A detachment algorithm for inferring a graph from path frequency

Abstract: Inferring graphs from path frequency has been studied as an important problem which has a potential application to drug design and elucidation of chemical structures. Given a multiple set g of strings of labels with length at most K, the problem asks to find a vertex-labeled graph G that attains a one-to-one correspondence between g and the occurrences of labels along all paths of length at most K in G. In this paper, we prove that the problem with K = 1 can be formulated as a problem of finding a loopless and connected detachment, based on which an efficient algorithm for solving the problem is derived. Our algorithm also solves the problem with an additional constraint such that every vertex in an inferred graph is required to have a specified degree

A New Integer Linear Programming Formulation to the Inverse QSAR/QSPR for Acyclic Chemical Compounds Using Skeleton Trees

33rd International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, IEA/AIE 2020, Kitakyushu, Japan, September 22-25, 2020.Computer-aided drug design is one of important application areas of intelligent systems. Recently a novel method has been proposed for inverse QSAR/QSPR using both artificial neural networks (ANN) and mixed integer linear programming (MILP), where inverse QSAR/QSPR is a major approach for drug design. This method consists of two phases: In the first phase, a feature function f is defined so that each chemical compound G is converted into a vector f(G) of several descriptors of G, and a prediction function ψ is constructed with an ANN so that ψ(f(G)) takes a value nearly equal to a given chemical property π for many chemical compounds G in a data set. In the second phase, given a target value y∗ of the chemical property π , a chemical structure G∗ is inferred in the following way. An MILP M is formulated so that M admits a feasible solution (x∗, y∗) if and only if there exist vectors x∗, y∗ and a chemical compound G∗ such that ψ(x∗)=y∗ and f(G∗)=x∗. The method has been implemented for inferring acyclic chemical compounds. In this paper, we propose a new MILP for inferring acyclic chemical compounds by introducing a novel concept, skeleton tree, and conducted computational experiments. The results suggest that the proposed method outperforms the existing method when the diameter of graphs is up to around 6 to 8. For an instance for inferring acyclic chemical compounds with 38 non-hydrogen atoms from C, O and S and diameter 6, our method was 5×104 times faster

A Linear Programming Approach for Molecular QSAR analysis

Small molecules in chemistry can be represented as graphs. In a quantitative structure-activity relationship (QSAR) analysis, the central task is to find a regression function that predicts the activity of the molecule in high accuracy. Setting a QSAR as a primal target, we propose a new linear programming approach to the graph-based regression problem. Our method extends the graph classification algorithm by Kudo et al. (NIPS 2004), which is a combination of boosting and graph mining. Instead of sequential multiplicative updates, we employ the linear programming boosting (LP) for regression. The LP approach allows to include inequality constraints for the parameter vector, which turns out to be particularly useful in QSAR tasks where activity values are sometimes unavailable. Furthermore, the efficiency is improved significantly by employing multiple pricing

A novel method for inference of chemical compounds of cycle index two with desired properties based on artificial neural networks and integer programming

Inference of chemical compounds with desired properties is important for drug design, chemo-informatics, and bioinformatics, to which various algorithmic and machine learning techniques have been applied. Recently, a novel method has been proposed for this inference problem using both artificial neural networks (ANN) and mixed integer linear programming (MILP). This method consists of the training phase and the inverse prediction phase. In the training phase, an ANN is trained so that the output of the ANN takes a value nearly equal to a given chemical property for each sample. In the inverse prediction phase, a chemical structure is inferred using MILP and enumeration so that the structure can have a desired output value for the trained ANN. However, the framework has been applied only to the case of acyclic and monocyclic chemical compounds so far. In this paper, we significantly extend the framework and present a new method for the inference problem for rank-2 chemical compounds (chemical graphs with cycle index 2). The results of computational experiments using such chemical properties as octanol/water partition coefficient, melting point, and boiling point suggest that the proposed method is much more useful than the previous method

A novel method for inference of acyclic chemical compounds with bounded branch-height based on artificial neural networks and integer programming

Analysis of chemical graphs is becoming a major research topic in computational molecular biology due to its potential applications to drug design. One of the major approaches in such a study is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a novel two-phase framework has been proposed for inverse QSAR/QSPR, where in the first phase an artificial neural network (ANN) is used to construct a prediction function. In the second phase, a mixed integer linear program (MILP) formulated on the trained ANN and a graph search algorithm are used to infer desired chemical structures. The framework has been applied to the case of chemical compounds with cycle index up to 2 so far. The computational results conducted on instances with n non-hydrogen atoms show that a feature vector can be inferred by solving an MILP for up to n=40, whereas graphs can be enumerated for up to n=15. When applied to the case of chemical acyclic graphs, the maximum computable diameter of a chemical structure was up to 8. In this paper, we introduce a new characterization of graph structure, called “branch-height” based on which a new MILP formulation and a new graph search algorithm are designed for chemical acyclic graphs. The results of computational experiments using such chemical properties as octanol/water partition coefficient, boiling point and heat of combustion suggest that the proposed method can infer chemical acyclic graphs with around n=50 and diameter 30

A constructive approach for discovering new drug leads: Using a kernel methodology for the inverse-QSAR problem

<p>Abstract</p> <p>Background</p> <p>The inverse-QSAR problem seeks to find a new molecular descriptor from which one can recover the structure of a molecule that possess a desired activity or property. Surprisingly, there are very few papers providing solutions to this problem. It is a difficult problem because the molecular descriptors involved with the inverse-QSAR algorithm must adequately address the forward QSAR problem for a given biological activity if the subsequent recovery phase is to be meaningful. In addition, one should be able to construct a feasible molecule from such a descriptor. The difficulty of recovering the molecule from its descriptor is the major limitation of most inverse-QSAR methods.</p> <p>Results</p> <p>In this paper, we describe the reversibility of our previously reported descriptor, the vector space model molecular descriptor (VSMMD) based on a vector space model that is suitable for kernel studies in QSAR modeling. Our inverse-QSAR approach can be described using five steps: (1) generate the VSMMD for the compounds in the training set; (2) map the VSMMD in the input space to the kernel feature space using an appropriate kernel function; (3) design or generate a new point in the kernel feature space using a kernel feature space algorithm; (4) map the feature space point back to the input space of descriptors using a pre-image approximation algorithm; (5) build the molecular structure template using our VSMMD molecule recovery algorithm.</p> <p>Conclusion</p> <p>The empirical results reported in this paper show that our strategy of using kernel methodology for an inverse-Quantitative Structure-Activity Relationship is sufficiently powerful to find a meaningful solution for practical problems.</p

Reconstruction of Trees from Jumbled and Weighted Subtrees

Let T be an edge-labeled graph, where the labels are from a finite alphabet Sigma. For a subtree U of T the Parikh vector of U is a vector of length |Sigma| which specifies the multiplicity of each label in U. We ask when T can be reconstructed from the multiset of Parikh vectors of all its subtrees, or all of its paths, or all of its maximal paths. We consider the analogous problems for weighted trees. We show how several well-known reconstruction problems on labeled strings, weighted strings and point sets on a line can be included in this framework. We present reconstruction algorithms and non-reconstructibility results, and extend the polynomial method, previously applied to jumbled strings [Acharya et al., SIAM J. on Discr. Math, 2015] and weighted strings [Bansal et al., CPM 2004], to deal with general trees and special tree classes

A Novel Method for Inference of Acyclic Chemical Compounds with Bounded Branch-height Based on Artificial Neural Networks and Integer Programming

Analysis of chemical graphs is a major research topic in computational molecular biology due to its potential applications to drug design. One approach is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a framework has been proposed for inverse QSAR/QSPR using artificial neural networks (ANN) and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, a feature vector $f(G)$ of a chemical graph $G$ is introduced and a prediction function $\psi$ on a chemical property $\pi$ is constructed with an ANN. In the second phase, given a target value $y^*$ of property $\pi$, a feature vector $x^*$ is inferred by solving an MILP formulated from the trained ANN so that $\psi(x^*)$ is close to $y^*$ and then a set of chemical structures $G^*$ such that $f(G^*)= x^*$ is enumerated by a graph search algorithm. The framework has been applied to the case of chemical compounds with cycle index up to 2. The computational results conducted on instances with $n$ non-hydrogen atoms show that a feature vector $x^*$ can be inferred for up to around $n=40$ whereas graphs $G^*$ can be enumerated for up to $n=15$. When applied to the case of chemical acyclic graphs, the maximum computable diameter of $G^*$ was around up to around 8. We introduce a new characterization of graph structure, "branch-height," based on which an MILP formulation and a graph search algorithm are designed for chemical acyclic graphs. The results of computational experiments using properties such as octanol/water partition coefficient, boiling point and heat of combustion suggest that the proposed method can infer chemical acyclic graphs $G^*$ with $n=50$ and diameter 30