Principal component analysis on a torus: Theory and application to protein dynamics.
Principal component analysis on a torus: Theory and application to protein dynamics.
复制标题
环面的主成分分析：蛋白质动力学的理论和应用。
作者：
F. Sittel;T. Filk;G. Stock
提出了一种基于圆环上数据点的主成分分析的高维圆形数据降维方法。采用主成分分析的几何观点，引入了环面上的各种距离度量，并讨论了将数据投影到主子空间的相关问题。其主要思想是通过对数据进行变换，使采样的最大间隔向周期边界移动，从而使(周期性引起的)投影误差最小化。在第二步中，可以以标准方式计算协方差矩阵及其特征分解。采用分子动力学方法对两个成熟的生物分子体系(Aib9和Villin Headage)进行了分子动力学模拟，证明了该方法在分析主链二面角动力学方面的潜力。新的方法允许一个稳健的和明确定义的亚稳态结构，并提供准确描述自由能格局的低维反应坐标。此外，它还提供了关于角度变量的协方差和主成分的直接解释。除了在主成分分析中的应用外，最大空位移法具有通用性，可以应用于任何其他圆形数据的降维方法。
A dimensionality reduction method for high-dimensional circular data is developed, which is based on a principal component analysis (PCA) of data points on a torus. Adopting a geometrical view of PCA, various distance measures on a torus are introduced and the associated problem of projecting data onto the principal subspaces is discussed. The main idea is that the (periodicity-induced) projection error can be minimized by transforming the data such that the maximal gap of the sampling is shifted to the periodic boundary. In a second step, the covariance matrix and its eigendecomposition can be computed in a standard manner. Adopting molecular dynamics simulations of two well-established biomolecular systems (Aib9 and villin headpiece), the potential of the method to analyze the dynamics of backbone dihedral angles is demonstrated. The new approach allows for a robust and well-defined construction of metastable states and provides low-dimensional reaction coordinates that accurately describe the free energy landscape. Moreover, it offers a direct interpretation of covariances and principal components in terms of the angular variables. Apart from its application to PCA, the method of maximal gap shifting is general and can be applied to any other dimensionality reduction method for circular data.
影响因子：
3.3
作者：
Jain, Abhinav;Stock, Gerhard
通讯作者：
Stock, Gerhard
影响因子：
4.4
作者：
Prinz, Jan-Hendrik;Wu, Hao;Noe, Frank
通讯作者：
Noe, Frank
影响因子：
5.6
作者：
Maisuradze, Gia G.;Liwo, Adam;Scheraga, Harold A.
通讯作者：
Scheraga, Harold A.