将神经网络拓展到赛格尔空间，实现更优的分类性能。
Siegel Neural Networks
- 基于齐性空间结构与向量距离定义，构建赛格尔空间上的分类层。
- 在雷达杂波与节点分类任务中均达到当前最优效果。
- 适合从事流形学习、高维数据分类的研究者参考。
黎曼对称空间（RSS），如双曲空间和对称正定（SPD）流形，已成为表示学习中的热门空间。本文提出一种新方法，构建在赛格尔空间——一类尚未被充分探索的RSS——上的判别性神经网络。针对分类任务，近期研究聚焦于在双曲和SPD神经网络中构建多类逻辑回归（MLR）与全连接（FC）层。本文展示了如何在赛格尔神经网络中实现这些层。该方法依赖于这些空间的商结构及黎曼对称空间上的向量值距离概念。我们在两个应用中验证了方法的有效性：雷达杂波分类与节点分类。实验结果表明，在所有数据集上均实现了当前最优性能。
原文摘要 · Abstract (English)
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.
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