优化散射网络结构以提升低维数据的区分能力
Separation Capacity of Scattering Networks on Low-Dimensional Datasets
- 通过分析数据几何结构设计滤波器频率覆盖
- 滤波器需在多个频率上匹配数据特征
- 适合研究低维数据表示与特征提取的学者
我们旨在识别能最大化低内在维数数据分离能力的散射网络架构。所考虑的网络采用固定幂次非线性且无池化操作，因此唯一的设计变量是网络滤波器生成的框架。针对可参数化的集合模型数据，我们首先从数据集的几何结构出发，刻画并界定了通用特征提取器的分离能力。随后将结果具体化到散射网络，得出两个设计准则：(i) 滤波器应在足够多的频率上与数据相交；(ii) 将框架耦合至数据几何的矩阵应具有良好条件性。
原文摘要 · Abstract (English)
We aim to identify scattering network architectures that maximize the separation capacity on data with low intrinsic dimension. The networks we consider employ a fixed monomial nonlinearity and no pooling, so that the only design variable is the frame generated by the network filters. For data modeled as rectifiable sets, we first characterize and bound the separation capacity of general feature extractors in terms of the geometry of the dataset. We then particularize to scattering networks and obtain two design criteria: (i) the filters should meet the data on sufficiently many frequencies, and (ii) the matrices coupling the frame to the geometry of the data should be well-conditioned.
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