Spatial Perception Correntropy Matrix for Hyperspectral Image Classification

Abstract

With the development of the hyperspectral imaging technique, hyperspectral image (HSI) classification is receiving more and more attention. However, due to high dimensionality, limited or unbalanced training samples, spectral variability, and mixing pixels, it is challenging to achieve satisfactory performance for HSI classification. In order to overcome these challenges, this paper proposes a feature extraction method called spatial perception correntropy matrix (SPCM), which makes use of spatial and spectral correlation simultaneously to improve the classification accuracy and robustness. Specifically, the dimension reduction is carried out firstly. Then, the spatial perception method is designed to select the local neighbour pixels. Thus, local spectral-spatial correlation is characterized by the correntropy matrix constructed using the selected neighbourhoods. Finally, SPCM representations are fed into the support vector machine for classification. The extensive experiments carried out on three widely used data sets have revealed that the proposed SPCM performs better than several state-of-the-art methods, especially when the training set is small.

1. Introduction

Hyperspectral image (HSI) captures an enormous amount of spectral and spatial information with hundreds of subdivided spectral bands [1,2], which provides an effective tool to discriminate various land covers. Therefore, HSI classification, which predicts the label of each pixel, can be widely used in precision agriculture [3,4], environmental management [5], surveillance [6], and so forth. However, due to high dimensionality, limited or unbalanced training samples, spectral variability, and mixing pixels, it is challenging to achieve satisfactory performance for HSI classification methods [7,8,9].

To mitigate the issues mentioned above, a considerable amount of HSI classification methods have been designed in the past few years. According to the way of feature extraction, existing HSI classification methods can be split into two categories, i.e., spectral-based methods and spectral-spatial-based methods [2]. In the early stage of research, researchers usually focused on making use of spectral information for classification, where the raw pixel vectors are fed into the classifier without any feature extraction [10,11,12]. However, the original spectral information contains large-scale redundancy, and the relationship between spectrum and land cover is nonlinear, which increases the difficulty of classification. Therefore, many researchers began to pay attention to dimension reduction methods for HSI classification. Some dimension reduction methods are widely used for HSI classification, and typical methods include principal component analysis (PCA) [13], linear discriminant analysis(LDA) [14], local linear embedding (LLE) [15], independent component analysis (ICA) [16], and maximum noise fraction (MNF) [17]. Since only global statistical data are considered, the performance of PCA in extracting local features of HSI classification is not prominent [18]. In addition, existing researches also show that MNF is usually superior to PCA in HSI classification [19]. Nevertheless, the spectral-based approach usually leads to unsatisfactory results in the absence of the spatial feature. In HSI classification, the spatial information [20], which provides abundant shape, context and layout features, is very important for high precision HSI classification. It is commonly believed that the joint extraction of spatial and spectral features can improve the classification accuracy and robustness [21].

To incorporate the spatial information, many spectral-spatial-based classification methods have been developed in recent years [22,23,24]. Fang et al. introduced superpixel-based classification via multiple kernels (SCMK) [25,26] to obtain uniform regions for spatial-spectral feature extraction. Huang et al. [27] proposed a method based on local linear spatial-spectral probability distribution to make full use of HSI local geometry and spatial correlation. In the past few years, with the popularity of deep learning and its success in natural image processing, more and more deep learning methods have been designed to exploit the discriminative information for HSI classification [2,28,29], such as convolutional neural network (CNN) [30], deep brief network [31], and graph convolution network [32]. Recently, 3D CNN is also used to preserve the joint spatial and spectral information in the feature learning process, which can learn important discrimination information for HSI classification [33]. Furthermore, 3D generative adversarial network (3D-GAN) has also been applied to HSI classification [34]. Recurrent Neural Network (RNN) is used to characterize the sequence characteristics of hyperspectral pixel vectors for classification tasks. Mou et al. proposed a novel RNN with a specially designed activation function and modified gated recurrent unit (GRU) to solve the multiclass classification for HSI [35]. Although these methods based on deep learning have made great breakthroughs in HSI classification, there are still some important problems to be solved [2]. For example, deep learning-based methods usually need a large number of training data to produce better classification performance. However, labelling HSI data is always expensive and time-consuming.

It is well known that HSIs usually consist of a large number of correlated bands. More importantly, the current research indicates that correlation is important in many computer vision task, especially when the training set is small [36]. However, most of the existing HSI classification methods only focus on dimension reduction to remove redundancy. In order to make full use of the spectral correlation, Fang et al. proposed local covariance matrix representation (LCMR) for HSI classification, which represents each pixel by a covariance matrix [37]. This method uses the covariance matrix to characterize different pixels and achieves good classification performance. However, the high nonlinearity of the HSI decreases the performance of the covariance matrix-based method. Fortunately, correntropy has good advantages in tackling nonlinear and non-Gaussian data [38]. Consequently, Zhang et al. proposed local correntropy matrix (LCEM) and achieved good classification performance [39]. This method represents the pixel of HSI by a local correntropy matrix, which contains rich spatial and spectral information. However, the local correntropy matrix is constructed by a local window, where the centre of the window is aligned with the pixels being processed. In this way, when the pixel being processed is on an edge, its local correntropy matrix will be constructed by pixels belonging to different classes. In this case, this representation can not characterize the class being processed due to the mixing.

To reduce the impact of pixels belonging to different classes, a spatial perception method has been proposed for neighbourhood construction in this paper. This strategy aims to construct a neighbourhood by a suitably selected window rather than a fixed window. So, more pixels belonging to the same class can be obtained. In this way, a more discriminative local correntropy matrix can be constructed to improve the classification accuracy. The main contributions of this paper are as follows:

• This paper presents a neighbour selection method for sensing the spatial structure of local pixels. In this way, more pixels belonging to the same class can be selected. Therefore, the obtained representation is expected to well characterize the given class to which the pixel being processed belongs;

• This paper proposes a spatial perception correntropy matrix (SPCM) for feature representation. A larger proportion of similar pixels can improve the feature representation effect of the correntropy matrix. The experimental results obtained using three publicly available hyperspectral data sets indicate that the proposed HSI classification method can extract more discriminative spectral-spatial features without using a large amount of training data.

The rest of this article is structured as follows: Section 2 presents the proposed spatial perception correntropy matrix, which jointly learns spectral and spatial correlation. Section 3 introduces the HSI classification method based on SPCM. Section 4 shows the comparison results between the proposed method and five state-of-the-art methods, which are carried out on three hyperspectral data sets. Finally, conclusions and possible future research directions are given in Section 5.

2. Spatial Perception Correntropy Matrix

Spectral and spatial correlation plays an important role in HSI classification. It is a common strategy to extract spatial correlation through the local structure of HSI. However, the spectral correlation, which can offer important discriminative information, is not fully exploited in the field of HSI classification [37]. In this paper, we propose a new spectral-spatial feature extraction method based on spatial perception correntropy matrix to jointly exploit the spatial and spectral correlation. The focus of the proposed method is how to determine the spatial correlation in the process of the correntropy matrix construction. The correntropy matrix of a pixel is expected to be constructed by the pixels belonging to the same class. In this way, the correntropy matrix can discriminate different classes. Figure 1 describes the process of SPCM method in detail.

2.1. Spatial Perception of Window

In this paper, we propose a spatial perception method to select the neighbouring pixels for correntropy matrix construction. Let $\mathbf{A}\in {\mathbb{R}}^{W\times H\times N}$ be an HSI, where W, H, and N are the width, height, and spectral bands, respectively. The pixel ${\mathbf{p}}_{x,y}$ of $\mathbf{A}$ can be defined as a spectral vector ${\mathbf{p}}_{x,y}\in {\mathbb{R}}^N$. Figure 1 shows the definition of a window, where $(x,y)$ is the position of the pixel to be processed, and $(X,Y)$ is used to represent the centre of the side window. The region shown in Figure 2 can be defined as ${\mathbf{W}}_t\in {\mathbb{R}}^{L\times L\times N}$(with $t=1,2,\dots ,9$). The range is from $X-r$ to $X+r$ in the horizontal direction and from $Y-r$ to $Y+r$ in the vertical direction, so that all the pixels in the selected rectangular shape form a side window. r is the window radius, which is determined by the window width L, that is, $L=2r+1$. The choice of hyperparameters will be discussed in Section 4.2. Different windows are obtained by calculating the positions of the two coordinates, namely, changing $(X,Y)$. In this paper, a total of three hyperparameters are contained, which are represented by italics: L is the width of window; S is the first s pixel vectors involved in comparison when selecting the neighbouring pixels, and K is the first k pixels involved in the construction of correntropy matrix.

In this paper, we chose nine different windows by changing the value of $(X,Y)$. Figure 3 shows nine different windows obtained by changing the value of $(X,Y)$. The window is set to square with a fixed length $2r+1$. Thus, nine windows of a pixel being processed are taken as a candidate.

Next, the average cosine distance between the pixel being processed and the adjacent pixels within each window can be obtained. Then the window with maximum cosine distance is selected as the optimal window. Finally, the first k most similar pixels of the selected window are used for the construction of the correntropy matrix.

Let us define that the pixel in the window is ${\mathbf{p}}_1$ and the surrounding pixel is ${\mathbf{p}}_i,i=2,3,\dots ,L^2$. The cosine distance between the target pixel and the surrounding pixel can be expressed as:

(1)$\begin{array}{c}\hfill cos({\mathbf{p}}_1,{\mathbf{p}}_i)=\frac{<{\mathbf{p}}_1,{\mathbf{p}}_i>}{\Vert {\mathbf{p}}_1{\Vert }_2·{\Vert {\mathbf{p}}_i\Vert }_2},i=1,2,\dots ,L^2\end{array}$

where ⟨·⟩ and ${\Vert ·\Vert }_2$ represent the inner product and $L^2$-norm. Through this formula, the window ${\mathbf{W}}_t$ with the largest average value of the first S surrounding pixels is obtained. The pixel-averaged cosine distance ${\mathbf{CW}}_t$ of the window ${\mathbf{W}}_t$ is expressed as:

(2)$\begin{array}{c}\hfill {\mathbf{CW}}_t=\frac{1}{S}\sum _{i=1}^{S}cos({\mathbf{p}}_1,{\mathbf{p}}_i),t=1,2,\dots ,9\end{array}$

After selecting the optimal window ${\mathbf{W}}_t$, the correntropy matrix is constructed by the first K − 1 most similar pixel vectors in ${\mathbf{W}}_t$.

2.2. Construction of Correntropy Matrix

The optimal window is calculated by Equation (2), and then this window is used to construct the correntropy matrix. K − 1 similar pixel vectors selected by spatial perception are used to construct a correntropy matrix with a target pixel vector. Define ${\mathbf{q}}_i$ and ${\mathbf{q}}_j$ as two different spectral bands, ${\mathbf{q}}_{in}$ and ${\mathbf{q}}_{jn}$ as the n-th spectral value on the ${\mathbf{q}}_i$th and ${\mathbf{q}}_j$th spectral bands, then the correntropy between ${\mathbf{q}}_i$ and ${\mathbf{q}}_j$ can be expressed as:

(3)$\begin{array}{c}\hfill C({\mathbf{q}}_i,{\mathbf{q}}_j)=\frac{1}{K}\sum _{n=1}^K{k}_{\sigma }({\mathbf{q}}_{in},{\mathbf{q}}_{jn})\end{array}$

where

(4)$\begin{array}{c}\hfill k_{\sigma }({\mathbf{q}}_{in},{\mathbf{q}}_{jn})=\frac{1}{\sqrt{2\pi }\sigma }exp(-\frac{\Vert {\mathbf{q}}_{in}-{\mathbf{q}}_{jn}{\Vert }_2^2}{\sqrt{2{\sigma }^2}})\end{array}$

where $\sigma$ is the width parameter of the function, which controls the radial scope of the function. Set $\sigma$ to $\sigma =0.05$ in the experimental section. Then the following correntropy matrix can be obtained:

(5)$\begin{array}{c}\hfill M_c={\left\{C({\mathbf{q}}_i,{\mathbf{q}}_j)\right\}}_{i,j=1}^N\end{array}$

where N denotes the number of spectral channels. The nondiagonal element of the correntropy matrix is the correntropy between different bands, reflecting the relationship between different bands. Through the above process, each pixel in the HSI can be represented by a correntropy matrix. The obtained correntropy matrix not only contains spectral information, but also reflects the relationship between similar spectra. So SPCM can provide more distinguishing features for classification and improve classification performance.

3. HSI Classification Based on SPCM

Based on the proposed SPCM, a spectral-spatial HSI classification method is proposed for HSI classification in this paper. Figure 4 describes the general process of SPCM-based classification method in detail. Algorithm 1 details the pseudocode of SPCM. Firstly, the dimension reduction method MNF is used to reduce noise and computational complexity. This paper reduces the dimension to 20. Next, the window closest to the target pixel is selected according to spatial perception and similar pixels are obtained. The size of the window and the number of selected pixels are two important hyperparameters. Then, the correntropy matrix is constructed according to each pixel and its similar pixels. So, each pixel can be represented by a matrix. Finally, a set of matrices are fed into SVM for classification. It is easy to find that the matrix constructed in this paper is a symmetric positive definite matrix, but SVM cannot accept it as input. Therefore, a logm function mentioned in Refs. [40,41] can be used to transform points into Euclidean space for the input of SVM. The logarithm-Euclidean kernel can be defined by:

(6)$\begin{array}{c}\hfill k_{logm}(M_1,M_2)=trace[logm\left(M_1\right)·logm\left(M_2\right)],\end{array}$

where $M_1$ and $M_2$ are two different correntropy matrices. Given a symmetric positive definite matrix $C=U\sum U^T$, its logm can be defined as:

(7)$\begin{array}{c}\hfill logm\left(C\right)=Ulog(\sum )U^T.\end{array}$

This way, the proposed HSI classification method, making use of spectral and spatial correlation simultaneously, can achieve a high classification accuracy when the training sample set is small, which solves the problem of poor classification performance in the case of small training samples.

Algorithm 1: SPCM.

[Figure omitted. See PDF]

4. Experimental Results

This section demonstrates the effectiveness of our newly proposed method using three well-known HSI data sets. The proposed method is compared with five state-of-the-art methods, including LCMR [37], SCMK [25], CNN-enhanced GCN (CEGCN) [32], random patch network (RPNet) [42], and LCEM [39]. This paper uses three commonly used indicators, including overall accuracy (OA), average accuracy (AA), and k coefficient [43]. In this paper, the average OAs, AAs, and k coefficients of 10 random runs are reported. In addition, full classification maps of different methods are presented for visual analysis. On the Pavia University dataset, the training samples are set to 0.1% of each class; On KSC and Botswana datasets, the training samples are set to 1% per class, while the others were used for testing.

In the experiment, algorithms LCMR, SCMK, RPNet, LCEM, and SPCM are implemented by MATLAB R2020b, and are conducted using the Intel Core E5-2620 2.10 GHz CPU with 64 GB memory. However, algorithm CEGCN is conducted on a device with a 2.6 GHz CPU, 128 GB of RAM, and an A6000 GPU, and is performed on PyCharm 2021.

4.1. HSI Data Sets

In this section, three real public data sets, including Pavia University, Kennedy Space Center (KSC), and Botswana, were used to evaluate the performance of the proposed method. Figure 5 gives a brief overview of three HSI data sets.

• Pavia University: The first image is Pavia University, often used in HSI classification. The data were obtained by ROSIS sensors in Pavia, Italy. After processing, the size of the dataset is 610 × 340 × 103. The dataset contains 9 categories with 42,776 labelled pixels. The detailed information is tabulated in Figure 5.

• Kennedy Space Center: The second set of data comes from the Kennedy Space Center. It was collected on 23 March 1996, NASA AVIRIS (AVIRIS) at the Kennedy Space Center (KSC). A total of 176 bands were used in this experiment because of their absorptive capacity and low signal-to-noise ratio. There are 13 kinds of land covers, containing 5211 labelled pixels. The detailed information is tabulated in Figure 5.

• Botswana: The last dataset is Botswana. Between 2001 and 2004, NASA’s EO-1 satellite collected a set of data in the Okavango Delta in Botswana. On the EO-1, the Hyperion sensor can get 30-m pixels over a 7.7-km strip, and within a 10-nm window, 242 wavelengths in the 400–2500 nm band. The bands without calibration and noise are removed, and the remaining 145 bands are used for HSI classification. The detailed information is tabulated in Figure 5.

4.2. Parameters Setting

The SPCM proposed in this paper can effectively extract the spectral-spatial features. In the stage of spatial structure perception, parameter setting is particularly important. Figure 6 shows the effects of different L, S and K on OA, AA, and Kappa on the KSC dataset. S and K were set to $0.8L^2$, and then the size of L was changed. It can be found in the figure that the with increase of L, OA, AA and Kappa increased first and then decreased slightly. This is because when the window size is very small, the same kind of pixels that can be provided will be very few, which is not enough with the feature representation; when the window is too large, there will be too many heterogeneous pixels, which will affect the accuracy of feature representation. After determining the value of L, we fine-tuned S and K to achieve the best classification results. Finally, the three parameters that can produce the best classification result can be obtained.

4.3. Performance Evaluation

In this section, we show a comparison between SPCM and other advanced algorithms on three real datasets using small sample training sets.

4.3.1. Experiments with the Pavia University Data Set

In this section, the experimental results on the Pavia University data set were reported firstly, where the number of training samples per class was set to 0.1%, while the others were used for testing. Table 1 lists the average quantification results for each class. Table 1 shows that RPNet achieves the lowest accuracy. The reason for this may be that it is difficult to choose appropriate random patches when the training sample set is small. In addition, we can also find that CEGCN achieves low accuracy. This may be because the algorithm based on deep learning needs a large number of training samples, and 0.1% of the training samples are not enough. Thus, it does not provide satisfactory results. It is easy to find that the proposed SPCM obtains the best performance. Compared with the advanced method LCEM, the improved SPCM is about 2% higher in OA, AA, and Kappa. Both LCEM and SPCM can extract the spectral correlation features, but the performance of SPCM method is higher than that of LCEM. This is because SPCM adopts the spatial perception technique, which can better reflect the nonlinear relationship between spectral bands in HSI compared with the LCEM method. Additionally, SPCM emphasizes intraclass spectral correlation more than LCEM. Consequently, the local correntropy matrices obtained by the spatial perception method can extract more discriminative features, which facilitates the final classification.

In addition to the objective experimental results comparison, we visualize the results to verify the effectiveness of the method. The full classification maps of different methods are shown in Figure 7, and they are generated by one of the random experiments. As we can observe in Figure 7, the proposed method has achieved the best performance using only 0.1% samples for training, and some methods produced maps with more noise and lost some structural details. For example, LCMR and SCMK generate salt-and-pepper noise with a small training set. For PRNet, its classification map loses many edge structures. CEGCN produces an over-smooth classification map, which may be caused by its larger filter size. From Figure 7, it can be seen that the borders between classes are generally well defined and without salt and pepper noise.

4.3.2. Experiments with the KSC Data Set

The second experiment was based on the KSC data set. It was again repeated 10 times over the randomly split training and test data, where 1% per class were selected as training samples. Table 2 reports the average classification results of each method. Table 2 shows that SPCM and LCEM obtain the best and second results of 94.51% and 93.83%, respectively. These results prove again that correntropy matrix-based methods are fit for HSI classification. We can also find that LCMR, LCEM, and SPCM perform better than other compared methods. This phenomenon also verified the effectiveness of the spectral-spatial correlation learning.

Figure 8 shows the full classification maps, where only 1% of samples in each class are used for comparison. Figure 8 shows that in the classification results of SVM, the SCMK and CEGCN methods lose too much image structure. PRNet and LCEM produce severe salt-and-pepper noise. Although LCMR is very obvious in suppressing salt-and-pepper noise, it also has a oversmooth phenomenon. The proposed SPCM can effectively solve this problem. SPCM emphasizes the correlation of the spectrum and also makes use of the spectral and spatial information. As can be seen from Figure 8 and Table 2, compared with other methods, a good trade-off is achieved with SPCM.

4.3.3. Experiments with the Botswana Data Set

The last experiment was carried out on the Botswana data set, setting the number of training samples per class to 1% of the total samples, while the others were used for testing. This data set is collected by satellite, with low spatial resolution, complex shape, variety and irregular distribution of ground objects, so it poses a great challenge to many methods. On this data set, the hyperparameters were set to $L=9,S=35,K=45$. Table 3 lists the accuracy of different methods. As we can observe, RPNet obtains the worst accuracy. The reason for this may be that it is difficult to learn effective features for HSI with many details when the training sample is small. Compared with other methods, the proposed SPCM has significant improvement with respect to OA, AA, and Kappa. This also demonstrates the advantage of the joint learning of spectral-spatial correlation. Finally, the full classification maps of different methods are also shown in Figure 9. We can find that the result achieved by the proposed method is the best, as the details of HSI are well preserved.

In summary, as shown by the experimental results, the SPCM method proposed in this paper performs better than other state-of-the-art methods on three typical data sets. This section demonstrates that the spectral and spatial correlation is very important for HSI classification.

5. Conclusions

In this paper, an effective spectral-spatial feature extraction method called SPCM is proposed for HSI classification. It can not only characterize the non-linear relationship between different bands based on the kernel method, but also extract spatial structure features using the local neighbourhood construction method. The experimental results on three publicly available data sets have verified that the proposed SPCM-based classification method performs better than other base line methods, especially when the training set is small. The proposed method has achieved good results in respect to different indicators and visual effect. However, how to better combine spatial information and spectral information is still an open problem. In the future, we will further explore how to better learn spectral-spatial features to achieve better classification results.

Author Contributions

Conceptualization, W.C. and Y.W.; methodology, Y.W. and G.Z.; software, G.Z.; validation, G.Z., W.C., and Y.W.; formal analysis, G.Z., W.C. and Y.W.; investigation, G.Z., W.C., and Y.W.; resources, W.C. and Y.W.; data curation, G.Z., W.C., and Y.W.; writing—original draft preparation, G.Z.; writing—review and editing, W.C. and Y.W.; visualization, W.C.; supervision, W.C. and Y.W.; project administration, Y.W.; funding acquisition, Y.W. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Process of the SPCM method. Each pixel of HSI generates nine windows, and then the optimal one is selected. The red point is the pixel to be processed, and is collectively referred to as the target pixel in the following text. A correntropy matrix is constructed from all pixels in this optimal window. The input to the SPCM method is a single pixel and the output is a correntropy matrix.

Figure 2. Window definition for a single pixel. Specify [Forumla omitted. See PDF.] as the coordinates of the target pixel (red point), and [Forumla omitted. See PDF.] as the centre coordinates of the side window. First, the coordinates of the centre pixel are calculated from the coordinates of the target pixels. The illustrated example is [Forumla omitted. See PDF.]. The calculation formula of the centre position [Forumla omitted. See PDF.] coordinates of different side windows is different. Then, the shape of the side window is delineated by the central pixel, the horizontal range is from [Forumla omitted. See PDF.] to [Forumla omitted. See PDF.], and the vertical direction is from [Forumla omitted. See PDF.] to [Forumla omitted. See PDF.]. This results in a rectangular side window.

Figure 3. Let [Forumla omitted. See PDF.] be one of the windows, and the figure shows a total of nine windows. Different black centre pixels [Forumla omitted. See PDF.] are calculated based on the red target pixels, and then the window is determined by the centre pixels. The range of the window is horizontal reverse [Forumla omitted. See PDF.] to [Forumla omitted. See PDF.], vertical direction [Forumla omitted. See PDF.] to [Forumla omitted. See PDF.]. (a) The target pixel is in the center of the window; (b) The target pixels are in the lower middle and upper middle of the window; (c) The target pixels are in the right middle and left middle of the window; (d) The target pixels are in the lower right corner, lower left corner, upper right corner, and upper left corner of the window respectively.

Figure 4. Image display is an HSI classification method based on SPCM. First, we perform dimensionality reduction of a hyperspectral image based on MNF. Then we convert each pixel to a correntropy matrix in turn by SPCM. Finally, all the matrices are input to SVM for classification.

Figure 5. Details of Pavia University, KSC, and Botswana.

Figure 6. Effects of different L, S and K on the OA, AA, and Kappa on KSC dataset. (a) Setting S and K to [Forumla omitted. See PDF.], the influence of the change of L on OA, AA, Kappa; (b) Setting L to 9, K equals S, the effect of S on OA, AA, Kappa; (c) After the values of L and S were determined, the effect of K change on OA, AA, and Kappa was determined.

Figure 7. Classification maps of different methods on the Pavia University data set. (a) False Colour Image; (b) Ground Truth; (c) Training set; (d) Test set; (e) LCMR; (f) SCMK; (g) CEGCN; (h) PRNet; (i) LCEM; (j) SPCM.

Figure 8. Classification maps of different methods on the KSC data set. (a) False Colour Image; (b) Ground Truth; (c) Training set (d) Test set; (e) LCMR; (f) SCMK; (g) CEGCN; (h) PRNet; (i) LCEM; (j) SPCM.

Figure 9. Classification maps of different methods on the Botswana data set. (a) False Colour Image; (b) Ground Truth; (c) Training set; (d) Test set; (e) LCMR; (f) SCMK; (g) CEGCN; (h) PRNet; (i) LCEM; (j) SPCM.

Table 1

Classification results obtained by LCMR, SCMK, CEGCN, RPNet, LCEM, and SPCM using 0.1% of the available labelled data for training with the Pavia University data set. The best results are expressed in bold.

No.	LCMR	SCMK	CEGCN	RPNet	LCEM	SPCM
1	75.54	88.09	96.93	85.58	87.69	88.41
2	75.48	83.91	97.06	95.79	95.13	93.15
3	64.41	64.50	85.72	59.99	71.82	67.72
4	95.58	82.96	67.12	45.25	85.98	87.12
5	92.47	96.53	100.00	12.05	91.74	99.78
6	77.50	63.02	65.61	42.85	93.32	95.53
7	88.83	84.62	59.59	7.90	92.81	97.45
8	71.77	77.16	53.64	75.86	63.62	75.75
9	91.70	70.73	65.09	24.95	48.17	49.70
OA	77.61	80.63	85.13	73.96	88.04	90.97
AA	81.47	79.06	76.75	50.02	81.14	83.82
Kappa	71.48	74.63	79.89	62.78	84.20	86.97

Table 2

Classification results obtained by LCMR, SCMK, CEGCN, RPNet, LCEM, and SPCM using 1% of the available labelled data for training with KSC data set. The best results are expressed in bold.

No.	LCMR	SCMK	CEGCN	RPNet	LCEM	SPCM
1	92.69	86.97	99.53	85.13	97.33	94.65
2	91.51	73.79	70.46	63.07	80.88	88.46
3	92.39	84.35	87.08	94.07	82.53	87.55
4	85.95	59.08	27.05	38.15	78.31	82.97
5	90.19	53.33	57.07	68.55	81.76	78.49
6	91.38	67.88	79.83	43.17	78.14	92.35
7	95.20	88.64	75.50	29.81	92.23	98.35
8	87.72	81.24	80.45	82.67	95.26	91.46
9	92.89	90.49	90.95	89.32	98.00	97.39
10	99.70	83.33	92.99	64.00	98.25	97.02
11	92.03	94.25	95.08	81.69	94.25	91.88
12	94.74	87.77	68.81	98.80	98.77	97.85
13	100.00	99.60	100.00	99.46	100.00	100.00
OA	93.13	85.54	85.25	80.97	93.83	94.51
AA	91.79	80.82	79.11	72.14	90.44	92.34
Kappa	92.12	83.91	83.47	78.78	93.12	94.89

Table 3

Classification results obtained by LCMR, SCMK, CEGCN, RPNet, LCEM, and SPCM using 1% of the available labelled data for training with the Botswana data set. The best results are expressed in bold.

No.	LCMR	SCMK	CEGCN	RPNet	LCEM	SPCM
1	95.02	86.39	100.00	61.80	94.01	99.79
2	84.55	55.29	76.28	21.00	87.47	100.00
3	28.60	88.55	100.00	61.69	73.15	79.26
4	96.29	77.55	75.23	29.58	74.25	98.17
5	72.66	83.38	29.05	84.59	76.62	82.79
6	71.57	67.78	56.65	62.03	57.37	69.30
7	84.90	89.73	100.00	100.00	77.30	88.80
8	61.99	84.85	71.50	70.65	77.25	80.17
9	95.95	89.84	94.38	87.46	88.35	79.18
10	99.59	85.88	56.55	99.19	75.27	78.96
11	88.31	86.88	100.00	72.19	86.01	87.45
12	32.89	87.21	85.87	93.30	53.69	59.96
13	85.49	78.04	89.27	83.77	89.13	92.33
14	31.49	75.11	89.24	12.77	44.47	60.52
OA	76.62	80.56	80.47	72.34	77.20	83.53
AA	73.52	81.18	80.29	67.14	75.31	82.68
Kappa	74.63	79.45	78.82	69.95	75.24	82.13

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