Topological Volterra Filters

To deal with high-dimensional data, graph filters have shown their power in both graph signal processing and data science. However, graph filters process signals exploiting only pairwise interactions between the nodes, and they are not able to exploit more complicated topological structures. Graph Volterra models, on the other hand, are also...

Advances in Graph Signal Processing: Fast graph construction & Node-adaptive graph signal reconstruction

This thesis consists of two parts in both data science and signal processing over graphs. In the first part of this thesis, we aim to solve the problem of graph construction in big data scenario, which is critical for practical tasks, like collaborative filtering in recommender systems, spectral embedding or clustering in learning algorithms. We...

Node varying regularization for graph signals

While regularization on graphs has been successful for signal reconstruction, strategies for controlling the bias-variance trade-off of such methods have not been completely explored. In this work, we put forth a node varying regularizer for graph signal reconstruction and develop a minmax approach to design the vector of regularization...