*4.1. Datasets*

In this section, three typical hyperspectral datasets, namely Indian Pines, University of Pavia and Salinas, are employed to compare the proposed DBN classification method with other state-of-the-art methods. In these experiments, we randomly select 300 labeled pixels per class for training, of which 20 samples are utilized for validation. The remaining pixels of labeled data are used for testing. Furthermore, each pixel is uniformly scaled to the range of −1 to 1.

The first experiment is Indian Pines dataset, which was gathered by Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) sensor in northwestern Indiana. There are 220 spectral channels in 0.4 to 2.45 μm region with spatial resolution of 20 m. It consists of 145 × 145 pixels with 200 bands after removing 20 noisy and water absorption bands. Here, we employ 8 large classes in this experiment. The numbers of training and testing samples are listed in Table 2.


**Table 2.** Number of training and testing samples used in the Indian Pines dataset.

The second dataset with 610 × 340 pixels is the University of Pavia, which was acquired by the Reflective Optics System Imaging Spectrometer (ROSIS) during a flight campaign over Pavia, northern Italy. The ROSIS sensor cover 115 spectral bands from 0.43 to 0.86 μm and the geometric resolution is 1.3 m. Each pixel has 103 bands after discarding bad bands. There are 9 ground-truth classes with the number of labeled samples shown in Table 3.

**Table 3.** Number of training and testing samples used in the Pavia University dataset.


The third experiment is on Salinas dataset, which was also collected by the AVIRIS sensor, capturing an area over Salinas Valley, California, with a spatial resolution of 3.7 m. The area comprises 512 × 217 pixels with 204 bands after removing noisy and water absorption bands. It mainly contains vegetables, bare soils, and vineyard fields. There are 16 different ground-truth classes, and the numbers of training and testing samples are listed in Table 4.

Our experiments are implemented using Matlab 2015b which is manufactured by Mathworks in Massachusetts, US. The CPU we employed is Intel Core i5-3470. The basic frequency is 3.200 GHz. The operation system is Win7 with 64 bits.


**Table 4.** Number of training and testing samples used in the Salinas dataset.

#### *4.2. Parameters Tuning and Analysis*

In our proposed framework, we have several parameters that need to be adjusted: the number of hidden units, the learning rate, the max epoch and the number of hidden layers. In this section, some tuning experimental results are listed for selecting proper values. Both the number of hidden layers and the number of hidden units in hidden layers play an important role in classification performance. A suitable number of hidden layers and neurons can make full use of texture enhanced hyperspectral data without over-training, and can support a fitting mapping from original hyperspectral data to hyperspectral features. In the training process of DBN, the learning rate controls the pace of learning. It implies that a too large learning rate will lead an unstable output of training, and a too small learning rate will lead a longer training process. Therefore, an appropriate learning rate can expedite our training procedure with satisfactory performance.

In Figure 7, we can see that our proposed framework achieves best classification accuracy with 200 hidden neurons in each hidden layer. It demonstrates that 200 is a suitable number of hidden neurons. Figure 8 depicts the relationship between accuracies and the learning rates. It can be seen that the values of learning rate from 0.15 to 0.2 can obtain better performance. Therefore, we select 0.15 for the first RBM, and 0.2 for the second RBM. To determine the max epoch, we set the range of max epoch from 50 to 500. Figure 9 demonstrates that, when max epoch reaches 300, our proposed framework can achieve best classification performance. Consequently, the max epoch is set to 300. Table 5 lists the accuracies achieved with different numbers of hidden layers in DBN. When employing two hidden layers, the classification performance of DBN can achieve superior results. Thus, in our proposed framework, we set the number of hidden layers to 2.

In our paper, we utilize Graycomatrix function in Matlab to calculate the GLCM. The parameters used in experiments are "NumLevels" and "Offset", and they are set to 8 and [0, 3; −3, 3; −3, 0; −3, −3], respectively.

**Figure 7.** The relationship between accuracies and the number of hidden units in different datasets: (**a**) Indian Pines; (**b**) University of Pavia; and (**c**) Salinas.

**Figure 8.** The relationship between accuracies and the learning rates in different datasets: (**a**) Indian Pines; (**b**) University of Pavia; and (**c**) Salinas.

**Figure 9.** The relationship between accuracies and the numbers of Max epoch in different datasets: (**a**) Indian Pines; (**b**) University of Pavia; and (**c**) Salinas.

**Table 5.** The accuracies obtained via different numbers of hidden layers in DBN.


#### *4.3. Evaluation Criteria*

The evaluation criteria used in our paper are overall accuracy (OA), average accuracy (AA), precision, and Kappa. Especially, OA, Precision and Kappa are highlighted for assessment of the proposed framework.

Figure 10 demonstrates a p-class confusion matrix. Based on Figure 10, AA and precision can be derived as [35]

$$\mathbf{P\_{AA}} = \frac{1}{p} (\sum\_{i=1}^{p} \frac{n\_{ii}}{\sum\_{j=1}^{p} n\_{ji}}) \tag{17}$$

$$P\_{precision} = \frac{1}{p} (\sum\_{i=1}^{p} \frac{n\_{ii}}{\sum\_{j=1}^{p} n\_{ij}}) \tag{18}$$

where *p* is the number of classes. *N* is the total number of the hyperspctral image data samples and *N* = ∑*pi*=<sup>1</sup> *ni*. *nii* is the number of hyperspectral image samples in the *i*-th class to be classified into the *i*-th class, and *nji* is the number of hyperspectral image samples in the *i*-th class to be classified into the *j*-th class.


**Figure 10.** *P*-class confusion matrix.

We also take the nonparametric McNemar's test based on the standardized normal test statistic to evaluate the statistical significance in the improvement of OA with different hyperspectral classification algorithms. The McNemar's test statistic for two different algorithms noted as Algorithm 1 and Algorithm 2 can be calculated as [36]:

$$z = (f\_{12} - f\_{21}) / \sqrt{f\_{12} + f\_{21}} \tag{19}$$

where *f*12 denotes the number of samples misclassified using Algorithm 2 but not Algorithm 1, and *f*21 means the number of samples misclassified using Algorithm 1 but not Algorithm 2. |*z*| is the absolute value of *z*. For 5% level of significance, the |*z*| value is 1.96. If a |*z*| value is greater than this quantity, the two classification algorithms have significant discrepancy.

#### **5. Experimental Results and Discussion**

In this section, the proposed TFE and the novel classification framework will be evaluated and the relevant results will be summarized and discussed in detail.

#### *5.1. Compared Methods and Band Groups*

To analyze and evaluate our proposed algorithm, which combines the TFE and the optimal DBN efficiently, existing algorithm, such as SVM with Radial Basis Function kernel (SVM-RBF), the Radical Basis Function neural network (RBFNN) and CNN, are employed for comparison purpose. Besides, we also compare with a state-of-the-art spectral–spatial algorithm called EPF-G-c [22]. All these algorithms are widely used with excellent performance in hyperspectral image classification tasks, especially EPF-G-c. In addition, for evaluating our proposed texture feature enhancement (TFE) algorithm, we also applied TFE algorithm on the traditional SVM-RBF and RBFNN. All experiments are repeated 10 times with the average classification results demonstrated for comparison.

According to our proposed band grouping solution, the bands of Indian Pines can be divided into 41 groups: 1, 2, 3, 4–17, 18, 19–33, 34, 35, 36, 37–56, 57, 58–60, 61, 62, 63–74, 75, 76, 77–82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92–93, 94, 95, 96–97, 98–102, 103, 104, 105, 106–143, 144, 145, 146–198, 199 and 200. The bands of University of Pavia can be divided into 19 groups: 1, 2, 3, 4, 5, 6, 7, 8–68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78–84 and 85–103. The bands of Salinas can be divided into 21 groups: 1, 2, 3, 4, 5–35, 36, 37, 38, 39, 40, 41–104, 105–106, 107, 108, 109–146, 147, 148, 149–201, 202, 203 and 204. All these band groups are employed in the TFE algorithm.

#### *5.2. Discussion on Effectiveness of the Proposed TFE*

Figure 11 demonstrates the reconstructions of border and inner pixels of four classes after TFE in Indian Pines dataset. The first image of each row depicts the locations of border and inner pixels. The reconstruction and reconstructed error of the border pixel are demonstrated in the second image of each row. Meanwhile, the reconstruction and reconstructed error of the inner pixel are demonstrated in the third image.

**Figure 11.** The reconstructions of the border-pixels and inner-pixels of different classes in Indian Pines. First row is the reconstruction information of Class 2, second row is the reconstruction information of Class 4, third row is the reconstruction information of Class 6 and last row is the reconstruction information of Class 8.

In hyperspectral classification, some spectra of the hyperspectral image are distorted through imaging noise or low spatial resolution, especially border-pixels, therefore the difficulty of hyperspectral classification primarily focuses on the correct classification of the border pixels. In Figure 11, it can be seen that, by utilizing TFE, the reconstructed border pixels become different from the original border pixels, and the reconstructed inner pixels are nearly the same as the original inner pixels, which implies that TFE plays an important role for border pixels. TFE can make border pixels distinct with its characteristics and more similar to their original spectra. Hence, the texture feature of the hyperspectral image become more obvious and clear. Consequently, the pixels that are difficult to distinguish can be recognized more easily than before with clearer texture feature. In other words, TFE has a positive effect for enhancing hyperspectral classification performance.

#### *5.3. Discussion on Classification Results and Statistical Test*

Table 6 provides the classification performance on Indian Pines achieved by different classification algorithms: SVM, RBFNN, optimal DBN (O\_DBN), SVM combined with TFE (SVM\_TFE), RBFNN combined with TFE (RBFNN\_TFE), CNN, EFP-G-c and our proposed framework. O\_DBN denotes the optimal DBN we proposed but without TFE. The SVM\_TFE and RBFNN\_TFE are two algorithms combined with the TFE method. The classification accuracy of each class is also listed in this table. In Table 6, we can see that our proposed framework can obtain the superior performance compared with other algorithms. Meanwhile, the optimal DBN has the best classification accuracy compared to the other algorithms without TFE, such as SVM and RBFNN. Although EFP-G-c is an outstanding spectral–spatial hyperspectral classification algorithm, our proposed framework utilizing TFE still has slightly better classification accuracy. Besides, SVM\_TFE and RBFNN\_TFE outperform SVM and RBFNN, respectively. The OA of SVM\_TFE is 5.06% greater than SVM, and the OA of RBFNN\_TFE is 8.97% higher than RBFNN. Compared with O\_DBN, the OA obtained via our proposed framework improved by 8.08% and the Kappa increased by 9.98%. All these facts indicate the successful effects of TFE and demonstrates that our proposed framework and TFE have good influence on Indian Pines in hyperspectral classification.

**Table 6.** Classification accuracy of different algorithms on Indian Pines.


Table 7 lists the classification precision achieved via these different classification algorithms. In Table 7, we can see that the precision of our proposed algorithm outperforms SVM, RBFNN, O\_DBN, SVM\_TFE, RBFNN\_TEF, CNN and EPF-G-c. In addition, the methods associated with TFE have better classification precision than without TFE.

**Table 7.** Classification precision of different algorithms on Indian Pines.


Tables 8 and 10 present the classification accuracy acquired via different algorithms for University of Pavia and Salinas datasets. Meanwhile, Tables 9 and 11 also list the precisions obtained through our proposed model and other classification algorithms on different datasets. It is obvious in Tables 8 and 10 that our proposed framework has better performance than other classification methods. Especially, we can see that all algorithms that integrate TFE outperform those without TFE. By employing the TFE, the performance of SVM increased by 5.78% in University of Pavia and 1.75% in Salinas, while the performance of RBFNN improved by 6.8% in University of Pavia and 1.55% in Salinas. The OA achieved by the proposed framework is 6.55% higher than the OA achieved via optimal DBN in University of Pavia and 3.94% larger than the OA achieved via optimal DBN in Salinas. Furthermore, the proposed classification framework has better performance than CNN and EPF-G-c. As for kappa coefficients, we can see that our proposed framework has better consistency. The possible reason is the ability of our proposed framework, as a deep network, to extract high-level features of data is stronger than the RBFN and the SVM, as shallow networks, thus the description ability of our proposed framework is more stable. In Tables 9 and 11, the precisions obtained through our proposed model on different datasets are better than precisions achieved via other algorithms. Furthermore, our proposed TFE has a positive effect on classification accuracy.

**Table 8.** Classification accuracy of different algorithms on University of Pavia.


**Table 9.** Classification precision of different algorithms on University of Pavia.



**Table 10.** Classification accuracy of different algorithms on Salinas Dataset.

**Table 11.** Classification precision of different algorithms on Salinas Dataset.


Figures 12–14 demonstrate the classification maps obtained in Indian Pines, University of Pavia and Salinas, respectively. Clearly, the classification maps shown in Figures 12–14 achieved by our proposed framework are the smoothest and clearest. The classification accuracy of border pixels in these datasets is improved greatly and the boundaries of different classes are more distinct. Compared to other classification algorithms, the results of our proposed framework are better because they contain less salt-and-pepper noise.

**Figure 12.** The classification maps obtained via different algorithms in Indian Pines: (**a**) Ground truth; (**b**) SVM; (**c**) RBFNN; (**d**) O\_DBN; (**e**) SVM\_TFE; (**f**) RBFNN\_TFE; (**g**) CNN; (**h**) EFP-G-c; and (**i**) the proposed framework.

**Figure 13.** The classification maps obtained via different algorithms in University of Pavia: (**a**) Ground truth, (**b**) SVM, (**c**) RBFNN, (**d**) O\_DBN, (**e**) SVM\_TFE, (**f**) RBFNN\_TFE, (**g**) CNN, (**h**) EFP-G-c and (**i**) the proposed framework.

**Figure 14.** The classification maps obtained via different algorithms in Salinas Dataset: (**a**) Ground truth, (**b**) SVM, (**c**) RBFNN, (**d**) O\_DBN, (**e**) SVM\_TFE, (**f**) RBFNN\_TFE, (**g**) CNN, (**h**) EFP-G-c and (**i**) the proposed framework.

Table 12 presents the average |*z*| values achieved from Indian Pines, Pavia University and Salinas of the proposed classification framework as well as other classification algorithms. A "yes" here denotes the two classification algorithms in McNemar's test have significant performance discrepancy. Obviously, the proposed classification framework is statistically different from its counterparts with 5% significance level.


**Table 12.** (|*z*| values/Siginificant?) in the McNemar's Test.

Note: 5% significance level is selected.
