Georgia Institute of Technology College of Sciences

The sparse solution obtained from greedy-based optimization approach such as orthogonal matching pursuit can be very useful and have many applications in different directions. In this talk, I will present two research projects, one is about semi-supervised local clustering, and the other is about function approximation, which make use of the sparse solution technique. We will show that the target cluster can be effectively retrieved in the local clustering task and the curse of dimensionality can be overcome for a dense subclass of the space of continuous functions via Kolmogorov superposition theorem. Both the theoretical and numerical results will be discussed.