## 1 Introduction  
With spectral sampling from visible to short-wave infrared region, hyperspectral image (HSI) can provide a spatial scene in hundreds of narrow contiguous spectral channels [1; 2]. HSI data with high spectral resolution can provide fine spectral details for different ground objects, and they have been widely applied in many fields such as geological survey, environmental monitoring, precision agriculture, and mineral exploration [3; 4]. Classification of each pixel in HSI plays a crucial role in these real applications. However, the high dimensional characteristic of HSI poses a huge challenge to the traditional classification methods, and the [PERSON] effect may occur if only limited training samples are available [5; 6]. In general, dimensionality reduction (DR) is an effective way to reduce the volume of high-dimensional data with minimum loss of useful information by feature extraction or band selection, and it brings benefits for classification by achieving discriminating embedding features [7; 8; 9]. Many DR methods based on feature extraction have been proposed to reduce the dimension of high-dimensional data. Principal component analysis (PCA) [10] and linear discriminant analysis (LDA) [11] are the most popular subspace methods, but the two linear methods cannot discover the underlying manifold structure embedding in the original high-dimensional space. Many manifold learning-based DR methods are introduced to reveal nonlinear structure in high-dimensional data, such as locally linear embedding (LLE) [12], Laplacian eigenmap (LE) [13], isometric mapping (ISOMAP) [14], neighborhood preserving embedding (NPE) [15], and locality preserving projection (LPP) [16]. The above methodscan be unified under the graph embedding framework (GE), and the difference between them is how to define the similarity matrix of an intrinsic graph and the constraint matrix of a penalty graph [17; 18; 19; 20]. On the basis of GE, some supervised DR methods are designed to exploit the prior knowledge of training samples for improving classification performance, such as marginal Fisher analysis (MFA) [21], local Fisher discriminant analysis (LFDA) [22], and regularized local discriminant embedding (RLDE) [23]. However, these direct graph-based DR methods only consider the pairwise relationship between data points, while HSI data usually possess complex relationships such as one sample versus multiple samples (different classes) or one class versus multiple samples. Therefore, the pairwise relation cannot discover complex relations in HSI, which limit the discriminability of embedding features for classification [24; 25]. To explore the multiple adjacency relationships in high-dimensional data, hypergraph learning has been introduced to discover the complex geometric structure between HSI pixels [26; 27]. In [28], discriminant hyper-Laplacian projection (DHLP) was proposed using the hypergraph Laplacian for exploring the high-order geometric relationship of samples. Semi-supervised hypergraph embedding (SHGE) learns the discriminant structure form both labeled and unlabeled data, and it reveals the complex relationships of HSI pixels by building a semi-supervised hypergraph [29]. For analyzing the intrinsic properties of HSI pixels, a hypergraph Laplacian sparse coding method was constituted to capture the similarity among data points within the same hyperedge [30]. In addition, the heterogeneous network is explored to measure the relatedness of heterogeneous objects. [PERSON] et al. [31] introduced heterogeneous networks with an arbitrary structure to evaluate its performance for both clustering and classification tasks. [PERSON] et al. [32] proposed an ensemble learning approach to classify objects of different classes, which is based on the heterogeneous networks for extracting both correlation and autocorrelation that involve the observed objects.