Multiclass Data Segmentation using Diffuse Interface Methods on Graphs

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm is a uses a graph adaptation of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, grayscale and color images, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current state-of-the-art multiclass segmentation algorithms.Comment: 14 page

Graph Few-shot Learning via Knowledge Transfer

Towards the challenging problem of semi-supervised node classification, there have been extensive studies. As a frontier, Graph Neural Networks (GNNs) have aroused great interest recently, which update the representation of each node by aggregating information of its neighbors. However, most GNNs have shallow layers with a limited receptive field and may not achieve satisfactory performance especially when the number of labeled nodes is quite small. To address this challenge, we innovatively propose a graph few-shot learning (GFL) algorithm that incorporates prior knowledge learned from auxiliary graphs to improve classification accuracy on the target graph. Specifically, a transferable metric space characterized by a node embedding and a graph-specific prototype embedding function is shared between auxiliary graphs and the target, facilitating the transfer of structural knowledge. Extensive experiments and ablation studies on four real-world graph datasets demonstrate the effectiveness of our proposed model.Comment: Full paper (with Appendix) of AAAI 202