An Inverse QSAR Method Based on a Two-Layered Model and Integer Programming

Shi, Yu; Zhu, Jianshen; Azam, Naveed Ahmed; Haraguchi, Kazuya; Zhao, Liang; Nagamochi, Hiroshi; Akutsu, Tatsuya

doi:10.3390/ijms22062847

Cited by 7 publications

(17 citation statements)

References 21 publications

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“…Results on Phase 2. To execute Stages 4 and 5 in Phase 2, we used a set of seven instances I a , I i b , i ∈ [1,4], I c and I d based on seed graphs prepared by Shi et al [25]. We here present their seed graphs G C (see Appendix B for the details of I a and Appendix C for the details of I i b , i ∈ [1,4], I c and I d ).…”

Section: Resultsmentioning

confidence: 99%

“…Topological Specification A topological specification is described as a set of the following rules proposed by Shi et al [25] and modified by Tanaka et al [26] from G C by replacing some edges a = uv with paths P a between the end-vertices u and v and by attaching new paths Q v to some vertices v. For example, a chemical graph C in Figure 2 is constructed from the seed graph G C in Figure 4(a) as follows.…”

Section: Two-layered Modelmentioning

confidence: 99%

“…Two-layered Model Recently Shi et al [25] proposed a new model, called a two-layered model for representing the feature of a chemical graph in order to deal with an arbitrary graph in the framework and refined the set of rules for describing a topological specification so that a prescribed structure can be included in both of the acyclic and cyclic parts of C. In the two-layered model, a chemical graph C with a parameter ρ ≥ 1 is regarded as two parts: the exterior and the interior of the hydrogen-suppressed chemical graph C obtained from C by removing hydrogen. The exterior consists of maximal acyclic induced subgraphs with height at most ρ in C and the interior is the connected subgraph of C obtained by ignoring the exterior.…”

Section: Introductionmentioning

confidence: 99%

“…The exterior consists of maximal acyclic induced subgraphs with height at most ρ in C and the interior is the connected subgraph of C obtained by ignoring the exterior. Shi et al [25] defined a feature vector f (C) of a chemical graph C to be a combination of the frequency of adjacent atom pairs in the interior and the frequency of chemical acyclic graphs among the set of chemical rooted trees T u rooted at interior-vertices u. Recently, Tanaka et al [26] extend the model to treat a chemical graph with hydrogens directly so that more variety of chemical rooted trees represent the feature of the exterior.…”

Section: Introductionmentioning

confidence: 99%

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An Inverse QSAR Method Based on Linear Regression and Integer Programming

Zhu¹,

Azam²,

Haraguchi³

et al. 2021

Preprint

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Recently a novel framework has been proposed for designing the molecular structure of chemical compounds using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). In the framework, we first define a feature vector f (C) of a chemical graph C and construct an ANN that maps x = f (C) to a predicted value η(x) of a chemical property π to C. After this, we formulate an MILP that simulates the computation process of f (C) from C and that of η(x) from x. Given a target value y * of the chemical property π, we infer a chemical graph C † such that η(f (C † )) = y * by solving the MILP. In this paper, we use linear regression to construct a prediction function η instead of ANNs. For this, we derive an MILP formulation that simulates the computation process of a prediction function by linear regression. The results of computational experiments suggest our method can infer chemical graphs with around up to 50 non-hydrogen atoms.

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Section: Resultsmentioning

confidence: 99%

Section: Two-layered Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Inverse QSAR Method Based on Linear Regression and Integer Programming

Zhu¹,

Azam²,

Haraguchi³

et al. 2021

Preprint

Self Cite

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show abstract

“…In Stage 5, we generate other chemical graphs C * such that η(f (C * )) = y * based on the output chemical graph C † . Two-layered Model Recently Shi et al [17] proposed a new model, called a two-layered model for representing the feature of a chemical graph in order to deal with an arbitrary graph in the framework and refined the set of rules for describing a topological specification so that a prescribed structure can be included in both of the acyclic and cyclic parts of C. In the two-layered model, a chemical graph C with a parameter ρ ≥ 1 is regarded as two parts: the exterior and the interior of the hydrogensuppressed chemical graph ⟨C⟩ obtained from C by removing hydrogen. The exterior consists of maximal acyclic induced subgraphs with height at most ρ in ⟨C⟩ and the interior is the connected subgraph of ⟨C⟩ obtained by ignoring the exterior.…”

Section: Introductionmentioning

confidence: 99%

A Method for Molecular Design Based on Linear Regression and Integer Programming

Zhu

Azam

Haraguchi

et al. 2022

2022 12th International Conference on Bioscience, Biochemistry and Bioinformatics

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Recently a novel framework has been proposed for designing the molecular structure of chemical compounds using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). In the framework, we first define a feature vector f (C) of a chemical graph C and construct an ANN that maps x = f (C) to a predicted value η(x) of a chemical property π to C. After this, we formulate an MILP that simulates the computation process of f (C) from C and that of η(x) from x. Given a target value y * of the chemical property π , we infer a chemical graph C † such that η(f (C † )) = y * by solving the MILP. In this paper, we use linear regression to construct a prediction function η instead of ANNs. For this, we derive an MILP formulation that simulates the computation process of a prediction function by linear regression. The results of computational experiments suggest our method can infer chemical graphs with around up to 50 non-hydrogen atoms. CCS CONCEPTS• Computing methodologies → Machine learning; • Mathematics of computing → Integer programming; • Applied computing → Bioinformatics.

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