Combining Graph Convolutional Neural Networks and Label Propagation

Label Propagation Algorithm (LPA) and Graph Convolutional Neural Networks (GCN) are both message passing algorithms on graphs. Both solve the task of node classification, but LPA propagates node label information across the edges of the graph, while GCN propagates and transforms node feature information. However, while conceptually similar, theoretical relationship between LPA and GCN has not yet been systematically investigated. Moreover, it is unclear how LPA and GCN can be combined under a unified framework to improve the performance. Here we study the relationship between LPA and GCN in terms of feature/label influence , in which we characterize how much the initial feature/label of one node influences the final feature/label of another node in GCN/LPA. Based on our theoretical analysis, we propose an end-to-end model that combines GCN and LPA. In our unified model, edge weights are learnable, and the LPA serves as regularization to assist the GCN in learning proper edge weights that lead to improved performance. Our model can also be seen as learning the weights of edges based on node labels, which is more direct and efficient than existing feature-based attention models or topology-based diffusion models. In a number of experiments for semi-supervised node classification and knowledge-graph-aware recommendation, our model shows superiority over state-of-the-art baselines.

The interplay between communities and homophily in semi-supervised classification using graph neural networks

Graph Neural Networks (GNNs) are effective in many applications. Still, there is a limited understanding of the effect of common graph structures on the learning process of GNNs. To fill this gap, we study the impact of community structure and homophily on the performance of GNNs in semi-supervised node classification on graphs. Our methodology consists of systematically manipulating the structure of eight datasets, and measuring the performance of GNNs on the original graphs and the change in performance in the presence and the absence of community structure and/or homophily. Our results show the major impact of both homophily and communities on the classification accuracy of GNNs, and provide insights on their interplay. In particular, by analyzing community structure and its correlation with node labels, we are able to make informed predictions on the suitability of GNNs for classification on a given graph. Using an information-theoretic metric for community-label correlation, we devise a guideline for model selection based on graph structure. With our work, we provide insights on the abilities of GNNs and the impact of common network phenomena on their performance. Our work improves model selection for node classification in semi-supervised settings.

X-Mark: a benchmark for node-attributed community discovery algorithms

Grouping well-connected nodes that also result in label-homogeneous clusters is a task often known as attribute-aware community discovery. While approaching node-enriched graph clustering methods, rigorous tools need to be developed for evaluating the quality of the resulting partitions. In this work, we present X-Mark, a model that generates synthetic node-attributed graphs with planted communities. Its novelty consists in forming communities and node labels contextually while handling categorical or continuous attributive information. Moreover, we propose a comparison between attribute-aware algorithms, testing them against our benchmark. Accordingly to different classification schema from recent state-of-the-art surveys, our results suggest that X-Mark can shed light on the differences between several families of algorithms.

SketchGNN: Semantic Sketch Segmentation with Graph Neural Networks

We introduce SketchGNN , a convolutional graph neural network for semantic segmentation and labeling of freehand vector sketches. We treat an input stroke-based sketch as a graph with nodes representing the sampled points along input strokes and edges encoding the stroke structure information. To predict the per-node labels, our SketchGNN uses graph convolution and a static-dynamic branching network architecture to extract the features at three levels, i.e., point-level, stroke-level, and sketch-level. SketchGNN significantly improves the accuracy of the state-of-the-art methods for semantic sketch segmentation (by 11.2% in the pixel-based metric and 18.2% in the component-based metric over a large-scale challenging SPG dataset) and has magnitudes fewer parameters than both image-based and sequence-based methods.

TAXOGAN: Hierarchical Network Representation Learning via Taxonomy Guided Generative Adversarial Networks (Extended Abstract)

Network representation learning aims at transferring node proximity in networks into distributed vectors, which can be leveraged in various downstream applications. Recent research has shown that nodes in a network can often be organized in latent hierarchical structures, but without a particular underlying taxonomy, the learned node embedding is less useful nor interpretable. In this work, we aim to improve network embedding by modeling the conditional node proximity in networks indicated by node labels residing in real taxonomies. In the meantime, we also aim to model the hierarchical label proximity in the given taxonomies, which is too coarse by solely looking at the hierarchical topologies. Comprehensive experiments and case studies demonstrate the utility of TAXOGAN.

Unifying Node Labels, Features, and Distances for Deep Network Completion

Collected network data are often incomplete, with both missing nodes and missing edges. Thus, network completion that infers the unobserved part of the network is essential for downstream tasks. Despite the emerging literature related to network recovery, the potential information has not been effectively exploited. In this paper, we propose a novel unified deep graph convolutional network that infers missing edges by leveraging node labels, features, and distances. Specifically, we first construct an estimated network topology for the unobserved part using node labels, then jointly refine the network topology and learn the edge likelihood with node labels, node features and distances. Extensive experiments using several real-world datasets show the superiority of our method compared with the state-of-the-art approaches.

A comparison of statistical relational learning and graph neural networks for aggregate graph queries

Statistical relational learning (SRL) and graph neural networks (GNNs) are two powerful approaches for learning and inference over graphs. Typically, they are evaluated in terms of simple metrics such as accuracy over individual node labels. Complex aggregate graph queries (AGQ) involving multiple nodes, edges, and labels are common in the graph mining community and are used to estimate important network properties such as social cohesion and influence. While graph mining algorithms support AGQs, they typically do not take into account uncertainty, or when they do, make simplifying assumptions and do not build full probabilistic models. In this paper, we examine the performance of SRL and GNNs on AGQs over graphs with partially observed node labels. We show that, not surprisingly, inferring the unobserved node labels as a first step and then evaluating the queries on the fully observed graph can lead to sub-optimal estimates, and that a better approach is to compute these queries as an expectation under the joint distribution. We propose a sampling framework to tractably compute the expected values of AGQs. Motivated by the analysis of subgroup cohesion in social networks, we propose a suite of AGQs that estimate the community structure in graphs. In our empirical evaluation, we show that by estimating these queries as an expectation, SRL-based approaches yield up to a 50-fold reduction in average error when compared to existing GNN-based approaches.

Upper Bounding Graph Edit Distance Based on Rings and Machine Learning

The graph edit distance (GED) is a flexible distance measure which is widely used for inexact graph matching. Since its exact computation is [Formula: see text]-hard, heuristics are used in practice. A popular approach is to obtain upper bounds for GED via transformations to the linear sum assignment problem with error-correction (LSAPE). Typically, local structures and distances between them are employed for carrying out this transformation, but recently also machine learning techniques have been used. In this paper, we formally define a unifying framework LSAPE-GED for transformations from GED to LSAPE. We also introduce rings, a new kind of local structures designed for graphs where most information resides in the topology rather than in the node labels. Furthermore, we propose two new ring-based heuristics RING and RING-ML, which instantiate LSAPE-GED using the traditional and the machine learning-based approach for transforming GED to LSAPE, respectively. Extensive experiments show that using rings for upper bounding GED significantly improves the state of the art on datasets where most information resides in the graphs’ topologies. This closes the gap between fast but rather inaccurate LSAPE-based heuristics and more accurate but significantly slower GED algorithms based on local search.

Constructing smaller genome graphs via string compression

The size of a genome graph — the space required to store the nodes, their labels and edges — affects the efficiency of operations performed on it. For example, the time complexity to align a sequence to a graph without a graph index depends on the total number of characters in the node labels and the number of edges in the graph. The size of the graph also affects the size of the graph index that is used to speed up the alignment. This raises the need for approaches to construct space-efficient genome graphs.We point out similarities in the string encoding approaches of genome graphs and the external pointer macro (EPM) compression model. Supported by these similarities, we present a pair of linear-time algorithms that transform between genome graphs and EPM-compressed forms. We show that the algorithms result in an upper bound on the size of the genome graph constructed based on an optimal EPM compression. In addition to the transformation, we show that equivalent choices made by EPM compression algorithms may result in different sizes of genome graphs. To further optimize the size of the genome graph, we purpose the source assignment problem that optimizes over the equivalent choices during compression and introduce an ILP formulation that solves that problem optimally. As a proof-of-concept, we introduce RLZ-Graph, a genome graph constructed based on the relative Lempel-Ziv EPM compression algorithm. We show that using RLZ-Graph, across all human chromosomes, we are able to reduce the disk space to store a genome graph on average by 40.7% compared to colored de Bruijn graphs constructed by Bifrost under the default settings.The RLZ-Graph software is available at https://github.com/Kingsford-Group/rlzgraph

MET: a Java package for fast molecule equivalence testing

An important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.