Learning on Graph Orbifolds - talk af Brijnesh Jain
Fredag d. 29. august kl 11:00 giver Brijnesh Jain fra TU Berlin en talk i APL-gruppens mødelokale.
Patterns are typically represented by feature vectors living in a Euclidean or Banach space, because those spaces provide powerful analytical techniques for data analysis, which are usually not available for other representations such as point patterns, trees, and graphs. A standard technique to solve a learning problem in vector spaces consists in setting up a smooth error function, which is then minimized by using local gradient information. In this talk, we suggest a representation of attributed graphs as points of some quotient space, called graph orbifold. The graph orbifold framework enables us to transfer geometrical concepts such as length and angle as well as analytical concepts such as the derivative from vector spaces to the graph domain. We show, for example, that the gradient of a function on graphs is a well-defined graph pointing in direction of steepest ascent. Exploiting the analytical and geometrical properties of graph orbifolds, it will turn out that the principle of empirical risk minimization with differentiable loss function amounts in an optimization problem of locally Lipschitz risk functions on graphs that can be minimized with subgradient-like methods. We present and discuss some results in supervised and unsupervised learning on graphs showing that the orbifold framework complements existing learning methods on graphs.