Related papers: Pooling Strategies for Simplicial Convolutional Ne…

In convolutional neural networks (CNNs), pooling operations play important roles such as dimensionality reduction and deformation compensation. In general, max pooling, which is the most widely used operation for local pooling, is performed…

Graph-structured data naturally occurs in many research fields, such as chemistry and sociology. The relational information contained therein can be leveraged to statistically model graph properties through geometrical deep learning. Graph…

How to utilize deep learning methods for graph classification tasks has attracted considerable research attention in the past few years. Regarding graph classification tasks, the graphs to be classified may have various graph sizes (i.e.,…

Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly…

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…

We propose a new symplectic convolutional neural network (CNN) architecture by leveraging symplectic neural networks, proper symplectic decomposition, and tensor techniques. Specifically, we first introduce a mathematically equivalent form…

Convolutional Neural Networks (CNNs) are artificial learning systems typically based on two operations: convolution, which implements feature extraction through filtering, and pooling, which implements dimensionality reduction. The impact…

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…

Recent studies have shown that a Deep Convolutional Neural Network (DCNN) pretrained on a large image dataset can be used as a universal image descriptor, and that doing so leads to impressive performance for a variety of image…

Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graph-structured data. To address its scalability issue due to the recursive embedding of neighboring features, graph topology sampling has been…

Graph neural networks (GNNs) have revolutionized the field of machine learning on non-Euclidean data such as graphs and networks. GNNs effectively implement node representation learning through neighborhood aggregation and achieve…

Graph neural networks (GNN) extends deep learning to graph-structure dataset. Similar to Convolutional Neural Networks (CNN) using on image prediction, convolutional and pooling layers are the foundation to success for GNN on graph…

Downsampling produces coarsened, multi-resolution representations of data and it is used, for example, to produce lossy compression and visualization of large images, reduce computational costs, and boost deep neural representation…

Accurate traffic conditions prediction provides a solid foundation for vehicle-environment coordination and traffic control tasks. Because of the complexity of road network data in spatial distribution and the diversity of deep learning…

Convolutional neural networks (CNNs) are being applied to an increasing number of problems and fields due to their superior performance in classification and regression tasks. Since two of the key operations that CNNs implement are…

Last decade has seen the emergence of numerous methods for learning on graphs, particularly Graph Neural Networks (GNNs). These methods, however, are often not directly applicable to more complex structures like bipartite graphs (equivalent…

In this paper, a novel multi-view methodology for graph-based neural networks is proposed. A systematic and methodological adaptation of the key concepts of classical deep learning methods such as convolution, pooling and multi-view…

Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point clouds and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, inspired from finite differences…

Multiple sampling-based methods have been developed for approximating and accelerating node embedding aggregation in graph convolutional networks (GCNs) training. Among them, a layer-wise approach recursively performs importance sampling to…

Learning invariant representations from images is one of the hardest challenges facing computer vision. Spatial pooling is widely used to create invariance to spatial shifting, but it is restricted to convolutional models. In this paper, we…