May 28 (Fri): "K-Deep Simplex: Structured Manifold Learning with Simplex Constraints," Abiy Tasissa, Ass't. Prof., Tufts
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 a 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 application of KDS to the clustering problem on both real and synthetic datasets. If time permits, I will discuss how the sparsity regularization in KDS facilitates structured compressive sensing and leads to recovery guarantees under less stringent conditions.
Abiy Tasissa received B.Sc. in Mathematics and M.Sc. in Aeronautics and Astronautics from the Massachusetts Institute of Technology and a PhD in Applied Mathematics from the Rensselaer Polytechnic Institute. He is currently a Norbert Wiener Assistant Professor in the Department of Mathematics at Tufts University and a research associate in the CRISP group at Harvard University. His research interests include distance geometry, compressive sensing, matrix completion, graph matching and more recently structured deep learning and manifold learning.
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