Siegel Neural Networks
This work addresses the need for effective neural network methods on Siegel spaces, offering a novel approach for classification tasks in domains like radar and graph data, though it is incremental as it extends existing techniques to a new space.
The paper tackled the problem of building discriminative neural networks on Siegel spaces, an unexplored family of Riemannian symmetric spaces, by constructing multiclass logistic regression and fully-connected layers, achieving state-of-the-art performance in radar clutter and node classification tasks.
Riemannian symmetric spaces (RSS) such as hyperbolic spaces and symmetric positive definite (SPD) manifolds have become popular spaces for representation learning. In this paper, we propose a novel approach for building discriminative neural networks on Siegel spaces, a family of RSS that is largely unexplored in machine learning tasks. For classification applications, one focus of recent works is the construction of multiclass logistic regression (MLR) and fully-connected (FC) layers for hyperbolic and SPD neural networks. Here we show how to build such layers for Siegel neural networks. Our approach relies on the quotient structure of those spaces and the notation of vector-valued distance on RSS. We demonstrate the relevance of our approach on two applications, i.e., radar clutter classification and node classification. Our results successfully demonstrate state-of-the-art performance across all datasets.