Coarsegraining Markov state models with PCCA Coarsegraining Markov

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Coarse-graining Markov state models with PCCA

Coarse-graining Markov state models with PCCA

Coarse-graining Markov state models • Coarse-graining Markov state models here means finding a smaller

Coarse-graining Markov state models • Coarse-graining Markov state models here means finding a smaller transition matrix that does a similar job as the large original transition matrix.

Coarse-graining Markov state models • Coarse-graining Markov state models here means finding a smaller

Coarse-graining Markov state models • Coarse-graining Markov state models here means finding a smaller transition matrix that does a similar job as the large original transition matrix. • We have already seen eigendecomposition as a way of reducing the dimension of a transition matrix. Let’s take this as our starting point…

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

The truncated eigendecomposition •

• The dominant eigenvectors can be linearly transformed into indicator functions for the

• The dominant eigenvectors can be linearly transformed into indicator functions for the metastable states. • These indicators are called metastable memberships.

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Coarse-graining with PCCA •

Connection to HMMs (Simon‘s talk) metastable_memberships • metastable_distributions

Connection to HMMs (Simon‘s talk) metastable_memberships • metastable_distributions

Connection to VAMPnets • Soft-max VAMPnets fit indicator functions directly to the transition pairs.

Connection to VAMPnets • Soft-max VAMPnets fit indicator functions directly to the transition pairs. • The indicator functions are modelled as sigmoids.

Finding the metastable memberships

Finding the metastable memberships

Finding the metastable memberships

Finding the metastable memberships

PCCA in Py. Emma •

PCCA in Py. Emma •

Further reading • Susanna Röblitz, Marcus Weber, “Fuzzy spectral clustering by PCCA+: application to

Further reading • Susanna Röblitz, Marcus Weber, “Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification”, Advances in Data Analysis and Classification, 7, 147 (2013) • Marcus Weber, Konstantin Fackeldey, "G-PCCA: Spectral Clustering for Non-reversible Markov Chains", Konrad-Zuse-Zentrum für Informationstechnik Berlin, ZIB-Report 15 -35 (2015)

Appendix: Computing A

Appendix: Computing A

Coarsegraining Markov state models with PCCA Coarsegraining MarkovCoarsegraining Markov state models with PCCA Coarsegraining Markov
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