Professor Naoki Saito, UC Davis
Multiscale Hodge Scattering Networks for Data Analysis on Simplicial Complexes
Abstract
I will discuss Multiscale Hodge Scattering Networks (MHSNs), a new method to extract features from signals measured on simplicial complexes, which are robust against input signal perturbations. Our construction is based on multiscale basis dictionaries on simplicial complexes by generalizing those on nodes. MHSNs use a layered structure analogous to a convolutional neural network (CNN) to cascade the moments of the modulus of the dictionary coefficients. Importantly, the use of multiscale basis dictionaries in MHSNs admits a natural pooling operation that is akin to local pooling in CNNs, and which may be performed either locally or per-scale. As a result, we are able to extract a rich set of descriptive yet robust features that can be used along with very simple machine learning methods (i.e., logistic regression or support vector machines) to achieve high-accuracy classification systems with far fewer number of parameters to train than most modern graph neural networks. If the time permits, I will also discuss a new method to uncover the meaning of the scattering transform coefficients used by logistic regression using constrained zeroth-order optimization.