Before revision:  The proposed procedure applies a dimensionality reduction technique via principal component analysis to the point cloud of the Takens' embedding from the observed time series and then evaluates the persistence landscape and silhouettes based on the corresponding Rips complex .
After revision:  Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the underlying dynamical system for an observed time series and then evaluates the persistence landscape and silhouettes based on the corresponding Rips complex .