Graph U-Nets

We consider the problem of representation learning for graph data. Convolutional neural networks can naturally operate on images, but have significant challenges in dealing with graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied on many image pixel-wise prediction tasks, similar methods are lacking for graph data. This is due to the fact that pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling (gPool) and unpooling (gUnpool) operations in this work. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. We further propose the gUnpool layer as the inverse operation of the gPool layer. The gUnpool layer restores the graph into its original structure using the position information of nodes selected in the corresponding gPool layer. Based on our proposed gPool and gUnpool layers, we develop an encoder-decoder model on graph, known as the graph U-Nets. Our experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.Comment: 10 pages, ICML1

Wide-Area Crowd Counting: Multi-View Fusion Networks for Counting in Large Scenes

Crowd counting in single-view images has achieved outstanding performance on existing counting datasets. However, single-view counting is not applicable to large and wide scenes (e.g., public parks, long subway platforms, or event spaces) because a single camera cannot capture the whole scene in adequate detail for counting, e.g., when the scene is too large to fit into the field-of-view of the camera, too long so that the resolution is too low on faraway crowds, or when there are too many large objects that occlude large portions of the crowd. Therefore, to solve the wide-area counting task requires multiple cameras with overlapping fields-of-view. In this paper, we propose a deep neural network framework for multi-view crowd counting, which fuses information from multiple camera views to predict a scene-level density map on the ground-plane of the 3D world. We consider three versions of the fusion framework: the late fusion model fuses camera-view density map; the naive early fusion model fuses camera-view feature maps; and the multi-view multi-scale early fusion model ensures that features aligned to the same ground-plane point have consistent scales. A rotation selection module further ensures consistent rotation alignment of the features. We test our 3 fusion models on 3 multi-view counting datasets, PETS2009, DukeMTMC, and a newly collected multi-view counting dataset containing a crowded street intersection. Our methods achieve state-of-the-art results compared to other multi-view counting baselines.Comment: 29 pages, 13 figures, submitted to IJC