Abstract: In order to reduce the computational cost of dimensionality reduction of large-scale data sets, an orthogonal unsupervised graph embedding dimensionality reduction algorithm based on balanced hierarchical K-means is proposed. The necessary and sufficient conditions for locally preserving the equivalence of projection and spectral regression were obtained. An anchor generation strategy based on balanced hierarchical K-means was put forward, and a special similarity matrix was constructed to accelerate the process of local preserving projection. Combined with the orthogonal constraints, an orthogonal unsupervised large-scale graph embedding dimension reduction method is proposed. Experiments on several public data sets show that the proposed method can achieve efficient and fast dimensionality reduction for large-scale data sets.