Riemannian Local Mechanism for SPD Neural Networks
Riemannian Local Mechanism for SPD Neural Networks
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DOI：
10.1609/aaai.v37i6.25867
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发表时间：
2022-01
期刊：
影响因子：
64.8
通讯作者：
Ziheng Chen;Tianyang Xu;Xiaojun Wu;Rui Wang;Zhiwu Huang;J. Kittler
中科院分区：
文献类型：
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作者：
Ziheng Chen;Tianyang Xu;Xiaojun Wu;Rui Wang;Zhiwu Huang;J. Kittler
对称正定矩阵作为一种数据表示方法在许多科学领域受到了广泛的关注。虽然有许多不同的尝试来开发有效的深度架构，用于在SPD矩阵的黎曼流形上进行数据处理，但很少有解决方案明确地挖掘深度SPD特征表示中的局部几何信息。鉴于欧几里德方法中局部机制的巨大成功，我们认为，确保SPD网络中局部几何信息的保存是至关重要的。我们首先从范畴论提供的更高抽象层次的角度分析了通常用于捕获欧几里得深度网络中局部信息的卷积算子。在此基础上，我们定义了SPD流形中的局部信息，并设计了一个多尺度子流形块来挖掘局部几何。多个视觉任务的实验验证了该方法的有效性。
The Symmetric Positive Definite (SPD) matrices have received wide attention for data representation in many scientific areas. Although there are many different attempts to develop effective deep architectures for data processing on the Riemannian manifold of SPD matrices, very few solutions explicitly mine the local geometrical information in deep SPD feature representations. Given the great success of local mechanisms in Euclidean methods, we argue that it is of utmost importance to ensure the preservation of local geometric information in the SPD networks. We first analyse the convolution operator commonly used for capturing local information in Euclidean deep networks from the perspective of a higher level of abstraction afforded by category theory. Based on this analysis, we define the local information in the SPD manifold and design a multi-scale submanifold block for mining local geometry. Experiments involving multiple visual tasks validate the effectiveness of our approach.