Graph convolutional neural networks (Graph-CNNs) extend traditional CNNs to
handle data that is supported on a graph. Major challenges when working with
data on graphs are that the support set (the vertices of the graph) do not
typically have a natural ordering, and in general, the topology of the graph is
not regular (i.e., vertices do not all have the same number of neighbors).
Thus, Graph-CNNs have huge potential to deal with 3D point cloud data which has
been obtained from sampling a manifold. In this paper, we develop a Graph-CNN
for classifying 3D point cloud data, called PointGCN. The architecture combines
localized graph convolutions with two types of graph downsampling operations
(also known as pooling). By the effective exploration of the point cloud local
structure using the Graph-CNN, the proposed architecture achieves competitive
performance on the 3D object classification benchmark ModelNet, and our
architecture is more stable than competing schemes.

本文介绍了使用 Graph-CNNs 和 PointGCN 对 3D 点云数据进行分类的方法，通过局部图卷积和两种图降采样操作实现了对点云局部结构的有效探索，与竞争方案相比，该架构具有更稳定的性能。

基于图卷积神经网络的三维点云分类

A Graph-CNN for 3D Point Cloud Classification

Convolutional Neural Networks (CNNs) have recently led to incredible
breakthroughs on a variety of pattern recognition problems. Banks of finite
impulse response filters are learned on a hierarchy of layers, each
contributing more abstract information than the previous layer. The simplicity
and elegance of the convolutional filtering process makes them perfect for
structured problems such as image, video, or voice, where vertices are
homogeneous in the sense of number, location, and strength of neighbors. The
vast majority of classification problems, for example in the pharmaceutical,
homeland security, and financial domains are unstructured. As these problems
are formulated into unstructured graphs, the heterogeneity of these problems,
such as number of vertices, number of connections per vertex, and edge
strength, cannot be tackled with standard convolutional techniques. We propose
a novel neural learning framework that is capable of handling both homogeneous
and heterogeneous data, while retaining the benefits of traditional CNN
successes.
Recently, researchers have proposed variations of CNNs that can handle graph
data. In an effort to create learnable filter banks of graphs, these methods
either induce constraints on the data or require preprocessing. As opposed to
spectral methods, our framework, which we term Graph-CNNs, defines filters as
polynomials of functions of the graph adjacency matrix. Graph-CNNs can handle
both heterogeneous and homogeneous graph data, including graphs having entirely
different vertex or edge sets. We perform experiments to validate the
applicability of Graph-CNNs to a variety of structured and unstructured
classification problems and demonstrate state-of-the-art results on document
and molecule classification problems.

本文介绍了一种基于图卷积神经网络的新型神经学习框架并探讨了其在处理结构化和非结构化分类问题方面的应用，证明该方法在文档和分子分类问题方面具有国际领先水平。