The Manifold Scattering Transform for High-Dimensional Point Cloud Data
The Manifold Scattering Transform for High-Dimensional Point Cloud Data
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DOI：
10.48550/arxiv.2206.10078
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Joyce A. Chew;H. Steach;Siddharth Viswanath;Hau‐Tieng Wu;M. Hirn;D. Needell;Smita Krishnaswamy;Michael Perlmutter
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文献类型：
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作者：
Joyce A. Chew;H. Steach;Siddharth Viswanath;Hau‐Tieng Wu;M. Hirn;D. Needell;Smita Krishnaswamy;Michael Perlmutter
流形散射变换是黎曼流形上定义的数据的深度特征提取器。它是将类卷积神经网络算子扩展到一般流形的第一个例子。该模型的初始工作主要关注其理论稳定性和不变性，但没有提供数值实现的方法，除了具有预定义网格的二维表面的情况。在这项工作中，我们提出了基于扩散图理论的实用方案，用于对自然系统中出现的数据集实施流形散射变换，例如单细胞遗传学，其中数据是建模为位于低维流形上的高维点云。我们证明我们的方法对于信号分类和流形分类任务是有效的。
The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification tasks.