Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning

Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semisupervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires a considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits. First, we show that the graph convolution of the GCN model is actually a special form of Laplacian smoothing, which is the key reason why GCNs work, but it also brings potential concerns of over-smoothing with many convolutional layers. Second, to overcome the limits of the GCN model with shallow architectures, we propose both co-training and self-training approaches to train GCNs. Our approaches significantly improve GCNs in learning with very few labels, and exempt them from requiring additional labels for validation. Extensive experiments on benchmarks have verified our theory and proposals.Comment: AAAI-2018 Oral Presentatio

Implications of 3-step swimming patterns in bacterial chemotaxis

We recently found that marine bacteria Vibrio alginolyticus execute a cyclic 3-step (run- reverse-flick) motility pattern that is distinctively different from the 2-step (run-tumble) pattern of Escherichia coli. How this novel swimming pattern is regulated by cells of V. alginolyticus is not currently known, but its significance for bacterial chemotaxis is self- evident and will be delineated herein. Using an approach introduced by de Gennes, we calculated the migration speed of a cell executing the 3-step pattern in a linear chemical gradient, and found that a biphasic chemotactic response arises naturally. The implication of such a response for the cells to adapt to ocean environments and its possible connection to E. coli 's response are also discussed.Comment: 18 pages, 4 figures, submitted to biophysical journa