Computes Persistence Scores For a Single Time-Series Across a Single Lag

Takes a vector of numeric gene expression over time and computes the persistence score. The specified lag is used to transform the expression into a 3-D embedded space via time-delay embedding. A non-linear dimension reduction technique (laplacian eigenmaps) is used to transfrom the 3-D embedding to a 2-D embedding. Finally, the persistence score of the 2-D embedding is calculated via persistence homology. Returns the Max persistence score, returns 0 if no persistence score exists. For more details see TimeCycle's vignette: vignette("TimeCycle").

getPersistence(timeSeries, lag, laplacian = T)

Arguments

timeSeries	a vector of numeric time-series expression values.
lag	a numeric specifying the Lag to use for in the 3-D time delayed embedding.
laplacian	a logical scalar. Should the Laplacian Eigenmaps be used for dimensionality reduction? Default TRUE.

Value

the max persistence score at the specified lag, returns 0 if no persistence score exists.

References

• Wadhwa RR, Williamson DFK, Dhawan A, Scott JG. (2018). "TDAstats: R pipeline for computing persistent homology in topological data analysis." Journal of Open Source Software. 2018; 3(28): 860. doi:[10.21105/joss.00860]

• Bauer U. (2019). "Ripser: Efficient computation of Vietoris-Rips persistence barcodes." arXiv: 1908.02518.

See also

• calculate_homology for Persistence Homology calculation.

• buildTakens_ndim for for generating time-delay embedding.

• computeLaplacianEmbedding for 3-D to 2-D laplacian eigenmaps dimension reduction.

• computePersistence for use parallelized function for a data.frame of gene expression.