###### Abstract  
Hyperspectral images contain rich spatial-spectral information and have high dimensions, which can lead to challenges related to feature extraction for classification tasks, resulting in suboptimal performance. We propose a hyperspectral image dimensionality reduction algorithm based on spatial-spectral adaptive multiple manifolds to address the problem of small differences between features of dissimilar samples in the subspace caused by the uniform projection transformation in traditional dimensionality reduction methods. Firstly, to address spatial boundary mismatch problems caused by re-characterizing a pixel using pixels in a fixed area around it as its near neighbors in traditional algorithms, an adaptive weight representation method based on super-pixel segmentation is proposed, which enhances the similarity of similar samples and the dissimilarity of dissimilar samples. Secondly, to address the problem that a single manifold cannot completely characterize the near neighbor between samples of different categories, an adaptive multi-manifold representation method is proposed. The feature representation of the entire hyperspectral data in the low-dimensional subspace is obtained by adaptively fusing the intra- and inter-manifold maps constructed for each category of samples in the spatial and spectral dimensions. Experimental results on two public datasets show that the proposed method achieves better results when performing the hyperspectral image dimensionality reduction task. hyperspectral image; dimensionality reduction; manifold learning; hyperspectral classification; spatial-spectral feature extraction; adaptive weight +
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analysis (PCA) [16], independent component analysis (ICA) [17], and linear discriminant analysis (LDA) [18] are based on linear transformations of the data. This idea means that the projection from the original space to the lower-dimensional subspace involves linear combinations of the input features with fixed coefficients. These dimensionality reduction methods have achieved good effects to some extent. But since the features of HSIs are not linearly distributed, using such feature extraction methods will limit the subsequent classification performance. Therefore, the manifold learning method based on graph embedding (GE) is applied to the dimensionality reduction task of HSIs. It effectively improves the dimensionality reduction as a non-linear feature extraction method. [PERSON] [19] et al. proposed a graph embedding framework to describe the dimensionality reduction methods used in a unified manner. To further enhance the dimensionality reduction effect, [PERSON] [20] et al. proposed a supervised local geometric structure Fisher analysis (LGSFA) algorithm. The algorithm constructs graphs using labeled samples to improve the synergy of same-category data and reconstructed data and enhance the separation of dissimilar data and reconstructed data. However, the disadvantage of this method is that it can destroy the overall structure of the manifold in low-dimensional space. To better portray the local reconstruction relationships between data, [PERSON] et al. [21] proposed the subspace manifold learning algorithm based on neighborhood preserving embedding (NPE), which can better solve the new sample problem by preserving the local near neighbor structure of the original manifold space. Based on the local preservation discriminant analysis, [PERSON] et al. [22] proposed a new spatial-spectral similarity metric that maps the distance between two image blocks in an HSI, which can effectively deal with the redundancy problem caused by the spectral features, as well as the spatial relationship between pixels. [PERSON] et al. [23] proposed a modified tensor locality preserving projection (MTLPP) algorithm, which can improve the effect of noise on the near neighbor graph by constructing the neighbor graph on the pairwise feature space instead of the original space.