Identifying transition states of chemical kinetic systems using network embedding techniques. (English) Zbl 1471.92140
Summary: Many chemical and biochemical systems can be intuitively modeled using networks. Due to the size and complexity of many biochemical networks, we require tools for efficient network analysis. Of particular interest are techniques that embed network vertices into vector spaces while preserving important properties of the original graph. In this article, we introduce a new method for generating low-dimensional node embeddings for directed graphs, using random walk sampling methods for feature learning on networks. Additionally, we demonstrate the usefulness of this method for identifying transition states of stochastic chemical reacting systems. Network representations of chemical systems are typically given by weighted directed graphs, and are often complex and high dimensional. In order to deal with networks representing these chemical systems, therefore, we modified objective functions adopted in existing random walk based network embedding methods to handle directed graphs and neighbors of different degrees. Through optimization via gradient ascent, we embed the weighted graph vertices into a low-dimensional vector space \({\mathbb{R}}^d\) while preserving the neighborhood of each node. These embeddings may then be used to detect relationships between nodes and study the structure of the original network. We then demonstrate the effectiveness of our method on dimension reduction through several examples regarding identification of transition states of chemical reactions, especially for entropic systems.
MSC:
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 92E20 | Classical flows, reactions, etc. in chemistry |
| 60G50 | Sums of independent random variables; random walks |
References:
| [1] | P, Graph embedding techniques, applications, and performance: a survey, Knowledge-Based Syst., 151, 78-94, 2018 |
| [2] | H, A comprehensive survey of graph embedding: problems, techniques, and applications, IEEE Trans. Knowl. Data Eng., 30, 1616-1637, 2018 |
| [3] | F, Laplacians and the cheeger inequality for directed graphs, Ann. Combinatorics, 9, 1-19, 2005 · Zbl 1059.05070 |
| [4] | M. Chen, Q. Yang, X. Tang, Directed graph embedding, in IJCAI International Joint Conferenceon Artificial Intelligence, (2007), 2707-2712. |
| [5] | D. Zhou, J. Huang, B. Schoelkopf, Learning from labeled and unlabeled data on a directed graph, in Proceedings of the 22nd International Conference on Machine Learning, Association for Computing Machinery, (2005), 1036-1043. |
| [6] | M. Belkin, P. Niyogi, Laplacian eigenmaps and spectral techniques for embedding and clustering, in Advances in Neural Information Processing Systems, MIT Press, (2002), 585-591. |
| [7] | S, Nonlinear dimensionality reduction by locally linear embedding, Science, 290, 2323-2326, 2001 |
| [8] | A. Ahmed, N. Shervashidze, S. Narayanamurthy, V. Josifovski, A. Smola, Distributed large-scale natural graph factorization, in WWW 2013-Proceedings of the 22nd International Conference onWorld Wide Web, (2013), 37-48. |
| [9] | B. Perozzi, R. Al-Rfou, S. Skiena, Deepwalk: Online learning of social representations, in Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and DataMining, 2014. |
| [10] | A. Grover, J. Leskovec, node2vec: Scalable feature learning for networks, in KDD: ProceedingsInternational Conference on Knowledge Discovery and Data Mining, 2016 (2016), 855-864. |
| [11] | E, The transition state method, Trans. Faraday Soc., 34, 29-41, 1938 |
| [12] | P, Transition path sampling: throwing ropes over rough mountain passes in the dark, Ann. Rev. Phys. Chem., 53, 291-318, 2002 |
| [13] | E, Towards a theory of transition paths, J. Stat. Phys., 123, 503-523, 2006 · Zbl 1101.82016 |
| [14] | R, Sampling rare switching events in biochemical networks, Phys. Rev. Lett., 94, 018104, 2005 |
| [15] | S. Cao, W. Lu, Q. Xu, Grarep: Learning graph representations with global structural information, in CIKM’15: Proceedings of the 24th ACM International on Conference on Information andKnowledge Management, (2015), 891-900. |
| [16] | T. Mikolov, I. Sutskever, K. Chen, G. Corrado, J. Dean, Distributed representations of words and phrases and their compositionality, in Advances in Neural Information Processing Systems, 26 (2013). |
| [17] | F, The graph neural network model, IEEE Trans. Neural Networks, 20, 61-80, 2009 |
| [18] | P, Transition path theory for markov jump processes, Mult. Mod. Sim., 7, 1192-1219, 2008 · Zbl 1185.60086 |
| [19] | C, Handbook of stochastic methods for physics, chemistry and the natural sciences, Biometrics, 42, 226, 1986 · Zbl 0676.60004 |
| [20] | P, Illustration of transition path theory on a collection of simple examples, J. Chem. Phys., 125, 084110, 2006 |
| [21] | J. Du, D. Liu, Transition states of stochastic chemical reaction networks, Comm. Comp. Phys., in press. |
| [22] | R, Stochastic vs. deterministic modeling of intracellular viral kinetics, J. Theor. Biol., 218, 309-321, 2002 |
| [23] | D, Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys., 115, 1716-1733, 2001 |
| [24] | R, Stochastic kinetic analysis of the escherichia coli stress circuit using σ32-targeted antisense, Biotechnol. Bioeng., 75, 120-129, 2001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
