Agenda

Speaker:
Giacomo Elefante, Dalle Molle Institute for Artificial Intelligence, Università della Svizzera italiana

Link Zoom
Meeting ID: 884 9259 0044             Passcode: wR8aWn

Abstract:
Data associated with the vertices of a graph can be represented as a function on its vertex set, called a graph signals. Approximating such signals requires a certain balance between the approximation error and the number of coefficients used in the representation. Graph wedgelets provide piecewise constant approximations on adaptively chosen partitions. Dividing the graph into smaller regions allows these approximations to capture the local features of the data. This approach is extended by combining adaptive graph partitions with local polynomials of higher degree. Adapting both the partition and the polynomial degrees leads to adaptive methods inspired by hp-refinement in finite element methods. Starting from a graph partitioning tree, we select subtrees and local polynomial degrees to reduce the approximation cost while preserving the same total approximation error. Local embeddings into low-dimensional Euclidean spaces provide the basis for polynomial approximation on general graphs. Numerical examples illustrate the benefits of adapting both the partition and the local approximation.