Redefining the Graph Edit Distance

Serratosa, Francesc

doi:10.1007/s42979-021-00792-5

Cited by 10 publications

(7 citation statements)

References 35 publications

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Section: ■ Methodsmentioning

confidence: 99%

“…Since the chemical details have already been accounted for, the topology can be treated as a homogeneous version of the stochastic graph representation where all edges and nodes are treated identically (see gray topology graphs g A and g B in Figure ). To calculate the similarity between two different polymer topologies, GED ,, is utilized. GED, first reported by Sanfeliu and Fu in 1983, is a measure of similarity between two graphs, g 1 and g 2 .…”

Section: Methodsmentioning

confidence: 99%

“…The idea behind GED is to find the minimal set of transformations that can transform graph g 1 into graph g 2 by means of edit operations on graph g 1 . The set of elementary graph edit operators typically includes node and edge insertion, deletion, and substitution, although substitution is not considered here since the topology graphs are homogeneous. normalG normalE normalD .25em ( g 1 , g 2 ) = min ( e 1 , · · · , e k ) ∈ scriptP ( g 1 , g 2 ) ∑ i = 1 k c ( e i ) where scriptP ( g 1 , g 2 ) denotes the set of edit paths transforming g 1 into graph g 2 , and c ( e i ) is the cost of each graph edit operation e i . For simplicity, c ( e i ) = 1, the cost of each graph editing step is set to be one.…”

Section: Methodsmentioning

confidence: 99%

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Quantifying Pairwise Similarity for Complex Polymers

Shi,

Rebello,

Walsh

et al. 2023

Macromolecules

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Defining the similarity between chemical entities is an essential task in polymer informatics, enabling ranking, clustering, and classification. Despite its importance, the pairwise chemical similarity of polymers remains an open problem. Here, a similarity function for polymers with well-defined backbones is designed based on polymers’ stochastic graph representations generated from canonical BigSMILES, a structurally based line notation for describing macromolecules. The stochastic graph representations are separated into three parts: repeat units, end groups, and polymer topology. The earth mover’s distance is utilized to calculate the similarity of the repeat units and end groups, while the graph edit distance is used to calculate the similarity of the topology. These three values can be linearly or nonlinearly combined to yield an overall pairwise chemical similarity score for polymers that is largely consistent with the chemical intuition of expert users and is adjustable based on the relative importance of different chemical features for a given similarity problem. This method gives a reliable solution to quantitatively calculate the pairwise chemical similarity score for polymers and represents a vital step toward building search engines and quantitative design tools for polymer data.

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Section: ■ Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Quantifying Pairwise Similarity for Complex Polymers

Shi,

Rebello,

Walsh

et al. 2023

Macromolecules

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“…Once the molecules are represented as ErGs, we can compare them by means of the Graph Edit Distance (GED) [ 47 , 48 ]. The GED is defined as the minimum cost of transformations required to convert one graph into the other.…”

Section: Methodsmentioning

confidence: 99%

Ligand-Based Virtual Screening Based on the Graph Edit Distance

Rica

Álvarez

Serratosa

2021

IJMS

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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.

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“…When pattern represented using graphs, the pattern matching problem turns out to be determining the similarity of graphs, which is generally known as graph matching (3)(4)(5) . A basic concept for finding the similarity between graphs is the edit distance, based on a set of edit operations (6) . The matching process is the alternative name for searching a graph or subgraph isomorphism when using graphs for pattern representation.…”

Section: Introductionmentioning

confidence: 99%

Classification and Recognition of Bilingual Text Using Graph Edit Distance Based Degree of Similarity

Roopa¹,

Mahantesh²

2022

IJST

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Objectives: Graph Edit distance-based classification and recognition method is introduced in this study for bilingual characters. Specifically, this method aims to classify characters first and then recognize them in the 2nd level. Methods: This study combines both exact graph matching and inexact graph matching techniques to achieve better Recognition. The exact graph matching technique classifies characters by considering the number of vertices and edges as features to classify. Inexact graph matching uses an algorithmic model to measure the degree of similarity in the length of edit operations. Findings: The proposed model can compute, if not optimal, sequences all the time, at least near-optimal edit sequence. The proposed model is based on dynamic programming. Edit distance is estimated by comparing preorder sequences of the respective binary trees. Finally, this model uses the loss function to recognize text accurately. To bring out the practicality of the proposed model, we present a case study on the classification of English alphabets and Kannada conjunct consonants. Novelty: (i) A hybrid approach for converting a large class classification problem into a small classification problem that takes advantage of both exact and inexact graph matching techniques. (ii) An algorithmic model is designed to represent each character as a unique string. (iii) Uses dynamic programming in the right places to get the optimal tree, and (iv) to convert the graph matching problem to a string matching problem reduces the time complexity of the problem.

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Redefining the Graph Edit Distance

Cited by 10 publications

References 35 publications

Quantifying Pairwise Similarity for Complex Polymers

Quantifying Pairwise Similarity for Complex Polymers

Ligand-Based Virtual Screening Based on the Graph Edit Distance

Classification and Recognition of Bilingual Text Using Graph Edit Distance Based Degree of Similarity

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