Abstract: Graph-based unsupervised dimensionality reduction has become a research hotspot in machine learning. We review typical algorithms in this area and their research progress. We begin by defining the graphs and explaining their construction methods. Next, 12 classical and cutting-edge methods are introduced, categorized into four groups: graph-fixed unsupervised dimensionality reduction algorithms, graph-fixed fast unsupervised dimensionality reduction algorithms, graph-optimized unsupervised dimensionality reduction algorithms, and fast unsupervised dimensionality reduction algorithms based on graph optimization. We then analyze and summarize these methods. Finally, future research directions for graph-based unsupervised dimensionality reduction techniques are discussed.