###### Abstract
But the algorithm does not work for points distributed at the category boundaries, which limits the improvement in the dimensionality reduction performance to some extent. To improve this problem, several sparse representation methods have emerged in the field of signal processing in recent years. Moreover, sparse representation methods have been gradually applied to HSI dimensionality reduction, noise reduction, and classification tasks. [PERSON] et al. [24] proposed the sparsity preserving graph embedding (SPCE) algorithm in which the number of near neighbors can be adaptively adjusted. In the case of fixed dictionaries, SPCE has good robustness to noisy data. Therefore, its dimensionality reduction effect is somewhat improved. However, HSI datasets are composed of different ground object categories. Each category of ground object has common features belonging to it and unique features that distinguish it from other categories. Theoretically, different classes of ground objects should all be located on different smooth low-dimensional sub-manifolds. Therefore, the above algorithms that use single-manifolds to construct graphs cannot reveal the multi-manifold structure of hyperspectral data, thus limiting the improvement in dimensionality reduction performance. To explore the intrinsic multi-manifold structure of high-dimensional data, multi-manifold learning methods have become a focus of scholars' research. [PERSON] [25] et al. proposed a multi-manifold learning algorithm based on multi-linear local and global preserving embedding (MLGPE) by maintaining global-local near-neighbor features within each class data. The algorithm separately performs feature learning for each sub-manifold and then projects the data onto the different sub-manifold into the relevant low-dimensional space. To address the problem of multi-feature fusion and dimension reduction in HSIs, [PERSON] et al. [26] proposed a multi-feature manifold learning method based on spectral-texture features, which significantly improved the classification accuracy of HSI ground objects. It is useful for exploring efficient feature fusion methods. Compared to single-manifold learning methods, although the above feature extraction methods based on multi-manifold show strong performance in image classification tasks, they only seek low-dimensional representations of high-dimensional data from spectral feature information. They did not utilize the rich spatial near-neighbor information of HSIs, which significantly limits the improvement in classification performance of the images after dimensionality reduction. In recent years, many studies have shown that the rational use of spatial information is an effective way to improve the classification accuracy of an HSI. Thus, various dimensionality reduction methods based on space-spectrum strategies have emerged. [PERSON] et al. [27] proposed a cooperative representation algorithm based on multi-task learning for the classification tasks. [PERSON] [28] et al. proposed a fast HSI space-spectrum reduction technique based on edge-preserving filtering, which has the advantage of fast reduction speed and largely reduces the computational complexity of the traditional space-spectrum reduction algorithms. In addition, super-pixels can group pixels using the similarity of features between pixels. Using a small number of super-pixels instead of a large number of pixels to express image features can effectively reduce the complexity of image processing. Therefore, super-pixels are gradually used in dimensionality reduction methods based on spatial-spectral strategies. [PERSON] et al. [29] proposed a multiscale super-pixel-based sparse representation (MSSR) algorithm for HSI classification. The algorithm achieved good classification results using the joint sparse representation to classify the obtained multiscale super-pixels. [PERSON] et al.