# Classification of Hyperspectral Images Based on Supervised Sparse Embedded Preserving Projection
## 1 Introduction  
Alongside the development of hyperspectral remote sensing imaging technology, hyperspectral imaging (HSI) is providing increasingly useful information and is widely used in many fields, such as the military, agricultural industry, and geological exploration [1; 2; 3]. In recent years, hyperspectral imaging has become a research hotspot both locally and internationally. However, hyperspectral imaging involves a large number of bands and is computationally complex. In addition, it has a high degree of correlation and band redundancy, which makes the process prone to dimension disaster [4]. As a result, dimensionality reduction (DR) is an essential part in the classification of hyperspectral images [5].  
In the research field of high-dimensional data processing, scholars have proposed a series of classic algorithms. The common DR algorithms mainly include principal component analysis (PCA) [6] and liner discriminative analysis (LDA) [7]. PCA and LDA are both based on the assumption that the embedded subspace of the high-dimensional data space is linear. Therefore, the intrinsic properties of high-dimensional data are difficult to find and it is difficult to prevent the low-dimensional manifold structure of hyperspectral data from being revealed [8]. In recent years, sparse representation has been applied to signal processing, pattern recognition, and other fields, and has achieved certainresearch results [9]. In addition, sparse representation adaptively captures the intrinsic structural information of the sample data [10]. Due to its robustness to noise and natural discriminatory ability in the coding process, sparse representation [11] is used to extract the manifold structure of a sample in dimensionality reduction. [PERSON] et al. [12] proposed a method to analyze the principal components of data based on sparse solution methods in the Lasso and Elastic Net theories, referred to as sparse PCA (SPCA). [PERSON] et al. [13] used sparse principal component analysis in the reduction of hyperspectral remote sensing images. [PERSON] [14] proposed an unsupervised sparsity preserving projection (SPP) for the dimensionality reduction of data, which constructed a weight relationship between samples in a high-dimensional space using sparse representation theory. SPP only focuses on the sparse structure and ignores the discriminant information of labeled samples. In order to enhance the classification performance of SPP, some supervised sparse methods were proposed. [PERSON] et al. [15] proposed a sparse discriminant embedding (SDE) hyperspectral data reduction algorithm based on SPP, which utilized the merits of both the property of sparsity and its manifold structure.  
In this paper, we propose a supervised sparse embedding preserving projection (SSEPP) for the dimensionality reduction of hyperspectral remote sensing images. In this approach, SSEPP makes full use of the label information of samples in order to enhance the discriminative ability of the projection subspace. In addition to maintaining the sparse reconstruction error, the algorithm also minimizes the error between the samples of the same class. The experiments were performed on Indian Pines and HJ1A-HSI hyperspectral remote sensing imagery from the Zhangjiang estuary of Southeastern China. The results show that the proposed method effectively improves the classification accuracy of hyperspectral remote sensing imagery.  
The rest of this paper is arranged as follows: Section 2 briefly introduces the graph embedding (GE) and SPP. The supervised sparse embedding preserving projection for the dimensionality reduction (SSEPP) algorithm is presented in Section 3. The experimental results are given in Section 4, and finally, the conclusions are presented in Section 5.