
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)11823-3
10.1016/j.heliyon.2024.e35792
e35792
Research Article
Dynamic weighted residual ensemble learning for hyperspectral image classification driven by features and samples
Wang Jing wangjing@chzu.edu.cn
a⁎
Yang Guoguo a
Lu Hongliang bc
a Department of Geographic Information and Tourism, Chuzhou University, Chuzhou, 239000, China
b School of Earth Sciences and Engineering, Hohai University, Jiangning, Nanjing, 211100, China
c School of Architectural Engineering, Tongling University, Tongling, 244000, China
⁎ Corresponding author. wangjing@chzu.edu.cn
05 8 2024
30 8 2024
05 8 2024
10 16 e3579224 7 2023
2 8 2024
2 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Dynamic ensemble selection has emerged as a promising approach for hyperspectral image classification. However, selecting relevant features and informative samples remains a pressing challenge. To address this issue, we introduce two novel dynamic residual ensemble learning methods. The first proposed method is called multi-features driven dynamic weighted residuals ensemble learning (MF-DWRL). This method leverages various combinations of features to construct classifier pools that incorporate feature differences. The K-Nearest Neighbors algorithm is employed to establish the region of competence (RoC) in the dynamic ensemble selection process. By assessing the performance of the RoC, the feature sets that yield the highest classification accuracy are identified as the optimal feature combinations. Additionally, the classification accuracy is utilized as prior information to guide the residual adjustments of each classifier. The second method, known as features and samples double-driven dynamic weighted residual ensemble learning (FS-DWRL), further enhances the performance of the ensemble. This approach not only considers the selection of feature combinations but also takes into account the informative samples. By jointly optimizing the feature and sample selection processes, FS-DWRL achieves superior classification accuracy compared to existing state-of-the-art methods. To evaluate the effectiveness of the proposed methods, three hyperspectral datasets from China—WHU-Hi-HanChuan, WHU-Hi-LongKou, and WHU-Hi-HongHu—are used for classification experiments. For these datasets, the proposed methods achieve the highest classification accuracies of 90.57 %, 98.77 %, and 91.08 %, respectively. The MF-DWRL and FS-DWRL methods exhibit significant improvements in classification accuracy.

Keywords

Dynamic ensemble selection
Multi-feature
Bootstrap
Residual ensemble learning
Hyperspectral imagery
==== Body
pmc1 Introduction

Hyperspectral imaging (HSI) contains extensive spectral information with hundreds of contiguous spectral bands [1,2], enabling its wide application in various fields such as geoscience [3], biomedicine [4], agriculture [5], geological prospecting [6], and environmental studies [7]. However, HSI classification faces challenges, including redundancy, high dimensionality, and a scarcity of labeled samples [[8], [9], [10], [11], [12], [13], [14]]. To address these issues, advanced technologies such as deep learning and ensemble learning strategies have been developed.

Active learning [15,16], as a deep learning method, allows the model to proactively select samples it deems most informative for labeling, thereby serving for training. This is especially crucial for hyperspectral images, which require extensive annotation costs. The essence of this approach is that the model actively chooses data samples that are most beneficial for its training, thus reducing the need for manual labeling, especially in the expensive annotation realm of hyperspectral imaging. When applying deep learning models, such as Convolutional Neural Networks (CNNs) [17], to HSI classification, integrating active learning can more precisely select key samples. This not only enhances the model's classification accuracy but also effectively reduces training costs and time. Mainstream active learning strategies primarily include uncertainty-based sampling, which chooses samples where the model's prediction is most uncertain; representativeness-based sampling, which emphasizes selecting samples that can represent a large portion of unlabeled data; and model-improvement strategies, which opt for samples most likely to enhance model performance [[18], [19], [20]]. In summary, active learning offers an effective means of reducing annotation costs and boosting model performance in hyperspectral image classification. However, despite its commitment to minimizing labeling requirements, active learning might be affected by model bias, limitations in data selection, ongoing annotation costs, data imbalance, and scope of its application [21]. Ensemble learning [22], by combining multiple models, can balance out these biases, strengthen model generalization, and doesn't rely on continuous user annotation. It is also better equipped to handle data imbalances and showcases broader adaptability. Hence, compared to active learning, ensemble learning exhibits clear advantages in various aspects.

Firstly, hyperspectral data often contains redundant information because neighboring pixels in an image are likely to have similar spectral signatures. This redundancy can lead to inefficiencies in classification algorithms. Ensemble learning can help by combining multiple classifiers, each trained on a subset of the data or with different features, reducing the impact of redundancy. By aggregating the results of multiple classifiers, ensemble methods can capture a broader range of information and reduce the influence of redundant data. Secondly, hyperspectral data is characterized by a high number of spectral bands, resulting in high-dimensional feature spaces. High dimensionality can lead to increased computational complexity and overfitting. Ensemble learning can mitigate this by using techniques such as feature selection or dimensionality reduction in combination with individual classifiers. By reducing the dimensionality of the data before classification, ensemble methods can improve the efficiency and effectiveness of the classification process. Lastly, HSI classification often suffers from a lack of labeled training samples, making it challenging to train accurate classifiers. Ensemble learning can address this limitation by allowing the integration of weak or limited classifiers. It combines the predictions of multiple classifiers to make a final decision, enhancing overall classification performance even with few labeled samples. Some ensemble techniques [22], like bootstrapping and bagging, can generate multiple subsets of the available labeled data to train diverse classifiers, which can be particularly useful when data is limited. In summary, ensemble learning strategies can help improve HSI classification by leveraging multiple classifiers to handle redundancy, reduce dimensionality, and make the most of the available labeled data. By combining the strengths of multiple classifiers, ensemble methods aim to enhance classification accuracy and robustness in scenarios where traditional single classifiers may struggle due to the mentioned limitations.

Ensemble learning models can be mainly divided into two categories: static ensemble methods and dynamic ensemble selection (DES) methods. The static ensemble method [23] is based on the idea that a weak classifier can be promoted to a strong classifier through a specific ensemble strategy. Classic methods include bagging and boosting. In the bagging method [24,25], a diverse classifier pool is generated using the bootstrap strategy. Better classification results are then obtained based on the classifiers in the pool through a specific fusion strategy. Boosting [[26], [27], [28]] promotes a weak classifier to a strong classifier by weighting the samples, reducing variance and bias. Zhang et al. [29] proposed a new ensemble learning method based on sparse joint representation, incorporating both spectral and spatial features of hyperspectral data. The results show that the proposed method can perform better than traditional ensemble methods. Li et al. [30] proposed a new ensemble network for hyperspectral object tracking, which demonstrates effectiveness and better performance compared to other models. Su et al. [31] proposed a new ensemble learning framework using the tangent collaborative representation model as the base classifier, showing that representation models can also be used in ensemble learning. However, the static ensemble method does not consider each classifier's specific classification effects on different targets, and the accuracy of prior information for the base classification is difficult to obtain. The second category is the dynamic ensemble selection (DES) method [[32], [33], [34], [35]]. This method first uses K-NN or clustering to divide the classification targets into different regions, called regions of competence (RoC), and then selects the best classifier set for each local target according to some evaluation indicators. DES can better utilize the regional advantage of each base classifier compared to the static ensemble method. Even a less capable classifier may perform better in a local area. The purpose of DES is to leverage the unique classification advantages of each classifier [[36], [37], [38]]. Bharath and Rama [39] applied the idea of dynamic classifier selection (DCS) to hyperspectral image classification, combining dimensionality reduction and dynamic selection to construct a new DCS strategy. Meanwhile, Bharath et al. [40] proposed a DES method for heterogeneous classifiers, using the Markov random field (MRF), extreme learning machine (ELM), and random subspace method (RSM) as base classifiers. The results show that the dynamic classifier selection method can be effectively applied to HSI classification. Additionally, Lu et al. [41] proposed a new RoC construction method based on multi-view clustering for DES, which shows better classification accuracy than traditional DES models. However, current DES methods are limited to selecting classifiers without considering the adaptability of different samples and features to the target area. In summary, the static ensemble method can better utilize the advantages of different classifiers, but it often ignores the specific classification performance of multiple classifiers for different targets. Without prior selection of classifiers, the performance of classifier ensembles may be lower than that of a single classifier. Although the DES method focuses on the classifier's behavior, it does not consider the impact of features and samples on the classification target.

Therefore, this paper proposes a hyperspectral image classification strategy based on a diversity-guided dynamic sample and feature selection method. The research introduces a novel dynamic ensemble feature selection method for hyperspectral remote sensing image analysis, utilizing heterogeneous collaborative representation classification. Additionally, it presents a strategy that combines dynamic feature and sample selection to address the issue of insufficient sample information in existing classification methods through bootstrap sampling. Finally, a weighted residual ensemble framework is proposed, leveraging the prior behaviors of classifiers obtained from previous methods for residual-weighted ensemble, aiming to achieve more accurate classification results. The main contributions of the paper are as follows:1) In response to the lack of exploration of hyperspectral remote sensing image features in existing dynamic ensemble learning methods, a dynamic ensemble feature selection method based on heterogeneous collaborative representation classification is proposed in this paper for the first time. The K-NN method is used to construct a validation set to obtain priori information. Then, according to a certain accuracy measurement metrics, a feature or a feature set with higher classification accuracy is selected for HSI classification, which can better exploit the local classification advantages of each feature. Compared to traditional methods, the proposed approach introduces, for the first time, dynamic ensemble theory-based feature selection, which can more fully exploit the local classification advantages of each feature while simultaneously improving computational efficiency while ensuring classification accuracy.

2) To address the issue of inadequate exploration of sample information in existing hyperspectral remote sensing image classification, this paper proposes a strategy that combines dynamic feature and sample selection using bootstrap sampling based on the concept of dynamic selection. In contrast to traditional classification methods that use all samples for classification, this paper utilizes the RoC obtained in advance from dynamic ensembles to acquire prior information about the samples. Consequently, samples with higher confidence are selected for classification, providing better training samples and further enhancing classification accuracy.

3) A weighted residual ensemble framework is proposed in the paper. Unlike traditional ensemble learning methods, the classifier prior behavior obtained in 1) and 2) is utilized to directly perform a weighted ensemble with the residuals of the collaborative classifiers. According to the differences of multiple CR-based classifier sets, the method constrains the residuals of the classifiers by their prior behaviors, so as to obtain weighted classification results.

The remainder of this paper is organized as follows. In Section 2, the proposed FS-DWRS and MF-DWRL are presented. The results of the experiment are demonstrated in Section 3. In Section 4, the robustness, extensibility, transferability, and convergence of the proposed algorithms are discussed in detail. Finally, the conclusions of this study are drawn in Section 5.

2 methodology

2.1 Related works

2.1.1 Kernel collaborative representation classifiers (KCRC)

The basic idea of collaborative representation [[42], [43], [44], [45]] is to indicate the data measurement data with the least samples. Given a training set X=[x1,..,xn]∈Rm×n for n classes, a test sample ∈Rm. The target is to solve the l2 minimization problem.(1) xˆ1=argminx‖x‖2subjectto‖αX−y‖2<ε

where α is the representation coefficient. Compute the residuals.(2) ri(y)=‖y−αxi‖2,fori=1,…,n

where n represents the number of classes. Finally, sample y can be classified as.(3) class(y)=argminiri(y)

Meanwhile, to solve the problem of standard linearity, some studies have proposed an algorithm with kernel tricks, which is the KCRC [45] model. However, the residuals of KCRCs with different parameters are quite disparate. Therefore, a new weighted residual ensemble method to get more reliable classifier results is proposed in the paper.

2.1.2 Dynamic ensemble selection

Dynamic ensemble selection (DES) is a classifier selection strategy that can assign one or some classifiers with optimal competence for a specific test region. The basic idea of the DES method is that each weak classifier has its own unique classification advantages for predicting a particular region of the target. Therefore, the validation data and test data into regions with homogeneity, and uses the classification accuracy of the classifier on the validation set as the prior information in DES. Then the optimal classifier or classifier set is assigned to the target region. Finally, the final results are obtained by these regions which are ca lled region of competence (RoC). The processes of DES can be divided into three steps:

Similar to traditional methods, DES method also needs to obtain a classifier pool with diversity. The diversity of classifiers can be often obtained by setting different features, selecting different types of models, or using different training data (different samples, multiple features).

The clustering and K-NN methods are standard techniques for defining regions of competence (RoC) in dynamic ensemble selection (DES). The fundamental idea is to exploit the correlation between validation and test data. Specifically, the connection between labeled samples (test samples) and unlabeled samples (validation samples) is established through specific metrics. By partitioning them into the same regions and creating connections between unknown samples and labeled samples, the sample space is divided into several regions. Selecting well-performing base classifiers within each region enhances the classification performance and generalization ability of the ensemble model. In the K-NN method, k samples around each test point are obtained by calculating the distance between samples. These samples are then used as a validation set to provide prior information for each classifier. Based on the RoC constructed as described, the optimal classifier or classifier set is assigned to each capability area using specific evaluation indicators and selection methods. Finally, a voting method is employed to obtain the final classification result.

2.2 Proposed methods

2.2.1 Multi-features driven dynamic weighted residuals ensemble learning (MF-DWRL)

Algorithm 1 MF-DWRL

Input: Multiple feature combinations data set Xf; the k value; the empty ensemble of features EoFt; testing samples y	
for each testing sample t in do	
 Obtain Ψte as the K region of competence by K-NN based on validation set	
 for each classifier ci generation by feature combinations in Xfdo	
 1. Calculating the residuals of each ci according to Eqs. (5), (6), (7), (8), (9);	
 2. Obtaining the classification accuracy OA and weights matrices w of each ci according to Eq. (10), (11), (12);	
3. Using the classification accuracy in step.2 to screen the two best feature combinations as the best training features;	
4. Getting the final weighted residuals fusion results WR according to Eq. (13)	
 end for	
  Use the ensemble EoF*t to classify testing set according to Eq. (14)	
end for	
Output: class(y)	

The process of the two proposed algorithms is mainly divided into three parts: pool generation, weight matrices and accuracy calculating, dynamic residuals selection and fusion. The structure of two methods is shown in Fig. 1.1) Classifier pool generation by multi-features

Fig. 1 Flowchart of proposed methods.

Fig. 1

Three different features are used as input for the classifier pool: spectral features, Extend Morphological Profile (EMP) features, and Gabor features. In order to measure the influence of different features on the classification accuracy of hyperspectral images, the base classifiers with multiple features combination are constructed in the paper. It is mainly divided into three combinations: single feature, double features, and multi-features. They are denoted as(4) Xf=[xf1,…,xfm]

where xfm is different combinations of multiple features, and m represents the number of features.

Unlike traditional methods, in order to make the algorithms more focus on feature selection, only the kernel collaborative representation classifier (KCRC) as the base classifier for the construction of the classifier pool. At last, the pool with multiple classifiers is denoted as F={f1,f2,...,fc}, where c represents the number of base classifiers.2) Get residuals and accuracy by K-NN validation samples

Firstly, given a training set Xtr , according to formula (1), the representation coefficient of multiple features can be obtained by using the classifier fi.(5) Xˆtri=argminx‖xtri‖2subjectto‖αtriXtri−yi‖2<ε,i=1,…,c.

where xtri is the training samples of the ith classifier in the pool, and the αtri is the corresponding representation coefficients which is solved as(6) αtri=(XtriTXtri+λI)−1XtriTyi

Then a coefficient matrix of each classifier fi is obtained, as(7) α=[α1,…,αi],i=1,…,c.

Calculating the residual according to formula (2), and obtaining the residual matrix:(8) r(y)=‖y−αxtr‖2,i=1,…,c

Then the residual matrix is obtained(9) RES=[r1,…,ri],i=1,…,c

where RES is the residual matrix of each classifier fi. Then the validation set Xv=[xv1,…,xvk] is obtained by K-NN algorithm. For fi in the classifier pool, the classification performance in k validation set is obtained, which is denoted as(10) Xv=[xv1,…,xvk]

where the OAi is the overall accuracy of the ith classifier.

2.2.1.1 According to Eq. (4), the weight matrices is calculating

(11) W=[w1,…,wi]

(12) wi=OAi∑1iOAi

where wi represents the weight of the classification accuracy of the ith classifier in the pool for the validation.3) Dynamic residuals ensemble selection and fusion

According to Eq. (10), the two sets of feature combinations with the best performance are chosen as the optimal training features, denoted as wb1 and wb2.

Finally, the weighted residual is obtained by Eq. (4):(13) WR=wb1rb1+wb2rb2

where wb1 and wb2 are the optimal features selected by DES, rb1 and rb2 are the corresponding residuals. Then the final classification result is obtained according to formula (3):(14) class(y)=argminWR(y)

2.2.2 Features and samples double driven dynamic weighted residual ensemble learning (FS-DWRL)

Algorithm 2 FS-DWRL

Input: Optimal feature combinations data set X’f; numbers of resample times N; testing samples y for X’fdo	
 Use the bootstrap method to sampling X′ and get sub training set Xsub′ for each classifier ci generation by sub_Xf do	
 1. Calculating the residuals of each ci according to Eq. (15), (16), (17);	
 2. Obtaining the classification accuracy OA and weights matrices w of each ci according to Eq. (18), (19);	
3. Getting the final weighted residuals fusion results WR’ according to Eq. (20)	
 end for	
 Classify testing set by EoF*t according to (21) end for Output: class(y)	

1) New classifier pool generation by Bootstrap sampling

According to the optimal features Xsub′ based on MF-DWRL algorithm, the bootstrap is used to resample the training data in into n groups, denoted as(15) Xsub′=[xsub1′,…,xsubq′]

where xsubi′ is the sub-training set and q represents the number of subsets. Then the new classifier is constructed based on Xsub′ , which is denoted as(16) F′=[f1′,…,fq′]

where F′ is the new classifier pool generated based on a sub-training set.2) Get residuals and weight matrices by K-NN validation samples

Similar to the MF-DWRL, the residual of new classifier pool is calculating as,(17) r(y)=‖y−αx′‖2,i=1,…,qRES′=[r1′,…,rq′]

where RES′ is the residual matrix of each classifier fi′.

The prior accuracy information and weight matrix for each classifier is calculated by validation set using Xsub, denoted as(18) OA=[OA1,…,OAq]

(19) wi=OAi∑1iOAi

where wi represents the weight of the classification accuracy of the ith classifier in the pool for the validation.

2.2.2.1 Dynamic weighted residuals ensemble learning

Finally, the weighted residual is obtained(20) WR′=∑i=1nwi′ri′

where WR′ is the weighted residuals.

Then the final classification result is obtained(21) class(y)=argminWR′(y)

3 Results

3.1 Data source

The WHU-Hi-HanChuan data set [46] is the first hyperspectral image to evaluate the proposed methods. It contains 274 spectral bands with the wavelengths ranging from 0.4 to 1 μm, which is obtained by UAV hyperspectral remote sensing observation in Hanchuan, Hubei Province, China. The details of this data are listed in Table 1. The false-color image and ground truth are shown in Fig. 2 (a) and 2 (b).Table 1 The WHU-Hi-HanChuan data set.

Table 1No.	Samples	Name	
1	44735	Strawberry	
2	22753	Cowpea	
3	10287	Soybean	
4	5353	Sorghum	
5	1200	Water spinach	
6	4533	Watermelon	
7	5903	Greens	
8	17978	Trees	
9	9469	Grass	
10	10516	Red roof	
11	16911	Gray roof	
12	3679	Plastic	
13	9116	Bare soil	

Fig. 2 (a) False-color image and (b) ground truth of the WHU-Hi-HanChuan data set.

Fig. 2

The WHU-Hi-LongKou data set [46] contains 270 spectral bands with wavelengths ranging from 0.4 to 1 μm, which is acquired by UAV hyperspectral remote sensing observation in Longkou, Hubei Province, China. The details of nine classes in this HIS are listed in Table 2. The false-color image and ground truth are presented in Fig. 3 (a) and 3 (b).Table 2 The WHU-Hi-LongKou data set.

Table 2No.	Samples	Name	
1	34511	Corn	
2	8374	Cotton	
3	3031	Sesame	
4	63212	Broad-leaf soybean	
5	4151	Narrow-leaf soybean	
6	11,854	Rice	
7	67056	Water	
8	7124	Roads and houses	
9	5329	Mixed weed	

Fig. 3 (a) False-color image and (b) ground truth of theWHU-Hi-LongKou data set.

Fig. 3

The WHU-Hi-HongHu data [46] set is gathered by UAV hyperspectral remote sensing observation in Honghu, Hubei Province, China. It contains 270 spectral bands with 940 x 475 pixels. The detailed information of each class is shown in Table 3 and Fig. 4 (a) and 4 (b).Table 3 The WHU-Hi-HongHu data set.

Table 3No.	Samples	Name	
1	14041	Red roof	
2	3512	Road	
3	21821	Bare soil	
4	163285	Cotton	
5	6218	Cotton firewood	
6	44557	Rape	
7	24103	Chinese cabbage	
8	4054	Pakchoi	
9	10819	Cabbage	
10	12394	Tuber mustard	
11	11015	Brassica parachinensis	
12	8954	Brassica chinensis	
13	22507	Small Brassica chinensis	
14	7356	Lactuca sativa	
15	1002	Celtuce	
16	7262	Film covered lettuce	
17	3010	Romaine lettuce	
18	3217	Carrot	
19	8712	White radish	
20	3486	Garlic sprout	
21	1328	Broad bean	
22	4040	Tree	

Fig. 4 (a) False-color image and (b) ground truth of the WHU-Hi-HongHu data set.

Fig. 4

3.2 Experimental setup

All experiments are implemented on the platform of Python 3.8.6. The specific parameters of the proposed algorithms are set as follows.

3.2.1 Parameter setup

The range of k number n_k in DWR-DEL is set {1, 2, 3, 4, 5}. The number of resample n_r is set {5, 10, 15, 20, 25}. The regularization parameter λ is set {1e-1, 1e-2, 1e-3, 1e-4, 1e-5}. The data partitioning was conducted using a random sampling approach. Each class was separately sampled with {5, 10, 15, 20, 25} instances for experimentation. The presented results represent the outcomes obtained using 25 samples per class. Additionally, the hyperparameters of different algorithms for all the dataset are set to the same values.

3.2.2 Multi-features construct

To ensure the comparability and fairness, the compared and proposed algorithms are under the same experimental conditions. The classifier pool through different feature combinations, namely Spectral feature (sf), EMP feature (ef), and Gabor feature (gf) is used to evaluate the proposed methods in this paper. To focus on feature and sample selection, only KCRC classifier is used as base classifier in this paper.

3.2.3 Baseline and comparative algorithms

To evaluate the performance of the proposed algorithm, multiple classification algorithms were used for comparison. For example, the classic machine learning algorithms SVM and RF are the baselines. Moreover, the ensemble algorithm GBDT [47], LightGBM [48], and XGboost [49] are also used as a comparison algorithm. In addition, the two advanced DES algorithms, DES-MI [50] and META-DES [51] algorithm are used as comparative algorithms in the paper The overall accuracy (OA), average accuracy (AA), and kappa indexes are used to evaluate the classification of all the comparisons and proposed methods in this section. OA measures the proportion of correctly classified instances over the total, AA considers accuracy for each class and averages them, while the kappa index adjusts accuracy for chance agreement, making it valuable for comparing methods or assessing inter-rater agreement.

3.3 Classification performance and maps

The classification performance of proposed methods and comparative algorithms for the first data set are shown in Table 4. The classification images obtained by these methods are shown in Fig. 5 (a)–(l). For the WHU-Hi-HanChuan data set,Table 4 Classification results (%) for the WHU-Hi-HanChuan data set.

Table 4Class	SVM	RF	CRC	ProCRC	GBDT	DES-MI	Meta-DES	XGboost	LightGBM	DCNN	MF-DWRL	FS-DWRL	
1	33.99	88.39	57.92	32.50	89.93	90.02	85.11	82.55	88.62	86.45	95.35	93.87	
2	34.75	71.21	61.47	55.49	69.61	79.36	70.39	68.41	77.04	69.13	71.65	70.82	
3	37.53	83.46	68.32	56.24	79.65	85.13	80.95	84.23	89.05	73.43	92.51	95.91	
4	69.73	92.70	95.70	94.53	91.38	89.59	91.50	93.83	91.50	92.99	94.34	93.74	
5	60.00	99.48	95.65	99.83	95.30	99.39	99.65	94.17	98.35	97.30	99.83	99.83	
6	8.28	79.57	68.10	80.33	87.84	83.92	83.45	80.55	76.89	74.01	81.75	84.07	
7	79.58	92.86	90.98	81.68	79.38	93.87	92.35	90.48	94.57	92.31	97.18	96.70	
8	16.05	82.17	58.24	60.61	77.00	80.10	81.94	85.13	83.15	86.13	80.42	80.28	
9	20.04	81.74	58.69	53.59	77.11	77.45	78.46	65.54	80.40	61.86	85.44	83.26	
10	40.50	87.48	68.72	88.28	90.67	89.66	89.03	92.14	93.45	92.11	94.82	93.81	
11	79.59	96.89	95.80	83.69	83.99	96.70	97.05	91.64	95.10	92.87	98.24	98.46	
12	52.07	98.87	88.62	99.53	92.04	97.63	98.76	97.44	98.02	96.31	99.86	99.89	
13	23.76	70.83	63.04	48.80	77.13	68.42	75.07	80.00	81.56	68.39	78.91	79.01	
14	16.80	93.74	92.31	93.51	89.35	89.52	91.72	93.19	94.43	94.38	93.06	92.17	
15	50.83	93.20	87.50	93.47	88.42	90.53	93.11	95.86	97.06	93.84	93.66	92.37	
16	65.45	93.52	76.66	98.14	82.13	90.52	94.38	89.39	92.03	89.55	93.84	93.30	
OA	45.10	88.04	72.23	72.84	83.01	87.62	87.52	85.29	88.93	85.24	90.57	90.05	
AA	43.06	87.88	76.73	76.26	84.43	87.61	87.68	86.54	89.45	85.07	90.68	90.47	
Kappa	0.38	0.86	0.68	0.69	0.80	0.86	0.85	0.83	0.87	0.83	0.89	0.88	

Fig. 5 Classification for the WHU-Hi-LongKou data set. (a) SVM. (b) RF. (c) CRC. (d) ProCRC. (e) GBDT. (f) DES-MI. (g) Meta-DES. (h) XGboost. (i) LightGBM. (j) DCNN. (k)MF-DWRL. (l) FS-DWRL.

Fig. 5

the classification performance of proposed methods is better than other comparative models. The accuracy of the MF-DWRL algorithm can reach 90.57 %, which is about 45 % and 3 % higher than the traditional SVM and RF algorithms, respectively. Meanwhile, compared with the latest DES algorithms DES-MI and Meta-DES, the classification accuracy of the proposed method is still higher. Notably, the MF-DWRS performs the best in the case of classification accuracy among all algorithms. Additionally, the highest kappa value (kappa = 0.89) was attained by the proposed MF-DWRL method, indicating that high consistency and accuracy in classification tasks were achieved. A kappa value close to 1 signifies that there is a high level of agreement among raters and a relatively low error rate. Consequently, it is suggested by this result that the MF-DWRL method is capable of yielding highly consistent results in the classification process and is likely to be considered a preferred classification approach.

Similar to the first experimental, the proposed algorithms MF- DWRL and FS-DWRS perform both better than other methods for the WHU-Hi-LongKou data set. The detailed performance of each algorithm is shown in Table 5, and the thematic maps are described in Fig. 6(a)–(l). The OA of the two proposed can reach 98.66 % and 98.77 %, respectively. Compared with the GBDT algorithm, the MF-DWRL and FS-DWRS methods perform better. Moreover, compared with three latest ensemble learning algorithms, the two proposed algorithms yield 8 %, 4 %, and 4 % improvements.Table 5 Classification results (%) for the WHU-Hi-LongKou data set.

Table 5Class	SVM	RF	CRC	ProCRC	GBDT	DES-MI	Meta-DES	XGboost	LightGBM	DCNN	MF-DWRL	FS-DWRL	
1	93.85	96.85	99.49	99.82	96.82	98.22	97.88	97.36	97.58	98.55	98.71	99.49	
2	81.61	98.32	98.22	98.24	97.60	98.61	98.26	98.79	98.38	95.11	99.08	99.05	
3	84.99	98.03	99.63	99.93	93.08	97.69	97.86	93.08	97.19	99.83	98.66	99.03	
4	54.99	88.12	84.93	71.09	87.77	90.70	85.62	90.38	93.11	93.97	97.38	97.32	
5	75.12	97.91	99.56	99.42	95.14	96.59	96.94	96.57	96.42	99.34	98.95	99.15	
6	90.39	83.99	91.53	87.99	86.08	85.38	89.47	78.49	92.18	98.73	99.14	99.17	
7	99.88	99.97	99.99	100.00	99.92	99.94	99.96	99.14	99.95	99.89	99.96	99.94	
8	62.48	93.65	91.13	83.46	83.89	88.14	91.46	95.02	95.16	97.92	97.92	98.07	
9	56.65	87.21	93.14	74.01	81.85	75.70	74.91	86.90	82.99	95.13	96.11	95.61	
OA	80.57	94.17	94.19	89.01	93.53	94.77	93.47	94.33	96.21	97.37	98.66	98.77	
AA	77.77	93.78	95.29	90.44	91.35	92.33	92.48	92.86	94.77	97.61	98.43	98.54	
Kappa	0.76	0.92	0.92	0.86	0.92	0.93	0.92	0.93	0.95	0.97	0.98	0.98	

Fig. 6 Classification for the WHU-Hi-HongHu data set. (a) SVM. (b) RF. (c) CRC. (d) ProCRC. (e) GBDT. (f) DES-MI. (g) Meta-DES. (h) XGboost. (i) LightGBM. (j) DCNN. (k)MF-DWRL. (l) FS-DWRL.

Fig. 6

For the last data set, the classification performance of all algorithms is shown in Table 6, and the thematic images are shown in Fig. 7(a)–(l). For the third data set, the MF-DWRL and FS-DWRS perform better than other comparative methods. Compared with CRC and ProCRC models, the proposed methods yield 10 % and 13 % improvements, respectively. Moreover, the classification performance of FS-DWRS is better than MF-DWRL.Table 6 Classification results (%) for the WHU-Hi-HongHu dataset.

Table 6Class	SVM	RF	CRC	ProCRC	GBDT	DES-MI	Meta-DES	XGboost	LightGBM	DCNN	MF-DWRL	FS-DWRL	
1	66.89	92.37	72.45	89.84	88.75	95.51	94.10	88.21	89.29	92.00	97.08	97.28	
2	50.06	90.67	92.69	91.74	89.63	89.14	89.37	89.43	89.51	92.26	94.74	94.86	
3	70.21	84.67	86.90	83.16	82.32	86.47	85.58	84.50	84.12	82.99	85.12	85.44	
4	58.95	96.70	91.47	82.89	90.44	96.52	96.91	92.81	96.93	89.90	96.78	97.41	
5	30.50	96.40	83.35	84.65	92.09	92.64	93.30	97.13	96.92	91.94	95.98	96.81	
6	77.14	89.30	92.56	92.64	90.27	90.32	89.48	89.58	88.82	88.79	92.42	91.11	
7	18.96	64.74	43.96	43.19	59.15	67.52	65.28	60.06	62.40	67.64	62.52	58.17	
8	8.37	91.28	77.97	82.49	92.11	86.51	83.47	98.78	99.58	84.52	95.63	97.80	
9	79.07	94.64	92.96	96.00	92.65	93.00	92.74	92.18	92.49	91.22	92.72	92.13	
10	29.16	79.49	65.57	53.47	71.95	77.20	74.28	85.97	87.31	75.43	85.21	89.28	
11	34.84	60.28	54.80	47.44	79.04	64.33	59.17	73.23	78.85	60.73	80.67	81.04	
12	34.27	83.85	67.77	71.97	85.42	80.69	77.59	89.22	90.86	85.68	90.35	92.49	
13	48.02	77.82	34.37	33.57	66.99	76.11	74.95	72.77	74.67	68.61	82.83	84.69	
14	43.54	81.60	65.07	69.60	84.38	76.02	79.14	83.73	85.89	84.01	87.09	87.89	
15	58.55	95.17	91.19	95.59	91.92	94.54	94.65	95.70	95.80	95.49	97.06	94.75	
16	48.13	98.43	99.49	99.81	99.71	97.99	99.00	99.72	99.72	97.09	99.64	99.75	
17	65.81	90.24	93.95	94.80	91.79	85.20	89.59	91.79	91.79	90.88	93.31	93.72	
18	37.09	91.79	91.76	86.14	85.70	87.37	87.44	86.36	86.77	95.01	94.44	94.73	
19	26.09	73.54	66.10	62.31	76.85	66.17	70.63	78.35	80.24	79.47	76.04	72.28	
20	45.87	94.62	92.99	88.01	90.13	88.97	93.36	90.83	95.34	97.50	99.04	99.04	
21	73.98	95.86	99.30	94.69	98.75	93.75	97.81	98.28	99.14	100.00	99.61	99.69	
22	44.21	99.12	99.00	98.67	97.44	96.59	97.87	98.27	98.45	97.37	98.95	98.97	
OA	54.56	89.00	80.94	77.20	85.48	88.69	88.39	87.45	89.77	85.51	90.96	91.08	
AA	47.71	87.39	79.80	79.21	86.25	85.57	85.71	88.04	89.31	86.75	90.78	90.88	
Kappa	0.47	0.86	0.76	0.72	0.82	0.86	0.85	0.84	0.87	0.82	0.89	0.89	

Fig. 7 Classification accuracy of three data set versus varying samples of proposed methods. (a) SVM. (b) RF. (c) CRC. (d) ProCRC. (e) GBDT. (f) DES-MI. (g) Meta-DES. (h) XGboost. (i) LightGBM. (j) DCNN. (k)MF-DWRL. (l) FS-DWRL.

Fig. 7

4 Discussions

4.1 Extendibility of proposed methods

To verify the generalization ability of the proposed algorithm, three sets of classical hyperspectral data are also used for experiments. The overall accuracy (OA), average accuracy (AA), and kappa indexes are used to evaluate the classification of all the comparisons and proposed methods in this section.

According to Table 7, for the Indian Pines data set, the classification performance of proposed methods is better than other comparative models. The accuracy of the MF-DWRL algorithm can reach 89.50 %, which is about 31 % and 3 % higher than the traditional SVM and RF algorithms, respectively. Meanwhile, compared with the classical ensemble learning algorithm GBDT and the latest DES of the proposed method is still higher. Notably, the FS-DWRS performs the best in the case of classification accuracy among all algorithms.Table 7 Classification results (%) for the Indian Pines data set.

Table 7Class	SVM	RF	CRC	ProCRC	GBDT	DES-MI	Meta-DES	XGboost	LightGBM	DCNN	MF-DWRL	FS-DWRL	
1	94.12	100.00	100.00	100.00	88.24	100.00	100.00	100.00	100.00	93.75	100.00	100.00	
2	20.36	69.86	69.35	72.23	76.69	79.86	77.99	76.33	73.02	77.00	78.99	78.49	
3	34.39	77.24	77.62	79.27	84.07	87.23	86.09	81.16	84.45	86.28	82.81	82.68	
4	44.50	93.50	80.50	88.00	80.00	94.50	94.00	98.00	99.50	71.50	98.00	98.50	
5	63.60	82.02	88.99	88.54	75.28	88.54	86.29	82.47	82.92	85.98	89.89	90.56	
6	74.20	94.06	95.80	93.91	90.14	96.96	97.25	91.01	93.19	94.44	94.93	95.07	
7	100.00	100.00	100.00	100.00	83.33	100.00	100.00	83.33	100.00	100.00	100.00	100.00	
8	100.00	100.00	100.00	100.00	99.55	100.00	100.00	100.00	100.00	100.00	100.00	100.00	
9	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	
10	73.55	79.01	84.80	86.83	80.09	76.23	82.23	70.99	77.52	85.61	82.66	82.01	
11	66.14	79.06	85.31	88.41	82.24	76.86	80.88	84.81	82.57	75.47	90.73	90.60	
12	34.71	72.12	79.50	81.65	82.37	60.43	70.50	90.11	86.87	77.02	81.12	80.04	
13	93.45	96.43	97.62	99.40	86.90	95.24	96.43	95.24	97.62	98.75	97.62	97.62	
14	78.12	94.45	99.67	100.00	93.47	91.18	97.22	99.02	99.18	98.60	99.76	99.76	
15	40.35	88.76	91.35	85.88	95.68	75.50	89.63	96.54	96.83	96.17	97.98	97.98	
16	93.44	100.00	100.00	100.00	100.00	100.00	98.36	100.00	100.00	100.00	100.00	98.36	
OA	58.76	82.43	85.87	87.39	84.49	82.81	85.79	86.09	86.06	84.74	89.50	89.69	
AA	69.43	89.16	90.66	91.51	87.38	88.91	91.05	90.56	92.10	90.03	93.40	93.23	
Kappa	0.54	0.80	0.84	0.86	0.82	0.80	0.84	0.84	0.84	0.83	0.88	0.88	

Similar to the first experimental, the proposed algorithms MF-DWRL and FS-DWRS perform both better than other models for the University of Pavia data set. The OA of the two proposed can reach 94.40 % and 94.17 %, respectively. Moreover, compared with three DES methods, the two proposed algorithms yield 12 %, 11 %, and 11 % improvements (Table 8). Meanwhile, both proposed methods can achieve the highest kappa coefficient value.Table 8 Classification results (%) for the University of Pavia data set.

Table 8Class	SVM	RF	CRC	ProCRC	GBDT	DES-MI	Meta-DES	XGboost	LightGBM	DCNN	MF-DWRL	FS-DWRL	
1	50.43	72.39	86.07	81.89	75.59	88.66	87.63	90.24	91.06	96.95	96.24	92.60	
2	57.19	73.83	92.36	84.42	61.59	81.34	79.38	77.99	70.12	89.94	90.20	93.01	
3	66.19	76.62	88.70	96.49	77.59	87.21	81.14	88.70	90.28	83.16	83.13	89.27	
4	67.94	87.94	95.73	95.80	64.62	83.61	92.18	71.09	78.19	98.91	97.56	97.73	
5	86.43	99.25	99.77	100.00	92.84	96.15	99.40	93.74	93.74	99.92	100.00	100.00	
6	50.35	80.95	91.14	91.99	86.30	71.09	76.56	93.09	70.85	99.48	97.76	97.30	
7	83.89	97.86	98.55	99.24	92.98	95.95	98.24	98.09	97.94	100.00	99.54	98.93	
8	60.46	76.27	88.72	46.86	80.31	71.41	78.62	79.00	86.16	99.23	96.60	95.77	
9	98.49	99.78	98.81	99.89	85.13	95.69	100.00	79.42	91.92	100.00	99.89	100.00	
OA	59.45	77.90	91.55	84.37	71.72	82.09	82.92	82.92	78.46	94.08	94.40	94.17	
AA	69.04	84.99	93.32	88.51	79.66	85.68	88.13	85.71	85.58	96.40	96.07	96.58	
Kappa	0.50	0.72	0.89	0.80	0.65	0.77	0.78	0.78	0.73	0.92	0.93	0.92	

For the third data set, the MF-DWRL and FS-DWRS perform better than other comparative methods. Compared with CRC and ProCRC models, the proposed methods yield 5 % and 7 % improvements, respectively. Moreover, the classification performance of FS-DWRS is better than MF-DWRL (Table 9). The proposed method MF-DWRL and FS-DWRS outperforms other comparison algorithms in terms of kappa coefficient performance.Table 9 Classification results (%) for the Salinas data set.

Table 9Class	SVM	RF	CRC	ProCRC	GBDT	DES-MI	Meta-DES	XGboost	LightGBM	DCNN	MF-DWRL	FS-DWRL	
1	80.04	99.90	99.80	100.00	89.44	100.00	99.70	94.10	92.25	100.00	100.00	100.00	
2	56.22	100.00	99.81	99.95	95.24	98.01	99.68	99.76	99.89	99.62	99.95	100.00	
3	63.38	92.12	99.49	93.34	95.07	99.03	93.13	80.32	92.22	92.37	99.79	99.80	
4	52.60	98.70	96.68	98.12	98.70	97.11	90.03	96.46	99.28	99.70	99.70	99.13	
5	73.80	91.45	91.83	92.43	61.99	90.55	92.99	81.71	86.88	98.48	97.69	97.34	
6	90.15	99.14	99.29	99.85	86.60	98.89	98.35	95.09	91.16	99.97	99.85	98.61	
7	85.91	99.75	98.40	99.92	96.05	97.65	99.36	99.47	99.72	99.91	99.80	99.89	
8	51.59	68.49	61.08	49.41	63.70	94.41	90.65	97.62	93.88	51.71	90.02	71.27	
9	91.25	96.84	99.19	98.05	88.28	95.01	96.80	79.41	88.68	99.72	99.98	99.98	
10	55.23	88.95	92.35	94.86	91.52	77.91	86.57	86.02	88.68	98.76	98.58	95.26	
11	59.36	88.75	95.94	97.35	77.98	87.43	88.75	74.67	75.14	93.42	99.81	94.33	
12	16.95	90.82	87.85	94.73	17.79	87.79	93.90	79.92	84.19	100.00	100.00	100.00	
13	72.08	97.79	90.40	92.60	97.90	94.92	98.01	98.68	98.45	99.54	97.83	98.23	
14	33.30	93.40	92.45	90.00	33.96	66.04	90.09	87.26	90.38	92.07	99.13	94.43	
15	54.22	70.46	65.21	67.31	69.04	40.71	45.95	69.14	60.47	87.20	87.30	78.15	
16	85.92	97.72	98.72	100.00	92.32	89.71	95.27	99.44	100.00	100.00	98.64	99.00	
OA	64.78	86.81	85.10	83.27	77.41	86.23	87.73	88.30	88.25	87.32	90.22	93.24	
AA	63.87	92.14	91.78	91.74	78.47	88.45	91.20	88.69	90.08	95.53	95.34	96.53	
Kappa	0.61	0.85	0.83	0.81	0.75	0.85	0.86	0.87	0.87	0.86	0.89	0.92	

4.2 The effect of different sample sizes

For the three real HSI data set, the number of samples significantly impacts the classification performance. Fig. 8. (a) – (c) show the accuracy of the MF-DWRL and FS-DWRL algorithms when the number of samples changes in range.Fig. 8 Classification accuracy versus varying λ of proposed methods. (a) Han Chuan data set. (b) Long Kou data set. (c) Hong Hu data set.

Fig. 8

For the WHU-Hi-HanChuan data set dataset, the accuracy of the MF-DWRL and FS-DWRL algorithms shows the same trend as the sample changes. The best classification accuracy can be obtained when the number of samples is 25. Meanwhile, it can be seen that when the number of samples is from 10 to 20, the classification accuracy of FS-DWRL is higher than MF-DWRL.

For the WHU-Hi-LongKou data set, when the number of samples is 20, the classification accuracy of the two algorithms reaches the highest. However, unlike WHU-Hi-HanChuan data, the classification accuracy of MF-DWRL has always been higher than the FS-DWRL algorithm.

Finally, the classification accuracy of MF-DWRL and FS-DWRL is affected by the number of samples for the WHU-Hi-HongHu data set, similar to the previous two data. Unlike the first two data, the overall classification accuracy of the two algorithms is large, and the classification performance of FS-DWRL is much higher than MF-DWRL.

4.3 Parameters analysis for number of λ

Fig. 9 shows the effects of parameter λ on the classification accuracy. For WHU-Hi-HanChuan data (Fig. 9(a)), the classification accuracy of MF-DWRL increases with the gradual decrease in regularization parameter λ. The classification accuracy of MF-DWRL and FS-DWRL is increasing first, and then the overall classification performance should be due to MF-DWRL. For theWHU-Hi-LongKou data (Fig. 9(b)), as the parameter λ decreases, the classification accuracy of the MF-DWRL algorithm is increases. For FS-DWRL, the classification accuracy rises first and then drops. When λ is 1e-3, both algorithms reach the highest accuracy.Fig. 9 Classification accuracy versus varying λ of proposed methods. (a) Han Chuan data set. (b) Long Kou data set. (c) Hong Hu data set.

Fig. 9

The classification performance of WHU-Hi-HongHu data (Fig. 9(c)) has gradually increased with the decrease when regularization parameter λ in range 1e-1 and 1e-3. When λ is 1e-3, both algorithms reach the highest accuracy.

4.4 Parameters analysis for number of bootstrap iterations n_r

For the FS-DWRL algorithm, the paper discusses the impact of the number of resamples times on the classification accuracy (Fig. 10). It can be seen from Fig. 10(a)–(c) that the number of resample times has little effect on the classification accuracy of the proposed method. Meanwhile, with the increase of the number of resample times, the classification accuracy has decreased first and then increased. It is worth noting that for three different hyperspectral data, when the parameter is set as 10, the classification accuracy reaches the highest. In summary, the model is not sensitive to the change of parameter, and has great generalization and robustness.Fig. 10 Classification accuracy versus varying number of bootstrap iterations of proposed methods. (a) Han Chuan data set. (b) Long Kou data set. (c) Hong Hu data set.

Fig. 10

4.5 Analysis of feature selection

Table 10 demonstrates the classification results for three groups using different datasets. Here, S, E, G represent spectral features, emp features, and Gabor features respectively, while SE, SG, EG, SEG denote different combinations of features. The last two methods incorporate a feature selection process. A paragraph of analysis indicates the advantages of the proposed methods. Based on the provided data, it can be observed that the proposed methods (MF-DWRL and FS-DWRL) achieve the highest classification accuracies across all combinations. This suggests that the proposed methods can effectively enhance classification performance when dealing with different feature combinations. Specifically, the classification accuracies of MF-DWRL and FS-DWRL methods are consistently higher than those of other methods across all feature combinations (S, E, G, SE, SG, EG, SEG). This indicates that these two methods not only fully utilize the information from individual features but also demonstrate stronger classification capabilities in feature combinations. In contrast, other methods may perform poorly in certain feature combinations, possibly due to differences in feature correlation or importance. Furthermore, the most prominent among these methods is FS-DWRL, with classification accuracies approaching or exceeding 98 % in most feature combinations. This suggests that FS-DWRL excels in feature selection, extracting the most representative features from the original set and significantly improving classification accuracy. In conclusion, the proposed methods demonstrate excellent performance across multiple feature combinations, with FS-DWRL particularly standing out for its superior feature selection capabilities, making it a highly promising classification approach.Table 10 Classification results (%) for the three data sets based on different feature combinations.

Table 10	S	E	G	SE	SG	EG)	SEG	MF-DWRL	FS-DWRL	
Han Chuan	59.57	85.19	35.73	85.10	44.24	57.73	60.00	90.57	90.05	
Long Kou	89.94	98.56	47.10	98.23	63.82	82.98	84.44	98.66	98.77	
Hong Hu	60.50	91.44	8.04	89.12	33.59	55.58	57.14	90.96	91.08	

5 Conclusion

In conclusion, this paper introduces a novel dynamic ensemble weighted residuals (DES) learning framework designed to integrate prior classification information and achieve superior classification performance. The DES framework presents an innovative approach for the weighted selection and fusion of multiple features, utilizing the DES methodology to acquire prior classification insights for various features within the region of competence (RoC). This prior information is effectively harnessed to constrain the residuals of each classifier, thereby enhancing overall classification accuracy.

Furthermore, the DES framework incorporates the bootstrap method for resampling the training set, thereby generating a diverse pool of classifiers. By leveraging the prior classification behavior of each classifier within the RoC, the DES framework derives weighted residual fusion outcomes for different samples. In contrast to conventional ensemble learning techniques and DES methods, the proposed framework dynamically selects both features and samples, which significantly improves classification performance.

Empirical evaluations substantiate the superiority of the proposed DES framework over existing models, demonstrating markedly improved classification accuracy. Additionally, the DES framework exhibits robustness to parameter variations, thereby mitigating the need for intricate parameter tuning in practical applications. The efficacy of the proposed methods is further corroborated by classification results obtained from three hyperspectral image (HSI) datasets.

Looking ahead, several promising avenues for future research are apparent. First, extending the DES framework to domains beyond image classification—such as natural language processing, time series analysis, and biomedical data analysis—represents an intriguing direction. Second, exploring the application of the DES framework to diverse remote sensing tasks, including object detection, land cover mapping, and change detection, holds considerable potential. Furthermore, the integration of advanced techniques, such as deep learning-based approaches and online learning strategies, could further augment the performance of the DES framework.

In summary, the proposed dynamic ensemble weighted residuals learning framework offers a robust methodology for incorporating prior classification information and achieving enhanced classification outcomes. This research provides valuable insights into the field of machine learning and remote sensing analysis, setting the stage for future advancements in ensemble learning methodologies.

Data availability

Data will be made available on request.

Funding

This research was funded by the Fund of National Sensor Network Engineering Technology Research Center (No. NSNC202103 ).

CRediT authorship contribution statement

Jing Wang: Writing – original draft, Software, Data curation. Guoguo Yang: Supervision, Investigation, Formal analysis, Conceptualization. Hongliang Lu: Writing – review & editing, Supervision, Methodology, Formal analysis, Conceptualization.

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.

Acknowledgments

The authors would like to thank Prof. Y. Zhong at the Wuhan University, for providing WHU-Hi hyperspectral data sets, Prof. P. Gamba at the University of Pavia, Pavia, Italy, for providing the ROSIS data and Prof. D. Landgrebe from Purdue University for providing the AVIRIS image of Indian Pines and Salinas valley.
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