Mathematics Colloquia and Seminars

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First, I will discuss the prerequisite information if you are interested in working with me for your PhD dissertation. Then, I will present two closely-related recent projects in which I would like you to participate: I will discuss potential tools to explain why a given set of features (either regular digital signals or signals on graphs) computed by a certain nonlinear transform (e.g., Scattering Transform) work well for signal classification. The key for such problems is the so-called Zeroth-Order (or Derivative Free) Optimization combined with constraints on the signal domain such as sparsity and smoothness. For graph signals, it turns out to be quite important to be able to visualize important basis vectors on a given graph. Except a certain class of graphs, however, the nodes of a given graph do not have physical coordinates to visualize it. Hence, we need to consider the "graph layout" problem, which can be viewed as an optimization problem to find the minimum energy configuration after embedding those nodes in $\mathbb{R}^d$ with $d=2$ or $3$. The energy functional is very interesting: it's a combination of "attraction" and "repulsion" potentials both of which are functions of distances between the nodes.