A Deep Neural Network for Manifold-Valued Data with Applications to Neuroimaging
A Deep Neural Network for Manifold-Valued Data with Applications to Neuroimaging
复制标题
用于多值数据的深度神经网络及其在神经影像学中的应用
DOI：
10.1007/978-3-030-20351-1_9
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Vemuri, B.C.
中科院分区：
文献类型：
--
作者：
Chakraborty, R.;Bouza, J.;Manton, J.;Vemuri, B.C.
为流形数据集开发深度神经网络(DNN)最近在深度学习研究界获得了极大的兴趣。医学成像领域的多值数据的例子包括(但不限于)扩散磁共振成像、基于张量的形态测量、形状分析等。受卷积神经网络(CNN)结构的启发，本文提出了一种新的DNN理论框架，用于处理多值数据输入。我们称我们的网络为流形网络。类似于向量空间中，卷积等价于计算加权平均，流形值数据卷积可以使用加权弗雷切特平均(WFM)来定义。为此，我们提出了一种可证明收敛的递归算法，用于计算给定数据的WFM，其中权重是要学习的。进一步，我们证明了所提出的WFM层实现了压缩映射，因此流形网不需要在标准CNN中使用额外的非线性REU单元来实现压缩映射；类似于欧氏空间中卷积到平移的等方差，我们证明了WFM与数据所在的黎曼流形所允许的等距群的作用是等变的。这种等方差特性便于网络内的权重分担。我们使用ManifoldNet框架进行实验，以实现帕金森病(PD)患者的扩散MRI扫描与临床信息(如他们的运动障碍协会的统一帕金森病评定量表(MDS-UPDRS)评分)之间的回归。在另一个实验中，我们提出了基于PD和对照组之间纤维束水平的大脑连接来发现组内差异的结果。
Developing deep neural networks (DNNs) for manifold-valued data sets has gained significant interest of late in the deep learning research community. Examples of manifold-valued data in the medical imaging domain include (but are not limited to) diffusion magnetic resonance imaging, tensor-based morphometry, shape analysis and more. In this paper we present a novel theoretical framework for DNNs to cope with manifold-valued data inputs, taking inspiration from the convolutional neural network (CNN) architecture. We call our network the ManifoldNet.Analogous to vector spaces where convolutions are equivalent to computing weighted means, manifold-valued data convolutions can be defined using the weighted Fréchet Mean (wFM). To this end, we present a provably convergent recursive algorithm for computation of the wFM of the given data, where the weights are to be learned. Further, we prove that the proposed wFM layer achieves a contraction mapping and hence the ManifoldNet need not have additional non-linear ReLU units used in standard CNNs to achieve a contraction mapping.Analogous to the equivariance of convolution in Euclidean space to translations, we prove that the wFM is equivariant to the action of the group of isometries admitted by the Riemannian manifold on which the data reside. This equivariance property facilitates weight sharing within the network. We present experiments using the ManifoldNet framework to achieve regression between diffusion MRI scans of Parkinson Disease (PD) patients and clinical information such as their Movement Disorder Society’s Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) scores. In another experiment, we present results of finding group differences based on brain connectivity at the fiber bundle level between PD and controls.
黎曼几何：主题索引
DOI：
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发表时间：
2006
期刊：
影响因子：
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作者：
I. Chavel
通讯作者：
I. Chavel
测量 ARMA 模型组之间的距离
DOI：
--
发表时间：
2016
期刊：
影响因子：
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作者：
U. Triacca
通讯作者：
U. Triacca
影响因子：
4.5
作者：
Chakraborty, Rudrasis;Vemuri, Baba C.
通讯作者：
Vemuri, Baba C.