Time-dependent principal component analysis: A unified approach to high-dimensional data reduction using adiabatic dynamics.

Systematic reduction of the dimensionality is highly demanded in making a comprehensive interpretation of experimental and simulation data. Principal component analysis (PCA) is a widely used technique for reducing the dimensionality of molecular dynamics (MD) trajectories, which assists our understanding of MD simulation data. Here, we propose an approach that incorporates time dependence in the PCA algorithm. In the standard PCA, the eigenvectors obtained by diagonalizing the covariance matrix are time independent. In contrast, they are functions of time in our new approach, and their time evolution is implemented in the framework of Car-Parrinello or Born-Oppenheimer type adiabatic dynamics. Thanks to the time dependence, each of the step-by-step structural changes or intermittent collective fluctuations is clearly identified, which are often keys to provoking a drastic structural transformation but are easily masked in the standard PCA. The time dependence also allows for reoptimization of the principal components (PCs) according to the structural development, which can be exploited for enhanced sampling in MD simulations. The present approach is applied to phase transitions of a water model and conformational changes of a coarse-grained protein model. In the former, collective dynamics associated with the dihedral-motion in the tetrahedral network structure is found to play a key role in crystallization. In the latter, various conformations of the protein model were successfully sampled by enhancing structural fluctuation along the periodically optimized PC. Both applications clearly demonstrate the virtue of the new approach, which we refer to as time-dependent PCA.