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首页> 外文期刊>Molecular informatics >Data Visualization, Regression, Applicability Domains and Inverse Analysis Based on Generative Topographic Mapping
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Data Visualization, Regression, Applicability Domains and Inverse Analysis Based on Generative Topographic Mapping

机译：基于生成地形映射的数据可视化，回归，适用性域和逆分析

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摘要

Abstract This paper introduces two generative topographic mapping (GTM) methods that can be used for data visualization, regression analysis, inverse analysis, and the determination of applicability domains (ADs). In GTM‐multiple linear regression (GTM‐MLR), the prior probability distribution of the descriptors or explanatory variables (X) is calculated with GTM, and the posterior probability distribution of the property/activity or objective variable (y) given X is calculated with MLR; inverse analysis is then performed using the product rule and Bayes’ theorem. In GTM‐regression (GTMR), X and y are combined and GTM is performed to obtain the joint probability distribution of X and y; this leads to the posterior probability distributions of y given X and of X given y, which are used for regression and inverse analysis, respectively. Simulations using linear and nonlinear datasets and quantitative structure‐activity relationship (QSAR) and quantitative structure‐property relationship (QSPR) datasets confirm that GTM‐MLR and GTMR enable data visualization, regression analysis, and inverse analysis considering appropriate ADs. Python and MATLAB codes for the proposed algorithms are available at https://github.com/hkaneko1985/gtm‐generativetopographicmapping.
机译：摘要本文介绍了两种生成的地形映射（GTM）方法，可用于数据可视化，回归分析，逆分析以及适用性域（广告）的确定。在GTM - 多个线性回归（GTM-MLR）中，用GTM计算描述符或解释变量（x）的先前概率分布，并且计算给定x的属性/活动或目标变量（Y）的后验概率分布与MLR;然后使用产品规则和贝叶斯定理进行逆分析。在GTM回归（GTMR）中，组合X和Y，并进行GTM以获得X和Y的关节概率分布;这导致y给定x的后验概率分布分别用于分别用于回归和反向分析。使用线性和非线性数据集和定量结构 - 活动关系（QSAR）和定量结构 - 属性关系（QSPR）数据集的模拟确认GTM-MLR和GTMR能够考虑适当的广告的数据可视化，回归分析和逆分析。用于所提出的算法的Python和Matlab代码可在https://github.com/hkaneko1985/gtm-generativetoppoickmapightmapightmapraphics中获得。

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