Ligand-Based Virtual Screening Based on the Graph Edit Distance

Chemical compounds can be represented as attributed graphs. An attributed graph is a mathematical model of an object composed of two types of representations: nodes and edges. Nodes are individual components, and edges are relations between these components. In this case, pharmacophore-type node descriptions are represented by nodes and chemical bounds by edges. If we want to obtain the bioactivity dissimilarity between two chemical compounds, a distance between attributed graphs can be used. The Graph Edit Distance allows computing this distance, and it is defined as the cost of transforming one graph into another. Nevertheless, to define this dissimilarity, the transformation cost must be properly tuned. The aim of this paper is to analyse the structural-based screening methods to verify the quality of the Harper transformation costs proposal and to present an algorithm to learn these transformation costs such that the bioactivity dissimilarity is properly defined in a ligand-based virtual screening application. The goodness of the dissimilarity is represented by the classification accuracy. Six publicly available datasets—CAPST, DUD-E, GLL&GDD, NRLiSt-BDB, MUV and ULS-UDS—have been used to validate our methodology and show that with our learned costs, we obtain the highest ratios in identifying the bioactivity similarity in a structurally diverse group of molecules.

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.

Redefining the Graph Edit Distance

Graph edit distance has been used since 1983 to compare objects in machine learning when these objects are represented by attributed graphs instead of vectors. In these cases, the graph edit distance is usually applied to deduce a distance between attributed graphs. This distance is defined as the minimum amount of edit operations (deletion, insertion and substitution of nodes and edges) needed to transform a graph into another. Since now, it has been stated that the distance properties have to be applied [(1) non-negativity (2) symmetry (3) identity and (4) triangle inequality] to the involved edit operations in the process of computing the graph edit distance to make the graph edit distance a metric. In this paper, we show that there is no need to impose the triangle inequality in each edit operation. This is an important finding since in pattern recognition applications, the classification ratio usually maximizes in the edit operation combinations (deletion, insertion and substitution of nodes and edges) that the triangle inequality is not fulfilled.

Learning Attributed Graph Representation with Communicative Message Passing Transformer

Constructing appropriate representations of molecules lies at the core of numerous tasks such as material science, chemistry, and drug designs. Recent researches abstract molecules as attributed graphs and employ graph neural networks (GNN) for molecular representation learning, which have made remarkable achievements in molecular graph modeling. Albeit powerful, current models either are based on local aggregation operations and thus miss higher-order graph properties or focus on only node information without fully using the edge information. For this sake, we propose a Communicative Message Passing Transformer (CoMPT) neural network to improve the molecular graph representation by reinforcing message interactions between nodes and edges based on the Transformer architecture. Unlike the previous transformer-style GNNs that treat molecule as a fully connected graph, we introduce a message diffusion mechanism to leverage the graph connectivity inductive bias and reduce the message enrichment explosion. Extensive experiments demonstrated that the proposed model obtained superior performances (around 4% on average) against state-of-the-art baselines on seven chemical property datasets (graph-level tasks) and two chemical shift datasets (node-level tasks). Further visualization studies also indicated a better representation capacity achieved by our model.

Random Graph-based Multiple Instance Learning for Structured IoT Smart City Applications

Because of the complex activities involved in IoT networks of a smart city, an important question arises: What are the core activities of the networks as a whole and its basic information flow structure? Identifying and discovering core activities and information flow is a crucial step that can facilitate the analysis. This is the question we are addressing—that is, to identify the core services as a common core substructure despite the probabilistic nature and the diversity of its activities. If this common substructure can be discovered, a systemic analysis and planning can then be performed and key policies related to the community can be developed. Here, a local IoT network can be represented as an attributed graph. From an ensemble of attributed graphs, identifying the common subgraph pattern is then critical in understanding the complexity. We introduce this as the common random subgraph (CRSG) modeling problem, aiming at identifying a subgraph pattern that is the structural “core” that conveys the probabilistically distributed graph characteristics. Given an ensemble of network samples represented as attributed graphs, the method generates a CRSG model that encompasses both structural and statistical characteristics from the related samples while excluding unrelated networks. In generating a CRSG model, our method using a multiple instance learning algorithm transforms an attributed graph (composed of structural elements as edges and their two endpoints) into a “bag” of instances in a vector space. Common structural components across positively labeled graphs are then identified as the common instance patterns among instances across different bags. The structure of the CRSG arises through the combining of common patterns. The probability distribution of the CRSG can then be estimated based on the connections and distributions from the common elements. Experimental results demonstrate that CRSG models are highly expressive in describing typical network characteristics.