novel evolutionary bi-objective genetic programming for dimensionality reduction in classification of hyperspectral data
Introduction
Hyperspectral imaging integrates spectroscopy with imaging technologies to generate three-dimensional hyperspectral images (HSIs) with extensive spatial and spectral information, which can be applied to accurate material identification [1]. During recent decades, this imaging technology has been used extensively for a variety of remote sensing applications, including land cover classification [2], mineral exploration [3], environmental monitoring [4], etc. Although the high spectral resolution of HSIs provides a wealth of information, it does so at the expense of greater storage requirements and comparatively high processing costs, which eventually impairs the classification of objects [5], [6]. Therefore, it is crucial and necessary to remove redundant components from HSIs before transmitting, storing, and processing them.
Currently, hyperspectral dimensionality reduction (DR) techniques are generally partitioned into two typical branches: feature extraction (FE) and band selection (BS). Using various linear or nonlinear transformations, the former projects the high-dimensional HSI data into a low-dimensional space. The transformed features, whose number is notably less than the number of bands in raw hyperspectral data, extract the principal properties of raw spectra and discard unimportant properties [7]. Currently, two ideal FE methods, including an unsupervised Principal Component Analysis (PCA) [8] and a supervised Linear Discriminant Analysis (LDA) [9], are prevalent in the DR task of HSI data and have yielded remarkable results. Previous literature has proven that distinct classes of objects exhibit excellent separability in the low-dimensional feature space; however, the transformations would distort the primitive physical attributes in HSI spectra, hence affecting the physical interpretation of the bands [10]. The latter directly selects several representative band subsets from raw HSI bands, which is simpler than the feature extraction methods. Since BS methods could retain the physical information of the raw HSI spectra, it has gained attention among HSI data-based object classification and detection tasks [11], [12]. Existing BS methods can be categorized into three types based on whether machine learning (ML) algorithms are used to evaluate band subsets: wrapper, filter, and hybrid methods [13]. Wrapper methods employ dimension-reduced labeled data to train an ML classifier, such as a Support Vector Machine (SVM) [14], Extreme Learning Machine (ELM) [15], Random Forest (RF) [16], and then evaluate a band subset depending on the accuracy of the classifier. Wang et al. developed a supervised BS method that employs a modified Ant Lion Optimizer (ALO) to evolve and select individuals (each of which represents a band subset) and generate the optimal band subset finally [17]. A wavelet SVM (WSVM) classifier is used to the fitness of individuals during the operation of ALO. Experiments demonstrate that the ALO-WSVM-based method can discover the optimal solution within a reasonable number of iterations and achieves satisfactory classification accuracy with a small number of bands. The performance of the wrapper methods is dependent on the quality of the ML classifier, and training the classifier would enlarge the computational complexity of the methods [18]. Filter methods rely primarily on statistical or probabilistic metrics instead of classification accuracy to evaluate band subsets. These methods have a cheap computational cost and are suitable for high-dimensional data [19]. In [20], a single-layer neural networks (SLN)-based filter BS method is proposed. In this case, the bands and labels serve as the input and output of the SLN, respectively. After training the SLN, the bands corresponding to the biggest and smallest weights are selected and eliminated. The selection procedure described previously is then performed for the remaining bands. Experiments show that the SLN-based BS yields higher accuracy than the three state-of-the-art BS approaches. Zhang et al. establish Shannon information entropy and distance-based redundancy index to evaluate band subsets, and furthermore employs a biobjective immune algorithm to search for the best band subset on the basis of population evolution [21]. In generally, filter methods are more efficient than wrapper methods but less performant [22]. Most common hybrid methods combining wrapper and filter methods may use their strengths and overcome their weaknesses, and both cascaded and parallel structured hybrid methods generate superior band subsets. Cascading hybrid method firstly uses the filter method to choose several candidate bands from all bands, and then employs the wrapper method to determine the appropriate band subset from the candidate bands [23]. The parallel hybrid method evaluates band subsets using a weak classifier with minimal computational cost and a class separability metric, generating a trade-off between the number of bands and the classification performance of the subset [24]. However, wrapper and filter methods should be designed separately based on expert experience. Although BS methods achieve high HSI classification accuracy, from a feature engineering perspective, these methods can only collect low-level features, resulting in classifiers that only learn object differences from single-level features. As the same, FE methods can only extract high-level features via transformations.
To overcome the limitations of DR techniques for obtaining single-level features, much effort has been put into the investigation of combined BS and FE methods for processing HSI data. Some DR methods for cascading BS and FE methods select information-rich bands and then transform them into newly extracted features [25], [26]. Such cascaded methods still suffer from the shortcoming of obtaining single-level features. In the field of computer vision, the collaborative use of multi-level features has been proven to improve the classification accuracy of images [27], [28]. Likewise, for HSI classification, previous literature reported that combining the features obtained by the FE and BS methods and feeding them into the corresponding classifier could improve accuracy [29]. For instance, a method proposed by Sellami and Farah employs tensor locality preserving projection and constrained band selection method to extract high-level features and select band features from raw HSI spectra, respectively, and then stacks and feeds these two types of features into the SVM classifier. Corresponding results demonstrate that the fusion of high- and low-level features is superior to single-level features [30]. However, this type of combination method conducts FE and BS methods independently on HSI data, which possibly results in redundant and mutually inhibiting information in the obtained feature. Additionally, domain experts must determine the combination of FE and BS methods according to the specific HSI classification task, and the laborious combination of methods may not apply to other HSI classification tasks. To solve the problem, Genetic Programming (GP), a powerful feature engineering tool, is commonly used to automatically extract such low- and/or high-level features from raw spectral data [31]. Recently, a novel variant of the standard GP method, namely the Multidimensional Multiclass Genetic Programming with Multidimensional Populations (M3GP) algorithm, was successfully used for generating a combined DR strategy for classification and regression tasks [32], [33]. However, the M3GP-based researches are essentially single-objective optimization methods, which are easy to fall into local optimum and make it challenging to obtain global optimum DR strategies [34]. The above representative DR methods for HSI image classification are summarized in Table 1.
To this end, in this study, a novel generic combined DR framework based on an Evolutionary Bi-objective M3GP algorithm, named EBM3GP, is proposed to extract significant multi-level features of HSI spectra. The main contributions of this work are to (1) use a type of multi-dimensional tree for selecting band features and extracting high-level features from raw HSI spectra; (2) design two measures, including the amount of information and the redundancy contained in the constructed features, to evaluate the individuals; (3) develop an efficient bi-objective genetic programming algorithm based on M3GP algorithm and nondominated sorting method for searching the optimal individuals; (4) apply least squares SVM (LS-SVM), RF, and ELM for classification to evaluate the efficacy of the stacked features.
Section snippets
Description of combined DR based on EBM3GP
For an HSI data , its weight, height, and channel (band) are , , and , respectively. is a ground truth map corresponding to , and each pixel value of represents the class of pixels at the same position in . Extract the band and class information in and to form a set , where m is equal to w multiplied by h, and and represent d dimensional spectrum and a label of the i-th sample, respectively. Furthermore, can be expressed as a
Research data
In this study, the performance of DR methods is evaluated on three public and widely used datasets, including the Indian Pines image [40], Salinas image [41], and Pavia University (PaviaU) [42]. The details of all the datasets are summarized below.
The Indian Pines dataset was captured by AVIRIS sensor over the Indian Pines test site in north-western Indiana. It contains 145 × 145 pixels, each of which consists of 220 bands in the range of 0.4–2.5 μm. As suggested by [13], 20 water
Setup
Four DR methods, including one image processing-based method [43], one neural network-based method named [20], two evolutionary algorithm-based hybrid methods [13], [24], and one single-objective M3GP-based method [32], are applied to compare with EBM3GP on the classification performance of the three HSI datasets. These four methods are referred to as ICS, SLN, GWO, Sr-NSGA, and SOM3GP, respectively. The parameters of each method follow the respective original reference. Classification
Conclusions
In this research, a novel Evolutionary Bi-objective Genetic Programming method EBM3GP is developed to reduce the dimensionality of HSI data. This approach encodes the raw spectra to low- and high-level features via multi-dimensional trees. The trees are crossed or mutated to generate new individuals. Shannon entropy-based and Cross entropy-based measures are applied to evaluate the individuals, furthermore, the nondominated sorting method is applied to select individuals on the Pareto front to
CRediT authorship contribution statement
Zheng Zhou: Conceptualization, Methodology, Investigation, Funding acquisition, Writing – original draft. Yu Yang: Software, Formal analysis, Writing – original draft, Writing – review & editing, Supervision. Gan Zhang: Investigation, Methodology, Writing – original draft, Writing – review & editing. Libing Xu: Formal analysis, Software, Writing – review & editing. Mingqing Wang: Writing – review & editing, Formal analysis.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the Open Foundation of Key Laboratory of Marine Science and Numerical Modeling (Grant No. 2020-ZD-05). The authors thank China Scholarship Council (CSC) for the financial support to the author (Yu Yang) to conduct his doctoral research in the Department of Bioresource Engineering at McGill University. Authors would like to thank Dr. Qibing Zhu amd Dr. Min Huang of China Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education) at Jiangnan
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