广义空间Poisson点过程的散射统计
Scattering Statistics of Generalized Spatial Poisson Point Processes
摘要：
我们提出了一个机器学习模型的随机生成的离散信号的分析，建模为一个非齐次，复合泊松点过程的点。像Mallat介绍的小波散射变换，我们的建设是自然不变的平移和反射，但它的规模和频率的作用，取代小波与Gabor型测量。我们发现，适当的非线性，我们的测量区分泊松点过程从常见的自相似过程，并分离不同类型的泊松点过程。
英文摘要：
We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples the roles of scale and frequency, replacing wavelets with Gabor-type measurements. We show that, with suitable nonlinearities, our measurements distinguish Poisson point processes from common self-similar processes, and separate different types of Poisson point processes.
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