论文标题
一个或两个组件？散射转换答案
One or Two Components? The Scattering Transform Answers
论文作者
论文摘要
为了构建机器聆听的生物学上合理的模型，我们研究了小波散射网络对多组分固定信号的表示。首先，我们表明，一阶父母将二阶节点重新归一化，给出了一个简单的数值标准，可以评估两个相邻的组件是否会精神上干扰。其次，我们在散射系数上运行一种多种学习算法（ISOMAP），以可视化参数添加综合的相似性空间。第三，我们将“一个或两个组件”框架概括为三个正弦波或更多波，并证明傅立叶系列的有效散射深度与其带宽的对数成比例增长。
With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by their first-order parents gives a simple numerical criterion to assess whether two neighboring components will interfere psychoacoustically. Secondly, we run a manifold learning algorithm (Isomap) on scattering coefficients to visualize the similarity space underlying parametric additive synthesis. Thirdly, we generalize the "one or two components" framework to three sine waves or more, and prove that the effective scattering depth of a Fourier series grows in logarithmic proportion to its bandwidth.
