property GPCCA.optimal_crispness: float | None

Crispness for clustering into n_m clusters.

The crispness \(\xi \in [0,1]\) quantifies the optimality of the solution (higher is better). It characterizes how crisp (sharp) the decomposition of the state space into m clusters is. It is given via (Eq. 17 from [Roeblitz13]):

\[\xi = (m - f_{opt}) / m = \mathtt{trace}(S) / m = \mathtt{trace}(\tilde{D} \chi^T D \chi) / m\]

with \(D\) being a diagonal matrix with \(\eta\) on its diagonal.