Recently, many researchers have been focusing on the definition of neural networks for graphs. The basic component for many of these approaches remains the graph convolution idea proposed almost a decade ago. In this paper, we extend this basic component, following an intuition derived from the well-known convolutional filters over multi-dimensional tensors. In particular, we derive a simple, efficient and effective way to introduce a hyper-parameter on graph convolutions that influences the filter size, i.e. its receptive field over the considered graph. We show with experimental results on real-world graph datasets that the proposed graph convolutional filter improves the predictive performance of Deep Graph Convolutional Networks.
Propagation kernels (PK) @cite_2 follow a different idea, inspired by the diffusion process in graph node kernels (i.e. kernels between nodes in a single graph), of propagating the node label information through the edges in a graph. Then, for each node, a distribution over the propagated labels is computed. Finally, the kernel between two graphs compares such distributions over all the nodes in the two graphs.
@cite_2
2185303849 2105295920 2280799770 2011953904
Learning from complex data is becoming increasingly important, and graph kernels have recently evolved into a rapidly developing branch of learning on structured data. However, previously proposed kernels rely on having discrete node label information. In this paper, we explore the power of continuous node-level features for propagation-based graph kernels. Specifically, propagation kernels exploit node label distributions from propagation schemes like label propagation, which naturally enables the construction of graph kernels for partially labeled graphs. In order to efficiently extract graph features from continuous node label distributions, and in general from continuous vector-valued node attributes, we utilize randomized techniques, which easily allow for deriving similarity measures based on propagated information. We show that propagation kernels utilizing locality-sensitive hashing reduce the runtime of existing graph kernels by several orders of magnitude. We evaluate the performance of various propagation kernels on real-world bioinformatics and image benchmark datasets. This paper presents a survey as well as an empirical comparison and evaluation of seven kernels on graphs and two related similarity matrices, that we globally refer to as ''kernels on graphs'' for simplicity. They are the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regularized Laplacian kernel, the commute-time (or resistance-distance) kernel, the random-walk-with-restart similarity matrix, and finally, a kernel first introduced in this paper (the regularized commute-time kernel) and two kernels defined in some of our previous work and further investigated in this paper (the Markov diffusion kernel and the relative-entropy diffusion matrix). The kernel-on-graphs approach is simple and intuitive. It is illustrated by applying the nine kernels to a collaborative-recommendation task, viewed as a link prediction problem, and to a semisupervised classification task, both on several databases. The methods compute proximity measures between nodes that help study the structure of the graph. Our comparisons suggest that the regularized commute-time and the Markov diffusion kernels perform best on the investigated tasks, closely followed by the regularized Laplacian kernel. We introduce a novel kernel that upgrades the Weisfeiler-Lehman and other graph kernels to effectively exploit high-dimensional and continuous vertex attributes. Graphs are first decomposed into subgraphs. Vertices of the subgraphs are then compared by a kernel that combines the similarity of their labels and the similarity of their structural role, using a suitable vertex invariant. By changing this invariant we obtain a family of graph kernels which includes generalizations of Weisfeiler-Lehman, NSPDK, and propagation kernels. We demonstrate empirically that these kernels obtain state-of-the-art results on relational data sets. This paper proposes a probabilistic graphical model for the problem of propagating labels in video sequences, also termed the label propagation problem. Given a limited amount of hand labelled pixels, typically the start and end frames of a chunk of video, an EM based algorithm propagates labels through the rest of the frames of the video sequence. As a result, the user obtains pixelwise labelled video sequences along with the class probabilities at each pixel. Our novel algorithm provides an essential tool to reduce tedious hand labelling of video sequences, thus producing copious amounts of useable ground truth data. A novel application of this algorithm is in semi-supervised learning of discriminative classifiers for video segmentation and scene parsing. The label propagation scheme can be based on pixel-wise correspondences obtained from motion estimation, image patch based similarities as seen in epitomic models or even the more recent, semantically consistent hierarchical regions. We compare the abilities of each of these variants, both via quantitative and qualitative studies against ground truth data. We then report studies on a state of the art Random forest classifier based video segmentation scheme, trained using fully ground truth data and with data obtained from label propagation. The results of this study strongly support and encourage the use of the proposed label propagation algorithm.