## 1 Introduction  
In modern intelligent image processing and application scenarios, one of the most tricky problems is dealing with high-dimensional data [1]. With the advancements in camera lenses and remote sensing technologies, obtaining high-quality images of a target object has gradually achieved breakthroughs [2]. However, high-quality images imply high-dimensional data, which not only contain a large amount of redundant information but also pose challenges for image processing algorithms due to the heavy computational resources they demand, so called \"the curse of dimensionality\" [3]. On the other hand, imprudently reducing the dimensionality of data may lead to the loss of valuable discriminative information, leading to the invalidation of recognition [4]. Therefore, a key points is to delicately reduce the dimensions while preserving the major details and relationships between samples. In the fields of pattern recognition and data mining, dimensionality reduction techniques have been developed for many years and continue to achieve new advancements in various applications [5]. [PERSON] et al. designed a two-stage dimensionality reduction technique for social media engagement classification [6]. [PERSON] et al. put forward a dimensionality reduction-based machine learning technique for tumor classification of RNA data [7]. [PERSON] et al. proposed a method for constructing multiple Peano curves to preserve the object proximity information in the course of dimensionality reduction [8]. [PERSON] et al. proposes a novel non-negative matrix factorization method with dual-graph regularization constrained for dimensionality reduction and clustering [9]. An algorithm that computes all rough sets constructed for dimensionality reduction was proposed by [PERSON] et al. [10]. [PERSON] et al. retrieved the wheat crop traits of hyperspectral data using machine learning and dimensionality reduction algorithms [11]. [PERSON] et al. proposed a framework named CoIAE for hyperspectral image feature extraction and clustering with auto-encoders and dimension reduction techniques [12]. [PERSON] et al. designed a dimension reduction method that combines feature extraction and selection for effective image classification [13]. Generally speaking, the goal of dimensionality reduction is to transform high-dimensional data from the original space into a new low-dimensional space by utilizing linear or non-linear transformation [1]. The most widely known techniques include linear discriminant analysis (LDA) [14], principle component analysis (PCA) [15], robust principle component analysis (RPCA) [16] and manifold learning-based algorithms [17]. LDA is a supervised technique that aims to reduce the dimensionality of high-dimensional pattern samples by projecting them onto an optimal discriminant vector space [18]. This process facilitates the extraction of discriminative information for classification purposes while simultaneously reducing the dimensionality of the feature space through compression. PCA is a linear transformation that selects multiple eigenvectors for feature extraction and dimension reduction [19]. RPCA assumes that observed data are composed of low-rank clean data and sparse noise and it achieves feature extraction and dimensionality reduction by solving an optimization problem [20]. Manifold learning aims to reveal the geometric relationship between samples in a high-dimensional manifold space. ISOMAP computes the geometric distance between two data points by constructing a neighborhood graph and searching for the shortest paths [21]. Locally linear embedding (LLE) [22] reconstructs the linear weights of two neighbors and maps it to the embedded coordinates. Laplacian eigenmaps (LE) [23] define a heart-kernel function for measuring the distance between two points and finds the best low-dimensional mapping by solving a trace minimization problem. However, the existing dimensionality reduction techniques basically treat data in the original domain.