Graph Convolutional Networks (GCNs) have been widely studied. The core of
GCNs is the definition of convolution operators on graphs. However, existing
Graph Convolution (GC) operators are mainly defined on adjacency matrix and
node features and generally focus on obtaining effective node embeddings which
cannot be utilized to address the graphs with (high-dimensional) edge features.
To address this problem, by leveraging tensor contraction representation and
tensor product graph diffusion theories, this paper analogously defines an
effective convolution operator on graphs with edge features which is named as
Tensor Product Graph Convolution (TPGC). The proposed TPGC aims to obtain
effective edge embeddings. It provides a complementary model to traditional
graph convolutions (GCs) to address the more general graph data analysis with
both node and edge features. Experimental results on several graph learning
tasks demonstrate the effectiveness of the proposed TPGC.

通过张量收缩表示和张量乘积图扩散理论，本文提出了一种名为 Tensor Product Graph Convolution (TPGC) 的图卷积算子，用于处理带有边特征的图数据分析，以获取有效的边嵌入表示。实验结果表明，所提出的 TPGC 对于多个图学习任务具有很好的效果。

基于张量乘积图卷积表征的图边表示

Graph Edge Representation via Tensor Product Graph Convolutional  Representation

Thanks to the application of deep learning technology in point cloud
processing of the remote sensing field, point cloud segmentation has become a
research hotspot in recent years, which can be applied to real-world 3D, smart
cities, and other fields. Although existing solutions have made unprecedented
progress, they ignore the inherent characteristics of point clouds in remote
sensing fields that are strictly arranged according to latitude, longitude, and
altitude, which brings great convenience to the segmentation of point clouds in
remote sensing fields. To consider this property cleverly, we propose novel
convolution operators, termed Twin Deformable point Convolutions (TDConvs),
which aim to achieve adaptive feature learning by learning deformable sampling
points in the latitude-longitude plane and altitude direction, respectively.
First, to model the characteristics of the latitude-longitude plane, we propose
a Cylinder-wise Deformable point Convolution (CyDConv) operator, which
generates a two-dimensional cylinder map by constructing a cylinder-like grid
in the latitude-longitude direction. Furthermore, to better integrate the
features of the latitude-longitude plane and the spatial geometric features, we
perform a multi-scale fusion of the extracted latitude-longitude features and
spatial geometric features, and realize it through the aggregation of adjacent
point features of different scales. In addition, a Sphere-wise Deformable point
Convolution (SpDConv) operator is introduced to adaptively offset the sampling
points in three-dimensional space by constructing a sphere grid structure,
aiming at modeling the characteristics in the altitude direction. Experiments
on existing popular benchmarks conclude that our TDConvs achieve the best
segmentation performance, surpassing the existing state-of-the-art methods.

通过学习纬度 - 经度平面和高度方向上的可变形采样点，我们提出了新颖的卷积算子 —— 双可变形点卷积 (TDConvs)，以实现自适应特征学习；在现有的流行基准测试上，实验证明我们的 TDConvs 达到了最佳的分割性能，超过现有的最先进方法。

遥感场景点云语义分割的双可变形点卷积

Twin Deformable Point Convolutions for Point Cloud Semantic Segmentation  in Remote Sensing Scenes

Steerable CNN imposes the prior knowledge of transformation invariance or
equivariance in the network architecture to enhance the the network robustness
on geometry transformation of data and reduce overfitting. It has been an
intuitive and widely used technique to construct a steerable filter by
augmenting a filter with its transformed copies in the past decades, which is
named as filter transform in this paper. Recently, the problem of steerable CNN
has been studied from aspect of group representation theory, which reveals the
function space structure of a steerable kernel function. However, it is not yet
clear on how this theory is related to the filter transform technique. In this
paper, we show that kernel constructed by filter transform can also be
interpreted in the group representation theory. This interpretation help
complete the puzzle of steerable CNN theory and provides a novel and simple
approach to implement steerable convolution operators. Experiments are executed
on multiple datasets to verify the feasibility of the proposed approach.

本文介绍一种名为 “可转向 CNN” 的神经网络结构，应用于数据的几何变换，通过滤波器变换技术构建可转向卷积核，通过群表示理论将此两者联系在一起，提高了网络的鲁棒性并减少了过拟合。