SCGG: A Deep Structure-Conditioned Graph Generative Model

Deep learning-based graph generation approaches have remarkable capacities for graph data modeling, allowing them to solve a wide range of real-world problems. Making these methods able to consider different conditions during the generation procedure even increases their effectiveness by empowering them to generate new graph samples that meet the desired criteria. This paper presents a conditional deep graph generation method called SCGG that considers a particular type of structural conditions. Specifically, our proposed SCGG model takes an initial subgraph and autoregressively generates new nodes and their corresponding edges on top of the given conditioning substructure. The architecture of SCGG consists of a graph representation learning network and an autoregressive generative model, which is trained end-to-end. Using this model, we can address graph completion, a rampant and inherently difficult problem of recovering missing nodes and their associated edges of partially observed graphs. Experimental results on both synthetic and real-world datasets demonstrate the superiority of our method compared with state-of-the-art baselines

Optical pattern generator for efficient bio-data encoding in a photonic sequence comparison architecture.

In this study, optical technology is considered as SA issues' solution with the potential ability to increase the speed, overcome memory-limitation, reduce power consumption, and increase output accuracy. So we examine the effect of bio-data encoding and the creation of input images on the pattern-recognition error-rate at the output of optical Vander-lugt correlator. Moreover, we present a genetic algorithm-based coding approach, named as GAC, to minimize output noises of cross-correlating data. As a case study, we adopt the proposed coding approach within a correlation-based optical architecture for counting k-mers in a DNA string. As verified by the simulations on Salmonella whole-genome, we can improve sensitivity and speed more than 86% and 81%, respectively, compared to BLAST by using coding set generated by GAC method fed to the proposed optical correlator system. Moreover, we present a comprehensive report on the impact of 1D and 2D cross-correlation approaches, as-well-as various coding parameters on the output noise, which motivate the system designers to customize the coding sets within the optical setup

Performance comparison on the Enzymes dataset in terms of GED (lower is better) as a function of the number of new nodes to be added (i.e., <i>m</i>).

Performance comparison on the Enzymes dataset in terms of GED (lower is better) as a function of the number of new nodes to be added (i.e., m).</p

Comparison of SCGG with its competitors for <i>m</i> = 10 in terms of GED (Avg. ± Std.).

Comparison of SCGG with its competitors for m = 10 in terms of GED (Avg. ± Std.).</p

An overview of the workflow employed to obtain the required nodes’ features in the training phase.

(a) An input training graph after applying the preparation procedure shown in Fig 2(b) Two versions are made from the main graph. The one on the left will be treated as the initial graph (i.e., the G0), and the graph on the right, which we denote in the paper by G′, is obtained from the original graph by removing the intra-connection between the new nodes, i.e., the red link. (c) The Graph Feature Learning Network, whose architecture is illustrated in detail in Fig 1. (d) The features computed for each node of the graphs. The ones around which blue dashed ovals are drawn will be further used by the RNN.</p

Details regarding hyperparameter tuning.

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Pairwise performance comparison between our proposed SCGG method and its competitors on the Protein dataset.

The results are reported in terms of GED (the lower the better) as a function of the number of new nodes (denoted by m) that are added to initial graphs (each represented by the notation G0 in the paper). (TIF)</p

An example of the SCGG model at training time.

For each graph node, including those in the initial graph (i.e., the G0) and the ones in the set of new nodes (i.e., the ), the model outputs a probability distribution of link existence between that node and each new node (grey squares depict the probabilistic outputs, and the darker the colors, the higher the probabilities). To do this, at each step, a recurrent unit takes the features computed for one of the graph nodes (see Fig 3), as well as the previous node’s true connections and the hidden state of the previous recurrent unit. In this regard, the nodes of G0 (ordered by πn) are first fed into the model, followed by the new nodes (ordered by πm). Thus, the model learns to first generate the inter-links between the new nodes and those of G0, and then predict the intra-links between the new nodes. The parameters of both the Graph Feature Learning Network and the RNN are updated by minimizing the total loss L that is obtained via aggregating the step losses Li.</p

An illustration of the procedure of preparing the training data.

(a) An input graph. (b) A number of m nodes are selected randomly to be further treated as the new nodes. In this picture, m = 2, and the selected nodes (i.e., the green and the purple ones) are shown with thick borders. Furthermore, the inter-connections between new nodes and those in G0 are depicted by blue lines, and the only intra-connection between the new nodes is shown using a red line. (c) An ordering πn is applied to the nodes in G0. Moreover, another node ordering, denoted by πm, is applied to the new nodes.</p

Pairwise performance comparison between our proposed SCGG method and its competitors on the IMDBBINARY dataset.

The results are reported in terms of GED (the lower the better) as a function of the number of new nodes (denoted by m) that are added to initial graphs (each represented by the notation G0 in the paper). (TIF)</p