Time-lagged independent component analysis

Time-lagged independent component analysis (tICA) is a dimensionality reduction tool for finding the slowest modes of motion in MD simulations (1,2). In contrast with PCA, which finds directions of maximal variance, tICA finds the rarest events. This is useful when building Markov State Models. Some studies have used independent components as collective variables for metadynamics simulations.

Details

1. Two covariance matrices, $\mathbf{C}(0)$ and $\mathbf{C}(\tau )$, are constructed from the MD data, where $\tau$ is a user-defined time lag.
2. $\mathbf{C}(\tau )$ is symmetrized: $\mathbf{C}(\tau )=\frac{{\mathbf{C}}_d(\tau )+{\mathbf{C}}_d^T(\tau )}{2}$
3. Generalized eigenvalue problem is solved: $\mathbf{C}(\tau )\mathbf{U}=\mathbf{C}(0)\mathbf{U\Lambda }$
4. Projection onto tICA space via a sub-matrix of $\mathbf{U}$: ${\mathbf{z}}^T(t)={\mathbf{r}}^T\mathbf{U}$

Figures

Ref http://docs.markovmodel.org/lecture_tica.html

1.

Schwantes CR, Pande VS. Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9. Journal of Chemical Theory and Computation. 2013;9(4):2000–9. Available from: https://doi.org/10.1021/ct300878a

2.

Pérez-Hernández G, Paul F, Giorgino T, De Fabritiis G, Noé F. Identification of slow molecular order parameters for Markov model construction. The Journal of Chemical Physics. 2013;139(1). Available from: https://doi.org/10.1063/1.4811489