Scattering transforms are non-trainable deep convolutional architectures that
exploit the multi-scale resolution of a wavelet filter bank to obtain an
appropriate representation of data. More importantly, they are proven invariant
to translations, and stable to perturbations that are close to translations.
This stability property dons the scattering transform with a robustness to
small changes in the metric domain of the data. When considering network data,
regular convolutions do not hold since the data domain presents an irregular
structure given by the network topology.
In this work, we extend scattering transforms to network data by using
multiresolution graph wavelets, whose computation can be obtained by means of
graph convolutions. Furthermore, we prove that the resulting graph scattering
transforms are stable to metric perturbations of the underlying network. This
renders graph scattering transforms robust to changes on the network topology,
making it particularly useful for cases of transfer learning, topology
estimation or time-varying graphs.

本文介绍了在网络数据中使用多分辨率图形小波的散射变换，并证明了生成的散射变换对底层网络度量摄动的稳定性。这使得图形散射变换变得稳健，特别适用于转移学习、拓扑估计或时变图的情况。

图散射变换的稳定性

Stability of Graph Scattering Transforms

We explore the generalization of scattering transforms from traditional
(e.g., image or audio) signals to graph data, analogous to the generalization
of ConvNets in geometric deep learning, and the utility of extracted graph
features in graph data analysis. In particular, we focus on the capacity of
these features to retain informative variability and relations in the data
(e.g., between individual graphs, or in aggregate), while relating our
construction to previous theoretical results that establish the stability of
similar transforms to families of graph deformations. We demonstrate the
application the our geometric scattering features in graph classification of
social network data, and in data exploration of biochemistry data.

本篇论文探讨了散射变换从传统（如图像或音频）信号到图数据的归纳推广，类似于 geometric deep learning 中 ConvNets 的归纳推广，并研究了提取的图特征在图数据分析中的实用性，尤其关注这些特征保留数据中的信息变量和关联的能力，同时将我们的构建与之前的一些理论结果联系起来，这些结果建立在类似变换到图变形的家族上的稳定性上。 我们证明了在社交网络数据的图分类和生物化学数据的数据探索中应用了我们的几何散射特征。

基于几何散射的图数据分析

Geometric Scattering for Graph Data Analysis

Stability is a key aspect of data analysis. In many applications, the natural
notion of stability is geometric, as illustrated for example in computer
vision. Scattering transforms construct deep convolutional representations
which are certified stable to input deformations. This stability to
deformations can be interpreted as stability with respect to changes in the
metric structure of the domain. In this work, we show that scattering
transforms can be generalized to non-Euclidean domains using diffusion
wavelets, while preserving a notion of stability with respect to metric changes
in the domain, measured with diffusion maps. The resulting representation is
stable to metric perturbations of the domain while being able to capture
"high-frequency" information, akin to the Euclidean Scattering.

本文论述了通过扩展散射变换到非欧几里得域并使用扩散小波，可以在保持度量变化稳定性的同时，获取能够捕获类似于欧几里得散射的高频信息的稳定表征的研究。

图上扩散散射变换

Diffusion Scattering Transforms on Graphs

We introduce general scattering transforms as mathematical models of deep
neural networks with l2 pooling. Scattering networks iteratively apply complex
valued unitary operators, and the pooling is performed by a complex modulus. An
expected scattering defines a contractive representation of a high-dimensional
probability distribution, which preserves its mean-square norm. We show that
unsupervised learning can be casted as an optimization of the space contraction
to preserve the volume occupied by unlabeled examples, at each layer of the
network. Supervised learning and classification are performed with an averaged
scattering, which provides scattering estimations for multiple classes.

本文介绍广义散射变换作为深度神经网络数学模型，并探讨其在无监督和有监督学习及分类中的应用。