# Spatial Perception Correntropy Matrix for Hyperspectral Image Classification
## 1 Introduction
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, [PERSON] 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, [PERSON] 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.