Dimensionality reduction techniques are widely used in data mining and machine learning. The goal is to map high dimensional data samples to a lower dimensional space in order to filter out noise, extract latent information, or preserve certain properties of the data. The process can be time-consuming when the data set is large. Inspired by the multilevel paradigm that has been successfully applied to graph and hypergraph partitioning, we have developed three multilevel frameworks for dimensionality reduction, with applications to face recognition, text information retrieval, and manifold learning, respectively. Our methods not only reduce the computational cost but also improve some existing techniques. This is joint work with Sophia Sakellaridi and Yousef Saad (mentor).