Vector Summaries of Persistence Diagrams.

Overwiew

The TDAvec package provides implementations of several vector summaries of persistence diagrams studied in Topological Data Analysis (TDA). Each is obtained by discretizing the associated summary function computed from a persistence diagram.

Installation

# install development version from GitHub
devtools::install_github("alexey-luchinsky/TDAvec")

# install development version with vignettes/tutorials
devtools::install_github("alexey-luchinsky/TDAvec", build_vignettes = TRUE)

Sample Code

Example below shows how to use the computeVPB function:

N <- 100 
set.seed(123)
# sample N points uniformly from unit circle and add Gaussian noise
X <- TDA::circleUnif(N,r=1) + rnorm(2*N,mean = 0,sd = 0.2)

# compute a persistence diagram using the Rips filtration built on top of X
D <- TDA::ripsDiag(X,maxdimension = 1,maxscale = 2)$diagram 

# switch from the birth-death to the birth-persistence coordinates
D[,3] <- D[,3] - D[,2] 
colnames(D)[3] <- "Persistence"

# construct one-dimensional grid of scale values
ySeqH0 <- unique(quantile(D[D[,1]==0,3],probs = seq(0,1,by=0.2))) 
tau <- 0.3 # parameter in [0,1] which controls the size of blocks around each point of the diagram 
# compute VPB for homological dimension H_0
computeVPB(D,homDim = 0,xSeq=NA,ySeqH0,tau)

xSeqH1 <- unique(quantile(D[D[,1]==1,2],probs = seq(0,1,by=0.2)))
ySeqH1 <- unique(quantile(D[D[,1]==1,3],probs = seq(0,1,by=0.2)))
# compute VPB for homological dimension H_1
computeVPB(D,homDim = 1,xSeqH1,ySeqH1,tau) 

More information can be found in the package vignette file or help pages of the other functions.

Citations

It you are using TDAvec, consider citing the article

Chan, K. C., Islambekov, U., Luchinsky, A., & Sanders, R. (2022). A computationally efficient framework for vector representation of persistence diagrams. Journal of Machine Learning Research, 23, 1-33.