论文标题
SPD神经网络的Riemannian局部机制
Riemannian Local Mechanism for SPD Neural Networks
论文作者
论文摘要
在许多科学领域，对称正定（SPD）矩阵已广泛关注数据表示。尽管有许多不同的尝试来开发有效的深层体系结构来在SPD矩阵的Riemannian歧管上进行数据处理，但很少有解决方案明确地在深层SPD特征表示中明确地挖掘了局部几何信息。鉴于局部机制在欧几里得方法中取得了巨大的成功，我们认为确保在SPD网络中保存本地几何信息至关重要。我们首先分析通常用于从类别理论提供的更高水平的抽象的角度来分析用于捕获欧几里得深网中局部信息的卷积操作员。基于此分析，我们在SPD歧管中定义了局部信息，并设计了用于采矿局部几何形状的多尺度submanifold块。涉及多个视觉任务的实验验证了我们方法的有效性。可以在https://github.com/gitzh-chen/msnet.git中找到补充和源代码。
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. The supplement and source code can be found in https://github.com/GitZH-Chen/MSNet.git.
