论文标题
歧管：扩展riemannian歧管上的正常化
ManifoldNorm: Extending normalizations on Riemannian Manifolds
论文作者
论文摘要
计算机视觉和机器学习中的许多测量表现为非欧几里得数据样本。一些研究人员最近扩展了许多深层神经网络体系结构，用于多种有价值的数据样本。研究人员提出了用于多种有价值的空间数据的模型，这些模型在医学图像处理中很常见，包括处理扩散张量成像（DTI），其中图像是$ 3 \ times 3 $对称的正面确定矩阵或取向分布场（ODF）的字段3 $ timess 3 $ timess 3 $ symmetric symmetric strictial districitie矩阵（ODF），其中该识别是在高脑识别的情况下。最近研究人员还显示，还有其他一些用于多种有价值数据的顺序模型，这些模型对神经差疾病的研究中的群体差异分析有效。尽管其中几种方法可有效处理多种有价值的数据，但瓶颈包括对更深层网络的优化的不稳定性。为了处理这些不稳定性，研究人员提出了剩余的剩余联系，以进行多种有价值的数据。处理包括梯度爆炸在内的不稳定性的其他补救措施之一是使用范围的技术，包括{\ it批处理norm}和{\ it组norm}等。但是，到目前为止，尚无适用于多种价值数据的归一化技术。在这项工作中，我们为多种有价值数据提出了一般的归一化技术。我们表明，我们提出的歧管归一化技术具有特殊案例，包括流行的批处理规范和组规范技术。在实验方面，我们专注于两种类型的歧管有价值的数据，包括对称阳性确定矩阵和超晶体的歧管。我们在一个合成实验中显示了用于移动MNIST数据集的合成实验和一个真实的大脑图像数据集中的性能增益，其中表示为方向分布字段（ODF）。
Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have proposed models for manifold valued spatial data which are common in medical image processing including processing of diffusion tensor imaging (DTI) where images are fields of $3\times 3$ symmetric positive definite matrices or representation in terms of orientation distribution field (ODF) where the identification is in terms of field on hypersphere. There are other sequential models for manifold valued data that recently researchers have shown to be effective for group difference analysis in study for neuro-degenerative diseases. Although, several of these methods are effective to deal with manifold valued data, the bottleneck includes the instability in optimization for deeper networks. In order to deal with these instabilities, researchers have proposed residual connections for manifold valued data. One of the other remedies to deal with the instabilities including gradient explosion is to use normalization techniques including {\it batch norm} and {\it group norm} etc.. But, so far there is no normalization techniques applicable for manifold valued data. In this work, we propose a general normalization techniques for manifold valued data. We show that our proposed manifold normalization technique have special cases including popular batch norm and group norm techniques. On the experimental side, we focus on two types of manifold valued data including manifold of symmetric positive definite matrices and hypersphere. We show the performance gain in one synthetic experiment for moving MNIST dataset and one real brain image dataset where the representation is in terms of orientation distribution field (ODF).
