Grassmann manifolds have emerged as a powerful tool for high-dimensional data analysis tasks such as image set classification and video action recognition, owing to their ability to mathematically represent collections of linear subspaces. However, the computational complexity of Grassmann manifolds and the challenges faced by traditional dimensionality reduction methods in effectively handling complex nonlinear structures have hindered their widespread application. To address this issue, we propose a novel unsupervised shallow dimensionality reduction method: the Grassmann manifold-based Neighborhood-preserving Autoencoder (GAE-LLE), applied to the task of image set classification. This approach integrates the global dimensionality reduction representation power of the Grassmann autoencoder with the local topology-preserving principle of Neighborhood Embedding. It constructs a dual-constrained optimization framework in the manifold space: on one hand, a neighborhood similarity graph is constructed on the Grassmann manifold using geodesic distances to enforce local structural constraints in the low-dimensional manifold space; on the other hand, the Grassmann autoencoder is employed to preserve the global manifold characteristics of the data. Our comparative experiments demonstrate that the proposed unsupervised shallow dimensionality reduction method outperforms existing traditional dimensionality reduction techniques, significantly improving classification accuracy across multiple image set classification tasks.