局部线性嵌入算法(Locally Linear Embedding LLE)是一种功能强大的数据降维方法,但它在处理稀疏数据源时的失效问题限制了其广泛应用,且至今没有一个完善的解决方案。为解决这一问题,从算法原理和执行过程两方面分析算法失效原因,把算...局部线性嵌入算法(Locally Linear Embedding LLE)是一种功能强大的数据降维方法,但它在处理稀疏数据源时的失效问题限制了其广泛应用,且至今没有一个完善的解决方案。为解决这一问题,从算法原理和执行过程两方面分析算法失效原因,把算法的两个优化过程联合优化,对算法进行改进。通过对S曲线稀疏采样模拟稀疏数据源,把改进前后的算法对样本点实验结果进行对比,验证了算法改进的有效性;同时,用改进后的算法处理人脸数据,展示了改进后算法的实用价值。改进后的算法将进一步促进局部线性嵌入在工程和研究领域的应用,极大地改善了算法的性能。展开更多
Deriving reaction coordinates for the characterization of chemical reactions has long been a demanding task.In our previous work[ACS Cent.Sci.3,407(2017)],the reaction coordinate of a(retro-)Claisen rearrangement in a...Deriving reaction coordinates for the characterization of chemical reactions has long been a demanding task.In our previous work[ACS Cent.Sci.3,407(2017)],the reaction coordinate of a(retro-)Claisen rearrangement in aqueous solution optimized through a Bayesian measure,a linear combination of bond lengths formation and breakage,was judged to be optimal among all trails.Here,considering the nonlinearity of the transition state,we use isometric mapping and locally linear embedding to obtain one reaction coordinate which is composed of a few collective variables.With these methods,we find a more reasonable and powerful one-dimensional reaction coordinate,which can well describe the reaction progression.To explore the reaction mechanism,we analyze the contribution of intrinsic molecular properties and the solventsolute interactions to the nonlinear reaction coordinate.Furthermore,another coordinate is identified to characterize the heterogeneity of reaction mechanisms.展开更多
文摘局部线性嵌入算法(Locally Linear Embedding LLE)是一种功能强大的数据降维方法,但它在处理稀疏数据源时的失效问题限制了其广泛应用,且至今没有一个完善的解决方案。为解决这一问题,从算法原理和执行过程两方面分析算法失效原因,把算法的两个优化过程联合优化,对算法进行改进。通过对S曲线稀疏采样模拟稀疏数据源,把改进前后的算法对样本点实验结果进行对比,验证了算法改进的有效性;同时,用改进后的算法处理人脸数据,展示了改进后算法的实用价值。改进后的算法将进一步促进局部线性嵌入在工程和研究领域的应用,极大地改善了算法的性能。
基金supported by the National Nature Science Foundation of China(No.21927901 and No.92053202 to Yi Qin Gao)Zhen Zhang is supported by the Education Department of Hebei Province(QN2018308)+1 种基金Post-doctoral Foundation Project of Tangshan Normal University(2018A03)the Nature Science Foundation of Hebei Province of China(E2019105073)。
文摘Deriving reaction coordinates for the characterization of chemical reactions has long been a demanding task.In our previous work[ACS Cent.Sci.3,407(2017)],the reaction coordinate of a(retro-)Claisen rearrangement in aqueous solution optimized through a Bayesian measure,a linear combination of bond lengths formation and breakage,was judged to be optimal among all trails.Here,considering the nonlinearity of the transition state,we use isometric mapping and locally linear embedding to obtain one reaction coordinate which is composed of a few collective variables.With these methods,we find a more reasonable and powerful one-dimensional reaction coordinate,which can well describe the reaction progression.To explore the reaction mechanism,we analyze the contribution of intrinsic molecular properties and the solventsolute interactions to the nonlinear reaction coordinate.Furthermore,another coordinate is identified to characterize the heterogeneity of reaction mechanisms.
