# A Novel Binary QUasi-Affine TRansformation Evolutionary (QUATRE) Algorithm
## 4 Experimental Results and Analysis
### Hyperspectral Imagery  
In this section, the proposed BQUATRE1 and BQUATRE2 are used for dimensionality reduction in hyperspectral dataset. The dataset used in the experiment is the Indian Pines image, which is obtained by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) sensor in 1992. The dataset captures the Indian Pines unlabeled agricultural site in northwestern Indiana and contains \(220\times 145\times 145\) bands. The spatial resolution of this image is 20 m per pixel. The water absorption bands of HSI are seriously polluted by noise and are not suitable for classification. Therefore, twenty water absorption bands have been deleted from the Indian Pines. In the image, there are 16 features, including corn, soybean, alfalfa, wheat, oat, grass, tree, etc. Some features are subdivided; for example, corn is divided into no-tillage, low-tillage and traditional tillage. Figure 12 is the false-color composite image and ground truth data of Indian Pines. As is known, the HSI cannot be displayed on the computer because it has too many bands. False color image is the color image obtained by the synthesis of different wavebands and is often used in the classification of remote sensing images. False color synthesis technology is one of the methods of image enhancement. It converts the images composed of many bands (more than four) into three-bands or four-bands synthesis images. Figure 12 is synthesized by three-bands synthesis technology. Classification performance is the main index of dimensionality reduction in HSI. In this manuscript, three common metrics are used to evaluate classifier performance, namely: overall accuracy(OA), average accuracy (AA) and Kappa coefficient. Therefore, the fitness function is Equation (17), where \(OA_{kfoldLoss}\), \(AA_{kfoldLoss}\) and \(Kappa_{kfoldLoss}\) are the OA, AA and Kappa coefficient errors of k-fold cross validation; \(W_{i}\), \(i=1,2,3\) are weight coefficients. In our experiment, we set \(k=5\) and set \(W_{1}=0.4\), \(W_{2}=0.3\), \(W_{3}=0.3\), for the OA is the most important index of the three classification performances. \[fitness=W_{1}*OA_{kfoldLoss}+W_{2}*AA_{kfoldLoss}+W_{3}*Kappa_{kfoldLoss} \tag{17}\]  
In this experiment, we use the first function of the families of the transfer function. In order to compare S-shaped, V-shaped, U-shaped and Z-shaped transfer functions, we adopt the approach BQUATRE1 with U-shaped and Z-shaped transfer functions, the BQUATRE2 with with S-shaped and V-shaped ones. The compared dimensionality reduction algorithms are classic PCA and LDA. The number of dimensions selected by PCA and LDA is 10, which is computed by the \"intrinsic dimensionality estimation\" function of \"Matlab toolbox for dimensionality reduction\" [66]. The classifier used in experiments is Support Vector Machine (SVM), which is implemented from a library for LIBSVM and used a Gaussian kernel [67]. Since it is difficult to obtain samples of hyperspectral images, the classification with fewer samples is of more practical significance. Thereby, in this experiment, the training samples are randomly chosen and account for 5% of the ground truth. Thereby,  
Figure 12: Thematic maps for the Indian Pines data set with 16 classes. (**a**) false-color composite; (**b**) ground truth data with 16 classes in different colors. seven algorithms are compared in this experiment; that is, the traditional SVM without dimensionality reduction (record as SVM), PCA performed to dimensionality reduction before SVM (record as PCA-SVM), LDA performed to dimensionality reduction before SVM (record as LDA-SVM), BQUATRE1 performed with U-shaped function to dimensionality reduction before SVM (record as BQUATRE1-U1-SVM), BQUATRE1 performed with Z-shaped function to dimensionality reduction before SVM (record as BQUATRE1-Z1-SVM), BQUATRE2 performed with improved S-shaped function to dimensionality reduction before SVM (record as BQUATRE2-S1i-SVM), and BQUATRE2 performed with improved V-shaped function to dimensionality reduction before SVM (record as BQUATRE2-V1i-SVM).