# Spatial Perception Correntropy Matrix for Hyperspectral Image Classification
## 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]. [PERSON] et al. introduced superpixel-based classification via multiple kernels (SCMK) [25; 26] to obtain uniform regions for spatial-spectral feature extraction. [PERSON] 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. [PERSON] 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].