An official website of the United States government
To deepen our understanding of graph neural networks, we investigate the representation power of Graph Convolutional Networks (GCN) through the looking glass of graph moments, a key property of graph topology encoding path of various lengths. We find that GCNs are rather restrictive in learning graph moments. Without careful design, GCNs can fail miserably even with multiple layers and nonlinear activation functions. We analyze theoretically the expressiveness of GCNs, arriving at a modular GCN design, using different propagation rules. Our modular design is capable of distinguishing graphs from different graph generation models for surprisingly small graphs, a notoriously difficult problem in network science. Our investigation suggests that, depth is much more influential than width and deeper GCNs are more capable of learning higher order graph moments. Additionally, combining GCN modules with different propagation rules is critical to the representation power of GCNs.
more »
« less
Multi-view spectral graph convolution with consistent edge attention for molecular modeling
Although graph convolutional networks (GCNs) that extend the convolution operation from images to graphs have led to competitive performance, the existing GCNs are still difficult to handle a variety of applications, especially cheminformatics problems. Recently multiple GCNs are applied to chemical compound structures which are represented by the hydrogen-depleted molecular graphs of different size. GCNs built for a binary adjacency matrix that reflects the connectivity among nodes in a graph do not account for the edge consistency in multiple molecular graphs, that is, chemical bonds (edges) in different molecular graphs can be similar due to the similar enthalpy and interatomic distance. In this paper, we propose a variant of GCN where a molecular graph is first decomposed into multiple views of the graph, each comprising a specific type of edges. In each view, an edge consistency constraint is enforced so that similar edges in different graphs can receive similar attention weights when passing information. Similarly to prior work, we prove that in each layer, our method corresponds to a spectral filter derived by the first order Chebyshev approximation of graph Laplacian. Extensive experiments demonstrate the substantial advantages of the proposed technique in quantitative structure-activity relationship prediction.
more »
« less
- Award ID(s):
- 1718738
- PAR ID:
- 10253605
- Date Published:
- Journal Name:
- Neurocomputing
- Volume:
- 445
- ISSN:
- 0925-2312
- Page Range / eLocation ID:
- 12-25
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract—Materials Genomics initiative has the goal of rapidly synthesizing materials with a given set of desired properties using data science techniques. An important step in this direction is the ability to predict the outcomes of complex chemical reactions. Some graph-based feature learning algorithms have been proposed recently. However, the comprehensive relationship between atoms or structures is not learned properly and not explainable, and multiple graphs cannot be handled. In this paper, chemical reaction processes are formulated as translation processes. Both atoms and edges are mapped to vectors represent- ing the structural information. We employ the graph convolution layers to learn meaningful information of atom graphs, and further employ its variations, message passing networks (MPNN) and edge attention graph convolution network (EAGCN) to learn edge representations. Particularly, multi-view EAGCN groups and maps edges to a set of representations for the properties of the chemical bond between atoms from multiple views. Each bond is viewed from its atom type, bond type, distance and neighbor environment. The final node and edge representations are mapped to a sequence defined by the SMILES of the molecule and then fed to a decoder model with attention. To make full usage of multi-view information, we propose multi-view attention model to handle self correlation inside each atom or edge, and mutual correlation between edges and atoms, both of which are important in chemical reaction processes. We have evaluated our method on the standard benchmark datasets (that have been used by all the prior works), and the results show that edge embedding with multi-view attention achieves superior accuracy compared to existing techniques.more » « less
-
Diffusion-based graph generative models are effective in generating high-quality small graphs. However, it is hard to scale them to large graphs that contain thousands of nodes. In this work, we propose EDGE, a new diffusion-based graph generative model that addresses generative tasks for large graphs. The model is developed by reversing a discrete diffusion process that randomly removes edges until obtaining an empty graph. It leverages graph sparsity in the diffusion process to improve computational efficiency. In particular, EDGE only focuses on a small portion of graph nodes and only adds edges between these nodes. Without compromising modeling ability, it makes much fewer edge predictions than previous diffusion-based generative models. Furthermore, EDGE can explicitly model the node degrees of training graphs and then gain performance improvement in capturing graph statistics. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by the proposed model have graph statistics more similar to those of training graphs.more » « less
-
Diffusion-based graph generative models are effective in generating high-quality small graphs. However, it is hard to scale them to large graphs that contain thousands of nodes. In this work, we propose EDGE, a new diffusion-based graph generative model that addresses generative tasks for large graphs. The model is developed by reversing a discrete diffusion process that randomly removes edges until obtaining an empty graph. It leverages graph sparsity in the diffusion process to improve computational efficiency. In particular, EDGE only focuses on a small portion of graph nodes and only adds edges between these nodes. Without compromising modeling ability, it makes much fewer edge predictions than previous diffusion-based generative models. Furthermore, EDGE can explicitly model the node degrees of training graphs and then gain performance improvement in capturing graph statistics. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by the proposed model have graph statistics more similar to those of training graphs.more » « less
-
Abstract Gene co-expression networks (GCNs) provide multiple benefits to molecular research including hypothesis generation and biomarker discovery. Transcriptome profiles serve as input for GCN construction and are derived from increasingly larger studies with samples across multiple experimental conditions, treatments, time points, genotypes, etc. Such experiments with larger numbers of variables confound discovery of true network edges, exclude edges and inhibit discovery of context (or condition) specific network edges. To demonstrate this problem, a 475-sample dataset is used to show that up to 97% of GCN edges can be misleading because correlations are false or incorrect. False and incorrect correlations can occur when tests are applied without ensuring assumptions are met, and pairwise gene expression may not meet test assumptions if the expression of at least one gene in the pairwise comparison is a function of multiple confounding variables. The ‘one-size-fits-all’ approach to GCN construction is therefore problematic for large, multivariable datasets. Recently, the Knowledge Independent Network Construction toolkit has been used in multiple studies to provide a dynamic approach to GCN construction that ensures statistical tests meet assumptions and confounding variables are addressed. Additionally, it can associate experimental context for each edge of the network resulting in context-specific GCNs (csGCNs). To help researchers recognize such challenges in GCN construction, and the creation of csGCNs, we provide a review of the workflow.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/https://doi.org/10.1016/j.neucom.2021.02.025
