###### Abstract
[30] proposed a super-pixel-wise collaborative-representation graph embedding (SPCRGE) algorithm, which computed the global projection matrix in low-dimensional space by reducing the differences between pixels in a single super-pixel block while increasing the differences between images with different super-pixels, thus achieving a good dimensionality reduction effect. [PERSON] et al. [31] proposed a new spatial-spectral manifold distance (SSMD) to improve the metric learning performance in HSI dimensionality reduction and classification by maintaining the integrity of the constructed manifolds. SSMD achieves good dimensionality reduction performance by selecting appropriate adjacent points in labeled and unlabeled data to construct manifolds with spatial-spectral information. In the current research into HSI dimensionality reduction methods, the following problems still exist:  
(1) The limited dimensionality reduction strategy based on multi-manifold learning hardly captures the intrinsic variations and discriminative features present in different classes within the data, which results from the poor representational power of HSIs. (2) When using spatial information, traditional dimensionality reduction methods often select the pixels located in a fixed window size region around a pixel as the near neighbors to find the spectral feature value of the central pixel. However, this strategy tends to set the same weights for all pixels in the fixed region and may be unable to identify and focus on the most informative features, thus losing essential information of his, such as boundary. Based on this observation, we propose an HSI dimensionality reduction algorithm based on spatial-spectral adaptive multi-manifold analysis (SSAMMA). The algorithm consists of two main modules: the super-pixel-based adaptive weight representation module (SAWRM) and the spatial-spectral multi-manifold module (SSMMM). SAWRM first performs super-pixel representation of HSIs via the image segmentation algorithm. Then, an adaptive weighted representation of the samples in each super-pixel block is performed. SSMMM constructs a multi-manifold map for the new image. By adaptively fusing the intra- and inter-manifold maps constructed for each category of samples in the spatial and spectral dimensions, the spatial-spectral intra-manifold maps and spatial-spectral inter-manifold maps on each sub-manifold map are obtained, meaning that the projection matrix corresponding to each sub-manifold is found. We aim to provide an alternative way to construct multi-manifold graphs, thus obtaining a new representation of HIS. The proposed method is able to improve the accuracy of classification. The experimental results using two public datasets show that the method achieves good dimensionality reduction results. The rest of the paper is organized as follows: Section 2 introduces the related work, including the super-pixel segmentation algorithm and the dimensionality reduction algorithm based on manifold learning; Section 3 introduces the proposed method SSAMMA, which consists of SAWRM and SSMMM; Section 4 performs experimental validation of the proposed method using two datasets and analyzes the experimental results to evaluate the dimensionality reduction performance of the model; and Section 5 summarizes the contents of the paper.