A band selection method for airborne hyperspectral image based on chaotic binary coded gravitational search algorithm

Abstract

Band selection is one of the most important topics in hyperspectral image classification for irrelevant band information and the high correlation between the adjacent bands. The main concern is to obtain the compact and effective bands to classify the image with the least impact for the classification accuracy. In general, band selection could be seen as a combinatorial optimization problem through defining an objective function based on the number of bands and classification accuracy. Therefore, in the paper, a novel band selection method based on a chaotic binary coded gravitational search algorithm (CBGSA) is proposed to reduce the dimensionality of airborne hyperspectral images. The proposed method is also compared with that of genetic algorithm (GA), binary coded particle swarm optimization (BPSO) algorithm, binary coded differential evolution (BDE) algorithm and binary coded cuckoo search (BCS) algorithm on some airborne hyperspectral images; furthermore, it is also compared with some other existing techniques such as Relief-F algorithm, minimum Redundancy Maximum Relevance (mRMR) criterion, and the optimum index (OI) criterion for a comprehensive comparison. Experimental results display that the proposed method is robust, adaptive and might be applied for practical work of airborne hyperspectral image classification.

Introduction

Recent advances in remote sensing technology have made hyperspectral image (HSI) more widely available, with dense sampling of several narrow contiguous bands [1]. This high spectral resolution provides potential for better discrimination of different physical objects, while also yielding large volumes of data. To reduce the data redundancy, band selection has been one of the hottest topics in the community of remote sensing [2]. Specifically, it is necessary to develop efficient and effective band selection techniques to improve the accuracy and efficiency of classification.

Feature selection is a fundamental task for pattern recognition and data mining applications especially for high-dimensional data sets, which is the process of selecting a subset of relevant features for use in model construction. Ideally, objects may be described more completely with more features and each feature should supplement an independent set of information [3]. Meanwhile, band selection is a specific application of feature selection in the field of HSI analysis. Many approaches have been proposed around the topic in recent years. For instance, Verrelst et al. [4] introduced an automated spectral band selection tool based on Gaussian processes regression (GPR) to identify an optimized number of spectral bands for vegetation properties estimation from hyperspectral data. Veera and Vasuki [5] explored a novel approach for band selection using K-means clustering on statistical feature in hyperspectral images, which involved the utilization of the effectiveness of simplex growing algorithm (SGA) on end member extraction in association with clustering. Yuan et al. [6] proposed a multigraph determinantal point process (MDPP) model to capture the full structure between different bands and efficiently find the optimal band subset in extensive hyperspectral applications. Zheng et al. [7] utilized determinantal point process to select the representative bands and to preserve the relevant original information of the spectral bands, which could lead to a significant advancement in HSI classification compared with the state-of-the-art methods. Feng et al. [8] proposed a novel band selection algorithm that first estimated the redundancy through analyzing relationships among spectral bands; and then, spectral bands were ranked according to their relative importance, and the classification results were close to the performance with original images. Jia et al. [9] put forward a novel band selection method based on Relief-F algorithm to effectively use the rich band information of the hyperspectral image objects. Kamandar and Ghassemian [10] presented a band selection technique that maximized relevance of selected bands and simultaneously minimized redundancy between them (mRMR), which could improve the performance of band selection for more accurate classification comparing with other usual methods. Qi et al. [11] proposed a multiple kernel ensemble optimum index (OI) criterion to make band selection for hyperspectral remote sensing image by comprehensively calculating the standard deviation, Kullback–Leibler divergence, and correlation coefficient.

On the other hand, airborne remote sensing has been a highlight in the field of remote sensing for recent years, because of the high spatial-temporal resolutions and low cost [12]. Unlike the high-resolution satellite remote sensing which usually provides large area and usable geographical position, the airborne remote sensing often provides a small observed range and less accurate geographical position information for each image [13]. Nowadays, a lot of classification methods based on airborne hyperspectral images have been proposed. Because of the limitation of information acquisition, the classification is mainly based on texture features [14] or inverse modeling [15]; the band information is less used in the process of classification. As the development of spectral imaging technology, airborne hyperspectral images with multi-band have been extracted, and band information could be directly utilized for classification. However, the increase of the number of bands leads to data redundancy; and the process of band selection could reduce the data dimension and redundancy of band information.

In nature, band selection is a typical combinational optimization and non-polynomial hard problem, the computing complexity of which is O(2^N), where N is the total number of bands. For non-polynomial hard problem, a lot of research has focused on how to obtain the satisfied solution by using optimization algorithms in limited time. Some typically evolutionary algorithms and newly proposed swarm intelligence algorithms (genetic algorithm (GA), particle swarm optimization (PSO) algorithm, differential evolution (DE) algorithm, and cuckoo search (CS) algorithm and so on) have been successfully applied continuous optimization and combinatorial optimization problems, such as function optimization [16], job-shop scheduling [17], travelling salesman problem (TSP) [18], path planning [19], time series forecasting [20] et al.. Moreover, evolutionary algorithms and swarm intelligence algorithms have been employed to solve the band selection problem. For example, Gong [21] presented a band selection technique based on a novel multi-objective model and genetic operation, which could obtain band subsets with a stable competitive performance in classification. Li [22] proposed a hybrid band selection strategy based on GA and support vector machine (SVM), which formed a wrapper to search for the best combination of bands with high classification accuracy. Su et al. [23] proposed a PSO-based optimization system to simultaneously determine the optimal number of bands and select the corresponding bands for hyperspectral dimensionality reduction, which could obviously outperform the popular sequential forward selection (SFS) method. Ghosh et al. [24] presented a new band selection technique by using DE algorithm for subset generation in hyperspectral images, which could make a significant improvement over the existing algorithms with respect to overall classification accuracy and Kappa coefficient. Medjahed [25] proposed a new procedure for band selection by using CS algorithm to optimize the objective function, which could obtain satisfactory results with regard to other band selection approaches and classifier systems that used all of bands.

Gravitational search algorithm (GSA) [26] is a newly proposed heuristic search algorithm. Nowadays, GSA has been widely used in diverse applications, e.g. Yazdain et al. [27] utilized GSA to find multiple solutions in multi-modal problems. Kumar and Sahoo [28] presented the compendious survey on the GSA and its applications as well as enlightened the applicability of GSA in data clustering. Duman et al. [29] used GSA to find the solution for optimal power flow (OPF) problem in a power system. In the field of classification, GSA was used to provide a prototype classifier to face the classification of instances in multi-class data sets [30]. Sarafrazi and Nezamabadi-pour [31] hybridized GSA with SVM and made a novel GSA-SVM hybrid system to improve classification accuracy in binary problems. However, as a stochastic global search algorithm, GSA may still converge to the local optimum like GA, PSO and DE algorithms et al., which will influence the optimization ability of the algorithm. Because of the ergodicity and randomness, chaotic operation has been widely used to solve the combinational optimization problem by combining with evolutionary algorithms and swarm intelligence algorithms, which could improve the global convergence by escaping from the local optimal solution [32]. Nowadays, there are some variants and modifications of GSA, such as Li [33] proposed a chaotic GSA (CGSA) for the parameter identification problem of chaotic system, which performed that the proposed algorithm had better performance than other algorithms in solving the parameter identification problem. Li et al. [34] presented a CGSA to optimize the membership function parameters of fuzzy model based on a novel fuzzy c-regression clustering algorithm (NFCRMA), which could improve the modeling accuracy significantly by comparing with several of previous results. However, band selection is a discrete optimization problem, which could not be directly solved by the standard GSA. Rashedi [35] proposed a binary coded GSA (BGSA) to solve the discrete optimization problem, and has been successfully utilized to figure out the problem of benchmark function [35], unit commitment [36] and face recognition [37].

Although GSA has not been utilized to solve the problem of band selection, the optimization ability is better than some commonly used evolutionary algorithms and swarm intelligence algorithms, such as GA, PSO and DE and so on [26], [29]. In addition, the binary coding is more adapted to solve the discrete optimization problem and choose the optimal band subset, and chaotic operation could avoid the algorithm trap into the local optimal, and easily converge to the optimal solution. In this paper, a chaotic binary coded gravitational search algorithm (CBGSA) is considered and employed for band selection in airborne hyperspectral images.

The rest of this paper is structured as follow. Section 2 illustrates the basic principle of CBGSA. The proposed band selection approach is detailed in Section 3. Section 4 displays the experimental results and discussion. In the final, the paper is concluded in Section 5.