landscape | R Documentation |
The function landscape
computes the landscape function corresponding to a given persistence diagram.
landscape(
Diag, dimension = 1, KK = 1,
tseq = seq(min(Diag[,2:3]), max(Diag[,2:3]), length=500))
Diag |
an object of class |
dimension |
the dimension of the topological features under consideration. The default value is |
KK |
a vector: the order of the landscape function. The default value is |
tseq |
a vector of values at which the landscape function is evaluated. |
The function landscape
returns a numeric matrix with the number of row as the length of tseq
and the number of column as the length of KK
. The value at ith row and jth column represents the value of the KK[j]
-th landscape function evaluated at tseq[i]
.
Fabrizio Lecci
Bubenik P (2012). "Statistical topology using persistence landscapes." arXiv:1207.6437.
Chazal F, Fasy BT, Lecci F, Rinaldo A, Wasserman L (2014). "Stochastic Convergence of Persistence Landscapes and Silhouettes." Proceedings of the 30th Symposium of Computational Geometry (SoCG). (arXiv:1312.0308)
silhouette
Diag <- matrix(c(0, 0, 10, 1, 0, 3, 1, 3, 8), ncol = 3, byrow = TRUE)
DiagLim <- 10
colnames(Diag) <- c("dimension", "Birth", "Death")
#persistence landscape
tseq <- seq(0,DiagLim, length = 1000)
Land <- landscape(Diag, dimension = 1, KK = 1, tseq)
par(mfrow = c(1,2))
plot.diagram(Diag)
plot(tseq, Land, type = "l", xlab = "t", ylab = "landscape", asp = 1)
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