A Band Selection Approach for Hyperspectral Image Based on a Modified Hybrid Rice Optimization Algorithm

Abstract

Hyperspectral image (HSI) analysis has become one of the most active topics in the field of remote sensing, which could provide powerful assistance for sensing a larger-scale environment. Nevertheless, a large number of high-correlation and redundancy bands in HSI data provide a massive challenge for image recognition and classification. Hybrid Rice Optimization (HRO) is a novel meta-heuristic, and its population is approximately divided into three groups with an equal number of individuals according to self-equilibrium and symmetry, which has been successfully applied in band selection. However, there are some limitations of primary HRO with respect to the local search for better solutions and this may result in overlooking a promising solution. Therefore, a modified HRO (MHRO) based on an opposition-based-learning (OBL) strategy and differential evolution (DE) operators is proposed for band selection in this paper. Firstly, OBL is adopted in the initialization phase of MHRO to increase the diversity of the population. Then, the exploitation ability is enhanced by embedding DE operators into the search process at each iteration. Experimental results verify that the proposed method shows superiority in both the classification accuracy and selected number of bands compared to other algorithms involved in the paper.

1. Introduction

Recently, hyperspectral remote sensing has been broadly and successfully applied in urban planning [1], precision agriculture [2], environmental monitoring [3] and other fields with the constantly increased spectral resolution of sensors. Hyperspectral remote sensing combines spectral features with spatial images that can accurately identify and detect ground objects, which provides strong technical support for ground feature extraction [4]. However, hyperspectral image (HSI) obtained in hundreds of narrow and contiguous bands from visible to infrared areas of the electromagnetic spectrum are characterized by high-dimensional space and a large number of spectral bands [5], which makes the processing and analysis of HSI a challenging task. Therefore, dimensionality reduction becomes a crucial task for hyperspectral data analysis [6].

Feature extraction and feature selection are two typical dimension-reduction methods. The original hyperspectral datasets are transformed into a low-dimensional and less-redundant feature space by feature extraction and common techniques such as independent component analysis (ICA) [7], principal component analysis (PCA) [8], and local linear embedding (LLE) [9]. Although these methods can extract valuable features from HSI datasets, they often lose physical information of the original data during the process of data compression [10]. In contrast, feature selection can select the feature subset with the most information while preserving the physical meaning of the original data, which is an important and popular method for reducing dimensions [11]. In the traditional filter methods, the feature subset is built independently of the classifier or classification algorithm and can be evaluated based on different measures such as distance measures, correlation measures and information measures [12], while wrapper methods use the classifier model to estimate feature subsets. Although filter methods are computationally simple and fast [13], they are generally less accurate than wrapper methods because they are not guided by classifiers [14]. In general, feature-selection methods can be divided into supervised and unsupervised according to the availability of sample tags [15]. Unsupervised methods can select a subset of bands without class labels, but they tend to be unstable and biased due to the lack of prior information [16]. In comparison, supervised methods tend to obtain better feature-selection results with the assistance of class labels.

Supervised feature-selection methods include three search strategies: exhaustive search, sequential search, and random search [10]. Exhaustive search requires enumerating all possible combinations of features [17], which results in unacceptable time complexity for HSI. Sequential search contains sequential forward search (SFS), sequential backward search (SBS), and sequential floating forward search (SFFS) [18]. These methods require much computation while tending to get stuck to the local optima, and it is difficult to perform well for the existence of bands with strong correlation in HSI [19]. By contrast, random search introduces randomness into the search process to distance from the local optima and deliver promising results with higher efficiency. Recently, a number of nature-inspired stochastic search algorithms have been extensively utilized for feature selection based on their strong search ability in the large-scale space [20]. These include genetic algorithm (GA) [21], differential evolution (DE) algorithm [22], particle swarm optimization (PSO) [23], gray wolf optimizer (GWO) [24], cuckoo search (CS) algorithm [25], artificial bee colony (ABC) algorithm [26] and whale optimization algorithm (WOA) [27], which may have superior performance in dealing with feature-selection problems.

For HSI band selection, Nagasubramanian et al. [28] used GA to select the optimal subset of bands and support vector machine (SVM) to classify the infected and healthy samples. Additionally, the classification accuracy was replaced by F1-Score to alleviate the skewness caused by unbalanced datasets. The results showed that the bands chosen by this approach were more informative compared to RGB images. Xie et al. [29] proposed a band selection method based on ABC algorithm and enhanced subspace decomposition to apply in HSI classification. Subspace decomposition was realized by computing the relevance between adjacent bands, and ABC algorithm was guided by enhanced subspace decomposition and maximum entropy to optimize the combination of selected bands, which provided high classification accuracy compared with six related techniques. Wang et al. [30] proposed a wrapper feature-selection approach based on improved ant lion optimizer (ALO) and wavelet SVM to reduce the dimension of HSI. Lévy flight was used to help ALO jump out of local optimum and the wavelet SVM was introduced to improve the stability of classification result. The results showed that the proposed method can provide satisfactory classification accuracy in fewer frequency bands. Subsequently, Wang et al. [31] designed a new band selection method using chaos operation to set corresponding indices for the top three gray wolves in GWO to improve the optimization ability of GWO, and experimental results demonstrated that a suitable band subset can be obtained and superior classification accuracy can be achieved by this approach. Kavitha and Jenifa [32] used Discrete Wavelet transform with eight taps and four taps for extracting the important features and applied PSO algorithm for searching the optimal band subsets and utilized SVM as a classifier to classify HSI effectively. Medjahed et al. [33] introduced a novel band selection framework based on binary CS algorithm. The experiment compared the optimization ability of CS under two different objective functions and proved that it could obtain more excellent results than relevant approaches by adopting a few instances for training. Su et al. [34] proposed a modified firefly algorithm (FA) to deal with the band selection problem by optimizing the minimum values of objective function, which outperformed superior results than SFS and PSO. In essence, band selection is a NP hard problem, as if the number of the bands increases, the above algorithms may suffer from premature convergence and even optimization stagnation.

Hybrid rice optimization (HRO) [35] is a newly proposed nature-inspired algorithm and has been successfully applied to image processing and knapsack problem because of its simple structure and strong optimization ability. For example, Liu et al. [36] presented an image segmentation method that used HRO to find the fittest multi-level thresholds by using Renyi’s entropy as the fitness function, and experiments proved that HRO prevailed over the other six commonly used evolutionary algorithms on most metrics. Su et al. [37] designed two different hybrid models for the complex large-scale 0–1 knapsack problem by using novel combinations of improved HRO and binary ant colony algorithm, which achieved better performance on different size datasets. In addition, Ye et al. [38] regarded the band selection problem as a combinatorial optimization problem and employed binary HRO to select the optimal band set for HSI, which obtained good results in classification precision and execution efficiency. Although HRO algorithm has contributed to acquiring satisfactory results, primary HRO performs the exploitation of the current best solution during each search process inadequately.

Recently, DE algorithm has been successfully combined with other swarm intelligence algorithms for solving diverse optimization problems. Tubishat et al. [39] employed evolutionary operators from DE algorithm to help each whale seek better positions and improve the local search capability of WOA for feature selection in sentiment analysis. Jadon et al. [40] proposed a hybrid DE algorithm with ABC algorithm to enhance the convergence and the balance between exploration and exploitation. Houssein et al. [41] hybridized the adaptive guided DE algorithm with slime mold algorithm for combinatorial optimization problems, which verified that evolutionary operators could boost the local search capability of swarm agents. Hence, a modified HRO (MHRO) based on opposition-based learning (OBL) strategy and differential evolution (DE) operators is proposed to overcome the disadvantages of standard HRO in the paper. The main contributions of this paper are concluded as follows:

(1)

OBL strategy is introduced to enhance the diversity of the initial population and accelerate the convergence of MHRO;

(2)

DE operators are embedded into the search process of MHRO to enhance the local exploitation ability;

(3)

The MHRO algorithm is applied in band selection and its performance is demonstrated on standard HSI datasets.

The remainder of the paper is organized as follows: Section 2 briefly gives a fundamental overview of the related technique and standard HRO algorithm. The methodology and the specific workflow of the proposed band selection approach are introduced in Section 3. Section 4 presents the experimental results and comparative studies. At last, conclusions and future work are summarized in the final section.

2. Background

2.1. Overview of Hybrid Rice Optimization Algorithm

HRO algorithm is a meta-heuristic algorithm that simulates the breeding process of three-line hybrid rice. At each iteration, the rice seed population is sorted by the fitness from superior to inferior and divided into three sub-populations. According to self-equilibrium and symmetry, each sub-population is designed as an equal number of individuals. The individuals in the top third of the fitness ranking are selected into the maintainer line, the bottom third as the sterile line, and the remaining belong to the restorer line. The algorithm consists of three stages: hybridization, selfing, and renewal.

2.1.1. Hybridization

Hybridization is performed to renew the rice seed genes in the sterile line. Two kinds of rice seeds presented to reconstruct one new individual are randomly chosen in the maintainer line and sterile line, respectively. If the new rice seed is superior to the current one, the current rice seed will be replaced by the new one. The new gene by hybridizing is shown in Equation (1).

$$X_{new(i)}^k=\frac{r_1{X}_{s,r}^k+r_2{X}_{m,r}^k}{r_1+r_2}$$

(1)

where $X_{new(i)}^k$ represents the new k-th gene of the i-th rice seed in sterile line, $X_{s,r}^k$ is the k-th gene of a individual randomly selected from the sterile line, $X_{m,r}^k$ is the k-th gene of a individual randomly selected from the maintainer line, $r_1$ and $r_2$ are random numbers between $[-1,1]$.

2.1.2. Selfing

Selfing is the behavior that optimizes the gene sequence of rice seeds in the restorer line, which makes rice seeds gradually approach the best one, and the updated Equation is shown in (2).

$$X_{new(i)}=rand(0,1)\cdot (X_{best}-X_{j,r})+X_i$$

(2)

where $X_{new(i)}$ is the new individual produced by selfing of the i-th restorer, $X_{best}$ represents the current optimal solution and $X_{j,r}$ is the j-th individual randomly selected from the restorer line ($i\ne j$). If the new individual is superior to the old individual, the old individual is replaced by the new and the current self-crossing number ($t_i$) is set to 0, otherwise the $t_i=t_i+1$.

2.1.3. Renewal

This stage is a reset operation for rice seeds in the restorer line that has not been updated for $t_{\max }$ consecutive times (i.e., reaching the maximum selfing time), and the renewal strategy is shown in Equation (3).

$$X_{new(i)}=X_i+rand(0,1)\cdot (R_{\max }-R_{\min })+R_{\min }$$

(3)

where $X_{new(i)}$ is the new individual produced by renewal of the i-th restorer, $R_{\max }$ is the upper bound of the search space and $R_{\min }$ is the lower bound.

In summary, the flow of HRO is described in Algorithm 1.

Algorithm 1. Pseudo-Code of HRO

1: Input: the predefined parameters of HRO

2: Output: the global best solution and its fitness function value

3: Initialize the rice seed population randomly

4: Initialize $t_i=0,k=0$

5: While ($k$ < maximum number of iterations)

6: Calculate the fitness function for each rice seed

7: Divide the rice seeds into three lines

8: for each rice seed in the sterile line

9:  Randomly select corresponding rice seeds in the sterile line and in the maintainer line

10:  The new gene is obtained by Equation (1)

11:  if the new rice seed is better

12:   Update the current rice seed

13:  end if

14: end for

15: for each rice seed in the restorer line

16:  if $t_i<t_{\max }$

17:   The new rice seed is obtained by Equation (2)

18:   if the new rice seed is better

19:    Update the rice seed

20:    $t_i=0$

21:   else

22:    $t_i=t_i+1$

23:   end if

24:  else

25:   The rice seed is renewed by Equation (3)

26:  end if

27: end for

26: $k=k+1$

27: end while

2.2. The Binary Coding

In general, data can be divided into two different types, that is, continuous or discrete. The basic HRO is presented for optimization problems with continuous search space. However, band selection for HSI is regarded as a discrete optimization problem, which is difficult to be solved by adopting the standard HRO. For binary coding, each individual in HRO is represented by a binary string where each element is only limited to 0 or 1. In order to solve the band selection problem, the continuous value of each candidate solution in the rice seeds population must be mapped to a probability value taking 0 or 1. Therefore, a sigmoid function is used to achieve data transform in the paper and is given as Equations (4) and (5).

$$S(x)=\frac{1}{1+e^{-x}}$$

(4)

$$X_i^k=\{\begin{array}{c}1,\hspace{1em}S(X_i^k)>0.5\hfill \\ 0,\hspace{1em}else \hfill \end{array}$$

(5)

where $x$ is a real number, $X_i^k$ represents the k-th gene of the i-th new rice seed.

2.3. The Opposition Based Learning

Generally, a good initial position of the population individual can accelerate the convergence speed of the algorithm. If the initial guess tends to be far from the position of the unknown optimal solution, the algorithm converges more slowly. OBL strategy can consider the current solution and its opposite solution to improve the diversity of the population. Then, the OBL method selected the fittest solutions from all initial solutions as the initial population, which can effectively broaden the search space of the algorithm.

Definition 1.

Let $x$ be a real number between $lb$ and $ub$, the opposite number $\tilde{x}$ of $x$ is calculated as Equation (6).

$$\tilde{x}=lb+ub-x$$

(6)

where $lb$ and $ub$ are the lower and upper bounds of the search space, respectively. Similarly, the opposite number can also be used in multidimensional space.

Definition 2.

Let $x=\{x_1,x_2,\dots ,x_D\}$ be a point in D-dimensional space, where $x_i\in [l{b}_i,u{b}_i]$. The opposite point $\tilde{x}=\{{\tilde{x}}_1,{\tilde{x}}_2,\dots ,{\tilde{x}}_D\}$ can be defined in Equation (7).

$${\tilde{x}}_i=l{b}_i+u{b}_i-x_i$$

(7)

Definition 3.

Let $x=\{x_1,x_2,\dots ,x_D\}$ be a bit string in D-dimensional space, where $x_i$ represents 0 or 1. The incomplete opposite point $\tilde{x}=\{{\tilde{x}}_1,{\tilde{x}}_2,\dots ,{\tilde{x}}_D\}$ can be expressed as Equation (8).

$${\tilde{x}}_i=\{\begin{array}{c}1-x_i, rand(0,1)>r\\ x_i, else \end{array}$$

(8)

where $r$ represents the proportion of taking the opposite value, and $r\in [0,1]$. It takes $r=0.5$ in the paper.

2.4. Differential Evolution

DE algorithm, which includes mutation, crossover and selection operators, is a simple and potential method to solve optimization problems.

2.4.1. Mutation

The aim of this step is to form a new vector by randomly selecting three different target vectors in the population. In each iteration, a mutant vector $V_i$ ($i=1,\dots ,N$, $N$ is the population size) is generated using Equation (9).

$$V_i=X_{r1}+F\cdot (X_{r2}-X_{r3})$$

(9)

where $X_{r1}$, $X_{r2}$ and $X_{r3}$ are random solution vectors selected from the population and $F$ is the mutation factor.

2.4.2. Crossover

After mutation operation, the mutant vector $V_i$ will crossover with its corresponding target vector $X_i$. The crossover process is defined as Equation (10).

$$U_i^j=\{\begin{array}{c}{V}_i^j, if rand(0,1)\le CR or j=j_{rand}\hfill \\ X_i^j,else\hfill \end{array}$$

(10)

where $j=1,\dots ,D$ and $D$ represents the dimension of the problem. $CR$ is the crossover rate and $j_{rand}$ is a randomly chosen integer within $[1,D]$.

2.4.3. Selection

The selection process is to evaluate the fitness function of the target vector $X_i$ and the trial vector $U_i$ obtained after crossover operator, and the better vector will remain in the next generation. The selection strategy is given as Equation (11).

$$X_i=\{\begin{array}{c}{U}_i,if f(U_i)\begin{array}{c}<\end{array}f(X_i)\hfill \\ X_i,else\hfill \end{array}$$

(11)

where $f(U_i)$ and $f(V_i)$ are the fitness value of vectors $U_i$ and $V_i$, respectively.

3. The Proposed Band Selection Method

To overcome the disadvantages of the primary HRO algorithm, two strategies are used to enhance the performance of HRO for handling the band selection problem. The main steps of the proposed technique are described in the following subsections.

3.1. The Coding Scheme

The key factor to handling the band selection issue is to make an appropriate mapping between the problem solution and algorithm coding. For band selection of HSI, each band has two candidate states of being selected or not being selected, which is suitable to be represented by binary coding. In HRO, each gene bit is represented by “1” or “0”, where “1” means that the corresponding band is selected and will be utilized for training, and “0” represents that the corresponding band is not chosen. Supposing that HSI contains ten bands, the binary coding of MHRO is “1001100101”. That is, the 1st, 4th, 5th, 8th and 10th bands will be selected to complete the subsequent classification task.

3.2. The Objective Function

Further, the proposed band selection method is developed to minimize the fitness function or the objective function by adopting MHRO algorithm. The main purpose of this method is to select the bands with the most informative subset from the original bands, so as to maximize the classification accuracy. Accordingly, SVM is adapted to conduct the classification on the HSI datasets, and the classification accuracy is selected as part of the objective function. In band selection technique, classification accuracy is an important measure metric, but how to reduce the number of redundant bands is also one of the most crucial goals. Therefore, the objective function as shown in Equation (12) is utilized in the paper.

$$Fitness=\alpha \cdot (1-\mathrm{OA})+(1-\alpha )\cdot \frac{n_s}{n_c}$$

(12)

where $Fitness$ denotes the fitness value, $\mathrm{OA}$ represents the overall classification accuracy and its concept is described in Appendix A.1. Note that $n_c$ and $n_s$ are the entire and the selected number of bands. $\alpha$ is a weight factor that balances classification accuracy and selected number of bands. It takes $\alpha =0.99$ in the paper.

3.3. The Implementation of the Proposed MHRO

The proposed band selection method is easy to implement, and its idea is to choose the optimal band subset with satisfactory classification results. Two improvements contained in the proposed algorithm MHRO are presented as shown in Figure 1. The first improvement is to adopt OBL in the initialization stage, whose aim is to improve the population diversity. The second improvement is the combination of DE operators and binary HRO algorithm, which improves the local search ability of the algorithm. The main procedure of these strategies utilized in MHRO is described as follows:

OBL: In the stage of population initialization, the position of each rice seed is randomly generated in the specified space. Then, a new population is formed by generating the corresponding opposite individual for each rice seed in the initial population by using OBL mechanism. Next, the individuals in the initial and new populations are sorted according to their fitness value, and the top $N$ individuals are selected to enter the final population. The main steps to initialize the population by OBL are as follows:

(1)

Initialize the location of each rice seed randomly, Let $X_i=\{x_{i1},x_{i2},\dots ,x_{ij},\dots ,x_{iD}\}$ be the i-th rice seed in the initial population $X$, where $i=1,2,\dots ,N$ and $j=1,2,\dots ,D$. $N$ denotes the population size and $D$ represents the dimension of the problem;

(2)

A new population OX was obtained by using the Equation (8) for each rice seed in the population X;

(3)

The $N$ fittest individuals are chosen from the set $\{\mathrm{X}\cup \mathrm{OX}\}$ to constitute the new initial population of the MHRO algorithm.

DE operators: In HRO, only individuals in sterile and restorer lines are updated, while maintenance lines are ignored, which reduces the search performance of the algorithm on high-dimensional band selection. Therefore, DE evolution operators are applied to the genetic sequences of each rice seed in the maintainer line to find better rice seeds by using Equations (9)–(11). In order to degrade the possibility of falling into the local optimum, the mutation factor $F$ in Equation (9) is set as a random number between 0 and 1, where $X_{r1}$, $X_{r2}$ and $X_{r3}$ are randomly selected individuals in the maintainer line. If the fitness value of the newly generated trial solution is better than the current individual, the current individual will be replaced. Otherwise, it is not replaced.

4. Experimental Results and Discussions

In this section, two sets of experiments are carried out to compare the proposed approach MHRO with multiple swarm intelligence algorithms and filter-based feature-selection methods. All the algorithms in these experiments are implemented by the language of python 3.9 and run on a PC with Intel(R) Core(TM) i7-10700 @ 2.9 GHz CPU and 16 GB memory under Windows 10 operating system.

4.1. Datasets Description

Five public HSI datasets are employed to evaluate the performance of the proposed band selection method, including the Kennedy Space Center (KSC), Botswana, Indian Pines, Salinas and Pavia University datasets.

KSC: KSC was captured by AVIRIS sensor over the Kennedy Space Center in Florida. The size of the KSC image is 512 × 614 pixels from 0.4 to 2.5 µm. The data contain 224 bands and have a spatial resolution of 18 m. The noisy bands of low signal-to-noise or water absorption are dropped, and the remaining 176 bands are utilized for analysis. Figure 2 shows the false-color image of the KSC dataset and the corresponding ground truth image. Details of the category information are listed in

Table 1. Detailed category information in KSC dataset.

Class Number	Class Name	Number of Samples
1	Scrub	761
2	Willow swamp	243
3	Cabbage palm hammock	256
4	Cabbage palm/Oak hammock	252
5	Slash pine	161
6	Oak/Broadleaf hammock	229
7	Hardwood swamp	105
8	Graminoid marsh	431
9	Spartina marsh	520
10	Cattail marsh	404
11	Salt marsh	419
12	Mud flats	503
13	Water	927
	Total	5211

.

Botswana: The Botswana images, built over Okavango Delta, Botswana on May 31, 2001 by the NASA EO-1 satellite, are of size 1476 × 256. EO-1 acquires data in 242 bands from the 0.4 µm to 2.5 µm portion of the spectrum in 10 nm windows. Noise bands are discarded, and the remaining 145 bands are chosen as candidate features. The false-color image of the Botswana dataset and the corresponding ground truth image are illustrated in Figure 3. The specific category information is listed in

Table 2. Detailed category information in Botswana dataset.

Class Number	Class Name	Number of Samples
1	Water	270
2	Hippo grass	101
3	Floodplain grasses 1	251
4	Floodplain grasses 2	215
5	Reeds	269
6	Riparian	269
7	Firescar	259
8	Island interior	203
9	Acacia woodlands	314
10	Acacia shrublands	248
11	Acacia grasslands	305
12	Short mopane	181
13	Mixed mopane	268
14	Exposed soils	95
	Total	3248

.

Indian Pines: The Indian Pines dataset was gathered by AVIRIS sensor in northwestern Indiana. The acquired image consists of 145 × 145 pixels and 224 original spectral bands with a spectrum range from 0.4 µm to 2.5 µm. The total number of bands is reduced to 200 by removing bands containing the area of water absorption. Figure 4 shows the false-color image of the Indian Pines dataset and the corresponding ground truth image. The specific category information is given in

Table 3. Detailed category information in Indian Pines dataset.

Class Number	Class Name	Number of Samples
1	Alfalfa	46
2	Corn-notill	1428
3	Corn-mintill	830
4	Corn	237
5	Grass-pasture	483
6	Grass-trees	730
7	Grass-pasture-mowed	28
8	Hay-windowed	478
9	Oats	20
10	Soybean-notill	972
11	Soybean-mintill	2455
12	Soybean-clean	593
13	Wheats	205
14	Woods	1265
15	Building-Grass-Trees-Drivers	386
16	Stone-Steel-Towers	93
	Total	10,249

.

Salinas: The Salinas dataset shown in Figure 5 was obtained by an AVIRIS sensor on Salinas Valley. The HSI is formed by 512 × 217 pixels and 224 bands in the spectrum range 0.4–2.5 µm. Further, 204 bands in this scene are retained by discarding 20 water absorption bands. The detailed category information of the Salinas dataset is given in

Table 4. Detailed category information in Salinas dataset.

Class Number	Class Name	Number of Samples
1	Brocoli_green_weeds_1	2009
2	Brocoli_green_weeds_2	3726
3	Fallow	1976
4	Fallow_rough_plow	1394
5	Fallow_smooth	2678
6	Stubble	3959
7	Celery	3579
8	Grapes_untrained	11,271
9	Soil_vinyard_develop	6203
10	Corn_senesced_green_weeds	3278
11	Lettuce_romaine_4wk	1068
12	Lettuce_romaine_5wk	1927
13	Lettuce_romaine_6wk	916
14	Lettuce_romaine_7wk	1070
15	Vinyard_untrained	7268
16	Vinyard_vertical_trellis	1807
	Total	54,129

.

Pavia University: The last dataset was collected from Pavia University in 2002. Pavia University is a 610 × 340 pixels image, and the number of spectral bands is 103. This image was taken by ROSIS on the wavelength range of 0.43 µm to 0.86 µm. The false-color image of Pavia University dataset and the corresponding ground truth image are illustrated in Figure 6. The concrete category information is listed in

Table 5. Detailed category information in Pavia University dataset.

Class Number	Class Name	Number of Samples
1	Asphalt	6631
2	Meadows	18,649
3	Gravel	2099
4	Trees	3064
5	Painted metal sheets	1345
6	Bare soil	5029
7	Bitumen	1330
8	Self-Blocking Bricks	3682
9	Shadows	947
	Total	42,776

.

4.2. Parameter Settings

Appropriate parameter settings can improve the optimization ability of the algorithm. In the following experiments, the proposed band selection technique is compared with GA [28], PSO [32], CS [33], FA [34] and HRO [38]. The corresponding parameter settings of each algorithm are listed in

Table 6. Parameters setting of each algorithm.

Algorithm	Parameters	Value
GA	$\mathrm{Crossover} \mathrm{rate} C_R$	0.8
	$\mathrm{Mutation} \mathrm{rate} C_M$	0.01
PSO	$\mathrm{Acceleration} \mathrm{coefficients} {\mathrm{c}}_1$$, {\mathrm{c}}_2$	2
	$\mathrm{Minimum} \mathrm{inertia} \mathrm{weight} {\mathsf{\omega }}_{\min }$	0.2
	$\mathrm{Maximum} \mathrm{inertia} \mathrm{weight} {\mathsf{\omega }}_{\max }$	0.9
CS	$\mathrm{Detection} \mathrm{probability} {\mathrm{p}}_{\mathrm{a}}$	0.25
	$\mathrm{Levy} \mathrm{flight} \mathrm{parameter} \mathsf{\beta }$	1.5
FA	$\mathrm{Absorption} \mathrm{coefficient} \mathsf{\gamma }$	1
	$\mathrm{Initial} \mathrm{attraction} {\mathsf{\beta }}_0$	1
	$\mathrm{Randomization} \mathrm{parameter} \mathsf{\alpha }$	0.5
HRO, MHRO	$\mathrm{Maximum} \mathrm{selfing} \mathrm{time} t_{max}$	10

. To make a fair comparison, all of the algorithms are adopted by binary coding and the corresponding band subset is used as input to SVM for classification. Each algorithm has an initial population size of 20 and a maximum number of iterations of 30. For all HSI datasets, 20% of samples are randomly selected as training data, and the remaining 80% are chosen as testing data. All algorithms are independently run 10 times for a case, and the average results are recorded.

4.3. Experiments for Different Optimization Algorithms

In this section, five benchmark datasets were used to test the performance of band selection based on MHRO. The overall classification accuracy (OA), kappa coefficient (The concept of kappa coefficient is described in Appendix A.2), number of selected bands and fitness function of each algorithm are utilized as evaluation indicators, as shown in

Table 7. OA and Kappa coefficient of six algorithms.

Dataset	Metrics	GA	PSO	CS	FA	HRO	MHRO
KSC	OA (%)	92.84 ± 0.14	93.24 ± 0.1	92.92 ± 0.07	92.83 ± 0.06	93.34 ± 0.19	93.60 ± 0.10
	Kappa	0.9201 ± 0.0016	0.9246 ± 0.0012	0.9211 ± 0.0007	0.9200 ± 0.0007	0.9257 ± 0.0021	0.9287 ± 0.0011
Botswana	OA (%)	94.69 ± 0.14	95.49 ± 0.23	94.79 ± 0.07	94.74 ± 0.09	95.63 ± 0.22	95.96 ± 0.10
	Kappa	0.9425 ± 0.0015	0.9511 ± 0.0024	0.9436 ± 0.0007	0.9431 ± 0.0010	0.9526 ± 0.0024	0.9562 ± 0.0010
Indian Pines	OA (%)	82.65 ± 0.85	88.75 ± 0.50	84.36 ± 0.62	83.08 ± 0.42	88.43 ± 0.27	89.25 ± 0.32
	Kappa	0.8018 ± 0.0098	0.8718 ± 0.0057	0.8215 ± 0.0072	0.8068 ± 0.0049	0.8682 ± 0.0031	0.8776 ± 0.0036
Salinas	OA (%)	94.39 ± 0.03	94.64 ± 0.07	94.49 ± 0.05	94.49 ± 0.03	94.59 ± 0.06	94.73 ± 0.04
	Kappa	0.9375 ± 0.0004	0.9403 ± 0.0008	0.9386 ± 0.0006	0.9386 ± 0.0003	0.9397 ± 0.0007	0.9413 ± 0.0005
Pavia University	OA (%)	95.19 ± 0.09	95.46 ± 0.04	95.30 ± 0.05	95.34 ± 0.07	95.41 ± 0.04	95.53 ± 0.06
	Kappa	0.9360 ± 0.0012	0.9396 ± 0.0005	0.9376 ± 0.0007	0.9380 ± 0.0010	0.9390 ± 0.0006	0.9406 ± 0.0008

and

Table 8. The number of selected bands and fitness value of six algorithms.

Dataset	Metrics	GA	PSO	CS	FA	HRO	MHRO
KSC	Num	81.3	65.5	82	89.7	41	37.5
	Fitness	0.0756 ± 0.0015	0.0707 ± 0.0008	0.0747 ± 0.0006	0.0761 ± 0.0007	0.0683 ± 0.0020	0.0655 ± 0.0009
Botswana	Num	70.5	56.2	72.4	77.6	37.9	35.3
	Fitness	0.0574 ± 0.0016	0.0486 ± 0.0025	0.0566 ± 0.0008	0.0574 ± 0.0006	0.0459 ± 0.0020	0.0425 ± 0.0010
Indian Pines	Num	96.5	69.4	89.1	106.4	41.1	44.1
	Fitness	0.1766 ± 0.0085	0.1149 ± 0.0051	0.1593 ± 0.0063	0.1728 ± 0.0042	0.1166 ± 0.0027	0.1086 ± 0.0030
Salinas	Num	99.6	91.8	102.8	109.5	82.6	85.8
	Fitness	0.0604 ± 0.0003	0.0575 ± 0.0009	0.0596 ± 0.0005	0.0599 ± 0.0002	0.0576 ± 0.0004	0.0564 ± 0.0004
Pavia University	Num	51.1	46.2	52.9	56.6	42.7	41.9
	Fitness	0.0526 ± 0.0008	0.0495 ± 0.0004	0.0516 ± 0.0004	0.0517 ± 0.0003	0.0496 ± 0.0003	0.0484 ± 0.0004

. It could be seen from Table 7 that the optimization ability of the proposed method is apparently superior to GA, PSO, CS, FA and HRO algorithms in terms of OA and kappa coefficients. It indicates DE operators employed by the individuals in the maintainer line have more probability to enhance the exploitation ability of MHRO in local search. For the Indian Pines dataset, OA of MHRO is 6.6% higher than GA, 4.89% higher than CS, and 6.17% higher than FA. In addition, the kappa coefficient of MHRO in Botswana, Salinas and Pavia University datasets are all over 0.94. This shows that the classification results are basically consistent with the real category labels.

According to Table 8, it is observed that the number of selected bands using HRO and MHRO is significantly less than those of GA, PSO, CS and FFA. The average number of selected bands with FA is 88 in the five datasets, nearly 1.8 times that of MHRO. About 79% of the high correlation and redundancy bands from the KSC dataset are removed by MHRO, with an average of only 37 bands with satisfactory classification accuracy remaining. Moreover, it is noticed that MHRO has slightly more band subsets than HRO for Indian Pines and Salinas datasets, which is caused by the fact that MHRO prioritizes the superior precision between high classification accuracy and a smaller number of bands at each iteration. With regard to the fitness, the proposed method has a better fitness value compared with the other five algorithms, and its corresponding standard deviation does not exceed 0.003 in any dataset, which verifies that MHRO has a slight fluctuation in HSI datasets. More importantly, the standard deviation of fitness value with MHRO is only 0.0004 for Salinas and Pavia University datasets, which is stable for independent operations. Figure 7 depicts the variation of average fitness with the number of iterations for all the algorithms used on five datasets.

As it is shown in Figure 7, the initial fitness value of MHRO is lower than HRO in all datasets, which proved that the OBL strategy used in the initial stage could enhance population diversity and provide more high-quality solutions. With the increase of iteration times, the iteration curves of GA, CS and FA gradually tend to be stable, while MHRO keeps a downward trend. This shows that DE operators can help to improve the exploration and exploitation ability, and also implies that MHRO has a powerful potential to find better solutions. As a result, MHRO has excellent optimization capability on HSI datasets and can obtain an optimal band subset with satisfactory classification accuracy.

4.4. Experiments for Other Related Techniques

To further verify the reliability of the proposed algorithm, the MHRO is compared with two common feature-selection methods, including Joint Mutual Information (JMI) and its improvement, named Joint Mutual Information Maximization (JMIM) [42] on five datasets. The experiments are implemented with bands varying from 10% to 30% of the total number of bands in each dataset. The results of classification accuracy for each class, OA and kappa coefficients are recorded in

Table 9. The classification results for KSC dataset via different number of bands.

Class Number	10%			20%			30%
	JMI	JMIM	MHRO	JMI	JMIM	MHRO	JMI	JMIM	MHRO
1	92.5750	93.4319	92.5350	94.1935	93.9145	93.9490	94.4805	93.3116	93.5024
2	92.8144	92.6554	90.0000	93.7500	93.2203	91.5344	93.7107	93.8889	91.9786
3	65.2985	91.2821	87.0466	77.8723	87.4419	89.9471	76.6520	87.7934	87.8307
4	58.9286	61.4504	73.0233	70.2564	63.6000	73.3032	66.5116	63.0522	74.0741
5	76.1364	78.0220	79.1304	79.6117	81.3187	82.7957	85.1852	81.4433	80.7692
6	76.5432	60.3659	78.9474	79.1667	68.1818	75.7225	75.2688	67.5497	80.2395
7	64.6552	71.6981	81.7073	65.2893	72.6415	88.8889	64.1667	75.2475	85.3659
8	84.6939	89.0141	93.6599	90.0990	88.5559	90.7609	89.0625	88.1081	91.1602
9	77.3469	93.9252	94.0909	83.5470	95.2038	94.3052	87.1681	96.5602	94.5205
10	89.1374	100.00	97.0297	95.8333	100.00	96.0784	95.2381	100.00	96.4286
11	89.6739	99.6997	99.7050	91.1932	99.3976	99.4030	91.1932	99.1018	99.7015
12	98.0609	97.6982	98.5000	96.6752	98.9848	98.7406	97.4026	98.4925	98.0000
13	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00
OA (%)	86.6635	91.3408	93.1638	89.9736	92.0844	93.3557	89.9496	92.1084	93.3797
Kappa	0.8514	0.9036	0.9238	0.8883	0.9119	0.9259	0.8881	0.9121	0.9262

,

Table 10. The classification results for Botswana dataset via different number of bands.

Class Number	10%			20%			30%
	JMI	JMIM	MHRO	JMI	JMIM	MHRO	JMI	JMIM	MHRO
1	100.00	99.5392	100.00	99.5392	99.5392	100.00	99.5392	99.5392	100.00
2	98.7500	98.7654	97.4359	100.00	100.00	98.7342	100.00	100.00	96.2963
3	98.0296	95.6522	99.0050	98.0100	97.5610	99.5050	98.0488	97.5728	99.0148
4	92.7374	94.9721	95.0276	92.2222	97.0930	96.6292	91.7582	94.3503	96.6480
5	85.2941	89.9471	88.7324	83.9623	90.0000	89.5735	88.4422	88.0597	90.3846
6	75.7576	76.9953	83.1050	80.9278	79.8122	88.6792	80.2885	80.4762	87.9070
7	100.00	99.5098	99.5074	100.00	100.00	100.00	99.5050	99.5000	100.00
8	94.8718	97.5155	96.3636	96.2025	99.3548	94.7368	98.7261	98.7421	96.4286
9	81.2977	86.3469	94.7154	86.5672	87.0370	96.4844	87.5472	88.3895	96.0784
10	83.5616	83.1776	91.3265	86.3014	87.0192	92.0213	88.6792	88.2075	94.2708
11	95.3191	94.7826	96.1373	97.0085	94.1423	94.1423	95.7627	96.1207	96.6102
12	93.8776	94.5946	91.2162	95.2381	93.3333	94.2857	91.4474	93.8776	94.3262
13	88.8889	95.2607	97.0588	93.5484	93.0556	96.1905	92.9245	92.2018	97.1154
14	97.3333	100.00	97.5000	98.6301	100.00	98.7342	98.6301	98.6486	98.7342
OA (%)	90.9196	92.4586	94.5748	92.6510	93.2282	95.4598	92.9588	93.2282	95.8830
Kappa	0.9016	0.9183	0.9412	0.9204	0.9266	0.9508	0.9237	0.9266	0.9554

,

Table 11. The classification results for Indian Pines dataset via different number of bands.

Class Number	10%			20%			30%
	JMI	JMIM	MHRO	JMI	JMIM	MHRO	JMI	JMIM	MHRO
1	55.5556	91.6667	100.00	76.1905	100.00	100.00	72.7273	92.8571	100.00
2	43.4932	80.5106	89.8605	58.5537	84.8908	89.2364	58.6438	85.1363	89.6140
3	26.0976	79.1209	86.7621	51.7355	84.2975	85.4430	57.3574	85.3135	85.8034
4	36.3636	76.3006	76.6169	56.0510	75.2747	73.7864	49.2754	75.7396	77.2021
5	68.4807	90.3226	94.9735	86.1461	89.5141	93.6869	89.2857	88.5496	92.1182
6	79.3939	87.2699	92.6350	83.4609	88.4013	94.6667	84.1079	88.1620	94.6932
7	0.0000	95.2381	95.4545	64.5161	90.9091	88.0000	73.0769	90.9091	100.00
8	79.7357	95.6853	97.2152	94.1919	96.6667	98.7113	89.3671	97.1503	98.7147
9	0.0000	62.5000	90.0000	0.0000	66.6667	87.5000	20.0000	71.4286	86.6667
10	57.6493	82.2102	78.0652	65.2226	85.1316	79.3143	74.5739	84.9490	80.9187
11	56.7493	83.2692	86.5589	73.9841	84.9903	88.6812	75.5808	86.6535	89.0834
12	34.8485	79.4769	86.0324	52.9968	84.2536	87.8351	59.7531	84.4622	87.5510
13	78.5714	96.2025	94.8276	96.7105	98.0892	96.5116	99.3506	98.0892	98.8095
14	89.2120	92.4027	92.5785	93.6770	93.6416	93.9189	93.2740	94.5259	93.1232
15	60.8696	77.9661	73.4615	71.1297	78.5088	79.9228	69.7479	76.3780	78.4000
16	98.4615	98.5507	98.6111	98.4848	97.1014	98.3607	98.0392	98.5075	98.3607
OA (%)	61.0366	84.7927	87.8780	73.1463	87.0244	88.9024	74.5366	87.5244	89.2317
Kappa	0.5475	0.8260	0.8618	0.6926	0.8517	0.8737	0.7084	0.8575	0.8774

,

Table 12. The classification results for Salinas dataset via different number of bands.

Class Number	10%			20%			30%
	JMI	JMIM	MHRO	JMI	JMIM	MHRO	JMI	JMIM	MHRO
1	99.8101	99.8101	100.00	99.7498	99.9373	100.00	99.9374	100.00	100.00
2	99.0017	99.0017	99.8321	99.5983	99.5654	99.7985	99.6317	99.8993	99.7650
3	87.9785	87.9785	96.1353	92.8571	93.1847	99.3769	95.1703	97.5686	99.5633
4	98.4889	98.4889	99.3789	98.6655	98.7533	99.2902	99.1063	98.9295	99.3783
5	88.9628	88.9628	99.5342	95.4922	95.3606	99.5818	98.4870	98.9686	99.6281
6	99.6211	99.6211	99.9373	99.9050	99.8735	99.9373	99.7472	99.7788	99.9373
7	99.3338	99.3338	99.9644	99.8252	99.7556	99.9288	99.9650	99.8602	99.9644
8	72.4820	72.4820	80.7262	77.6299	78.1479	83.2298	79.0656	81.4202	84.3931
9	93.7717	93.7717	99.4389	96.2108	96.3827	99.5787	97.1542	98.1235	99.5986
10	92.6040	92.6040	97.7493	95.2437	95.1362	98.3116	95.6164	95.9938	98.3109
11	79.8193	79.8193	98.9260	86.9677	87.5635	99.6433	88.6499	87.1111	99.4055
12	95.8543	95.8543	98.7630	96.9046	96.9562	99.0209	96.8434	97.4603	99.2801
13	95.7333	95.7333	99.3151	96.6622	98.5034	99.8626	97.8408	98.3762	99.8623
14	96.7153	96.7153	98.5849	97.8417	98.0000	98.8249	97.6387	98.2332	98.5899
15	66.6223	66.6223	84.2755	75.7640	75.5780	84.2284	77.6699	80.8717	84.7408
16	98.2244	98.2244	99.5830	98.8842	98.8137	99.2388	99.1028	99.1701	99.3070
OA (%)	86.9573	86.9573	93.2662	90.3589	90.5159	94.0467	91.3195	92.4834	94.3816
Kappa	0.8543	0.8543	0.9249	0.8924	0.8942	0.9336	0.9032	0.9162	0.9374

and

Table 13. The classification results for Pavia University dataset via different number of bands.

Class Number	10%			20%			30%
	JMI	JMIM	MHRO	JMI	JMIM	MHRO	JMI	JMIM	MHRO
1	86.7749	91.5299	94.2054	89.3364	93.0755	95.4459	91.6985	94.4086	95.5572
2	81.0733	90.0861	95.0046	83.7405	93.8672	96.2513	87.2954	95.9982	96.6656
3	69.8551	78.1069	87.9648	71.1213	82.0709	89.7384	76.1051	83.6127	89.7283
4	92.3801	96.3346	95.7699	92.0854	96.5762	97.3862	93.7824	97.6637	97.7580
5	99.7180	99.9065	99.4550	99.4403	99.9064	99.3642	99.5323	100.00	99.6357
6	89.9167	92.0507	93.0775	89.3754	91.2009	95.0250	88.6102	94.7454	95.7552
7	73.9530	79.6693	86.4476	77.1178	83.2370	89.2323	84.4828	85.8252	88.9437
8	79.6457	80.0737	84.4270	80.5669	82.9960	84.8779	82.3899	86.5560	86.2015
9	99.8681	99.8682	99.8682	99.8681	99.8681	99.8682	99.8681	99.8681	99.8681
OA (%)	83.1887	89.6701	93.4426	85.2138	92.1452	94.6992	88.1155	94.2082	95.1316
Kappa	0.7677	0.8607	0.9126	0.7976	0.8951	0.9295	0.8390	0.9229	0.9353

.

Table 9 shows OA and kappa values generated for the KSC dataset under different band subsets. It is clear that the proposed MHRO has the highest OA compared with other filter feature techniques. In particular, OA of MHRO is 6.5% higher than JMI and 1.8% higher than JMIM via 10% entire number of bands. In addition, only OA and Kappa coefficient of JMI are lower than 90% with different band subsets, and MHRO both exceed 92%. In brief, it is verified that the proposed band selection approach has good practicability for KSC dataset.

Table 10 reports OA and kappa values generated for the Botswana dataset under different band subsets. It is induced that OA corresponding to MHRO is satisfactory, which is more than 95% via exceeding 20% the number of bands. More importantly, the classification accuracy by MHRO is superior to JMI and JMIM in 12 categories with 30% of the total number of bands. Moreover, kappa coefficients of MHRO are approximately 0.02–0.04, 0.02–0.03 and 0.028–0.032 higher than other approaches in the total number of bands 10%, 20% and 30%, respectively. In sum, it is an effective band selection technique for the Botswana dataset.

OA and kappa values generated for the Indian Pines dataset under different band subsets are given in Table 11. It is observed that OA of the proposed MHRO significantly outperformed JMI, and the difference is over 14% even 26%. Further, the accuracy achieved by using MHRO reaches 100% on class number 1 and just 55.55% by using JMI via 10% of all number of bands. It is worth noting that the category named Oats is difficult to classify correctly by using JMI and JMIM, and the number of samples correctly distinguished by MHRO exceeded 86%. Therefore, it is a more promising technique than filtering feature-selection methods on the Indian Pines dataset.

Table 12 reports OA and kappa values generated for the Salinas dataset under different band subsets. It is obviously revealed that the proposed band selection approach can still obtain the best classification accuracy when the selected number of bands does not exceed 20%, and OA is lower than 87% by using JMI and JMIM techniques via 10% total number of bands. More than 98% of the samples could be correctly distinguished in the 13 categories by MHRO and the corresponding kappa coefficient is more than 0.92, which infers that the precisions are basically consistent with the real category labels. In short, the proposed MHRO has a strong optimization ability on the Salinas dataset.

According to Table 13, it has been concluded that the classification accuracy rate obtained by the proposed MHRO performs better than JMI and JMIM in most categories. For 10% total number of bands, OA is lower than 84% by using JMI and lower than 90% by JMIM. Kappa value by using MHRO has reached 0.91, 0.92 and 0.93 in the different number of bands, respectively, which are 0.9–15 higher than JMI. In conclusion, the proposed MHRO is a robust and feasible feature-selection approach for the Pavia University dataset.

5. Discussion

As shown in Table 7 and Table 8, the experimental results of MHRO on all datasets performed better than other swarm intelligence algorithms. Except for Indian Pines and Salinas, HRO has slightly smaller band subsets than MHRO. It can be seen from Figure 7 that the fitness function values of GA, CS and FA are only slight fluctuations throughout the iteration, indicating that they easily fall into local optimum at the early stage of iteration. In contrast, the fitness value of MHRO is always the lowest and keeps a decreasing trend, which implies that MHRO has strong optimization ability and is superior to algorithms GA [28], PSO [32], CS [33], FA [34] and HRO [38].

According to Table 9, Table 10, Table 11, Table 12 and Table 13, MHRO achieves higher accuracy than filter techniques JMI and JMIM [42] under different band subsets. This can be explained by the fact that the filter methods use mutual information to select feature subsets and they are independent of the classifier, while the wrapper approach MHRO proposed in the paper calculates the fitness function based on the accuracy of the classifier and the number of selected bands.

6. Conclusions

Band selection is a crucial phase to remove high-correlation bands and improve the classification accuracy for HSI. In the paper, a band selection approach based on MHRO is proposed and the basic idea is to obtain the fittest band combination. Experimental results are compared with commonly used feature-selection approaches optimized by GA, PSO, CS, FA and standard HRO on five datasets. In general, it is concluded that the proposed MHRO has excellent optimization capability and is able to achieve the highest classification accuracy with fewer bands. Moreover, OA and kappa coefficient are obviously higher than other related feature-selection techniques JMI and JMIM, which proved that the precisions are basically consistent with the real category labels. As a result, the proposed band selection technique has good robustness and practicability for HSI datasets. Future work will investigate other swarm intelligence algorithms and combine multiple optimization strategies and spatial information to further improve the performance of band selection. In addition, it is worthwhile to formulate different assessment criteria to solve the multi-objective optimization problem for feature selection on large-scale datasets.