silhouette | R Documentation |
The function silhouette
computes the silhouette function corresponding to a given persistence diagram.
silhouette(
Diag, p = 1, dimension = 1,
tseq = seq(min(Diag[, 2:3]), max(Diag[, 2:3]), length = 500))
Diag |
an object of class |
p |
a vector: the power of the weights of the silhouette function. See the definition of silhouette function, Section 5 in the reference. |
dimension |
the dimension of the topological features under consideration. The default value is |
tseq |
a vector of values at which the silhouette function is evaluated. |
The function silhouette
returns a numeric matrix of with the number of row as the length of tseq
and the number of column as the length of p
. The value at ith row and jth column represents the value of the p[j]
-th power silhouette function evaluated at tseq[i]
.
Fabrizio Lecci
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)
landscape
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 silhouette
tseq <- seq(0, DiagLim, length = 1000)
Sil <- silhouette(Diag, p = 1, dimension = 1, tseq)
par(mfrow = c(1, 2))
plot.diagram(Diag)
plot(tseq, Sil, type = "l", xlab = "t", ylab = "silhouette", asp = 1)
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