The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to outperform learned representations in certain tasks, particularly on limited labeled data and highly structured signals. The wavelet filters used in the scattering transform are typically selected to create a tight frame via a parameterized mother wavelet. In this work, we investigate whether this standard wavelet filterbank construction is optimal. Focusing on Morlet wavelets, we propose to learn the scales, orientations, and aspect ratios of the filters to produce problem-specific parameterizations of the scattering transform. We show that our learned versions of the scattering transform yield significant performance gains in small-sample classification settings over the standard scattering transform. Moreover, our empirical results suggest that traditional filterbank constructions may not always be necessary for scattering transforms to extract effective representations.
翻译:散落的波子变换会产生几何变异和变形稳定性。 在多个信号域中, 已经显示它与其他非学习的表达方式相比, 产生更具歧视性的表达方式, 并且在某些任务中表现优于所学的表达方式, 特别是在有限的标签数据和结构化强的信号上。 分散变换中使用的波子过滤器通常被选中, 以便通过参数化母波子建立紧凑的框架 。 在这项工作中, 我们调查这个标准波子过滤库的构造是否最理想 。 聚焦于摩尔列的波子, 我们提议学习过滤器的尺度、 方向和方位比率, 以产生分散变换的特有问题的参数化 。 我们显示, 我们所学的分散变换的版本在标准分散变换的大小分类设置中, 产生显著的性能增益 。 此外, 我们的经验显示, 传统的过滤库的构造可能并不总是必要来分散变换出有效的表达方式 。