Abstract: Sparse Manifold clustering and embedding (SMCE) is an algorithm to cluster nonlinear manifolds using self-representation in the dictionary of data points and a proximity regularization. A computational bottleneck of SMCE is its dependence on a dictionary that scales with the number of data points. In this talk, I will discuss K-Deep Simplex (KDS), a unified optimization framework for nonlinear dimensionality reduction that combines the strengths of manifold learning and sparse dictionary learning. KDS learns local dictionaries that represent a data point with reconstruction coefficients supported on the probability simplex. The dictionaries are learned using algorithm unrolling, an increasingly popular technique for structured deep learning. I will present the application of KDS to the clustering problem and demonstrate its scalability and accuracy on both real and synthetic datasets. This is a joint work with Pranay Tankala, James M. Murphy and Demba Ba.