Powerset Convolutional Neural Networks
This work addresses the challenge of processing set functions in machine learning, offering a novel approach that could benefit domains like hypergraph analysis, though it appears incremental in the context of convolutional methods.
The authors tackled the problem of learning set functions by introducing powerset convolutional neural networks, which use multiple basic shifts for set functions, and demonstrated their potential on synthetic and real-world hypergraph datasets.
We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions based on the Laplacian, as it provides not one but several basic shifts, one for each element in the ground set. Prototypical experiments with several set function classification tasks on synthetic datasets and on datasets derived from real-world hypergraphs demonstrate the potential of our new powerset CNNs.