persistenceChangePoint: Persistence Diagram Change Point Detection

In speegled/cpbaywave: Bayesian Wavelet based Change Point Detection

Persistence Diagram Change Point Detection

Description

Computes the persistence diagrams of a time series of multi-dimensional data. Determines where the most likely change point occurs.

Usage

persistenceChangePoint(
  multiSeries,
  maxDimension,
  maxScale,
  useWasserstein = TRUE,
  useBootstrap = FALSE,
  ...
)

Arguments

multiSeries	A list of matrices, where each row of the matrix corresponds to a point in Euclidean space.
maxDimension	Maximum dimensional topological features to detect in persistence diagram.
maxScale	Maximum scale to consider in persistence diagrams.
useWasserstein	set to False to use bottleneck L^\infty distance.
useBootstrap	set to TRUE if you want to bootstrap the change point locations. Not advisable unless the time series length is equal to a power of 2 or slighlty less than a power of 2.
...	additional parameters passed to the distance function

Details

The algorithm computes the wasserstein (L^2) distance between each pair of persistence diagrams, and finds the most likely change point in the distances. Note that the multiSeries in this case must be a *list* of matrices with N columns, where each row corresponds to a point in R^N.

Value

value The BFIC value associated with change point. Bigger than 3 is considered significant.

index The five most likely change points.

Examples

Circles <- lapply(1:30, function(x) {
Circle1 <- TDA::circleUnif(60);
Circle2 <- TDA::circleUnif(60, r = 2) + 3;
rbind(Circle1, Circle2);})
Circles2 <- lapply(1:34, function(x) {
  Circle1 <- TDA::circleUnif(40);
  Circle2 <- TDA::circleUnif(40, r = 2) + 5;
  Circle3 <- TDA::circleUnif(40,r = 3) - 10;
  rbind(Circle1, Circle2, Circle3);})
Circles <- c(Circles, Circles2)
persistenceChangePoint(Circles, maxDimension = 1, maxScale = 2) #True change point at t = 31

speegled/cpbaywave documentation built on Feb. 19, 2024, 11:13 a.m.