Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/alphaShapeDiag.R

The function `alphaShapeDiag`

computes the persistence diagram of the alpha shape filtration built on top of a point cloud in 3 dimension.

1 2 3 | ```
alphaShapeDiag(
X, maxdimension = NCOL(X) - 1, library = "GUDHI", location = FALSE,
printProgress = FALSE)
``` |

`X` |
an |

`maxdimension` |
integer: max dimension of the homological features to be computed. (e.g. 0 for connected components, 1 for connected components and loops, 2 for connected components, loops, voids, etc.) |

`library` |
either a string or a vector of length two. When a vector is given, the first element specifies which library to compute the Alpha Shape filtration, and the second element specifies which library to compute the persistence diagram. If a string is used, then the same library is used. For computing the Alpha Shape filtration, the user can use the library |

`location` |
if |

`printProgress` |
if |

The function `alphaShapeDiag`

constructs the Alpha Shape filtration, using the C++ library GUDHI.
Then for computing the persistence diagram from the Alpha Shape filtration, the user can use either the C++ library GUDHI, Dionysus, or PHAT.
See refereneces.

The function `alphaShapeDiag`

returns a list with the following elements:

`diagram` |
an object of class |

`birthLocation` |
only if |

`deathLocation` |
only if |

`cycleLocation` |
only if |

Jisu Kim and Vincent Rouvreau

Fischer K (2005). "Introduction to Alpha Shapes."

Edelsbrunner H, Mucke EP (1994). "Three-dimensional Alpha Shapes." ACM Trans. Graph.

Maria C (2014). "GUDHI, Simplicial Complexes and Persistent Homology Packages." https://project.inria.fr/gudhi/software/

Morozov D (2008). "Homological Illusions of Persistence and Stability." http://www.mrzv.org/publications/thesis/phd/

Edelsbrunner H, Harer J (2010). "Computational topology: an introduction." American Mathematical Society.

`summary.diagram`

, `plot.diagram`

, `alphaComplexDiag`

, `gridDiag`

, `ripsDiag`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
# input data generated from cylinder
n <- 30
X <- cbind(circleUnif(n = n), runif(n = n, min = -0.1, max = 0.1))
# persistence diagram of alpha shape
DiagAlphaShape <- alphaShapeDiag(
X = X, maxdimension = 1, library = c("GUDHI", "Dionysus"), location = TRUE,
printProgress = TRUE)
# plot diagram and first two dimension of data
par(mfrow = c(1, 2))
plot(DiagAlphaShape[["diagram"]])
plot(X[, 1:2], col = 2, main = "Representative loop of alpha shape filtration")
one <- which(DiagAlphaShape[["diagram"]][, 1] == 1)
one <- one[which.max(
DiagAlphaShape[["diagram"]][one, 3] - DiagAlphaShape[["diagram"]][one, 2])]
for (i in seq(along = one)) {
for (j in seq_len(dim(DiagAlphaShape[["cycleLocation"]][[one[i]]])[1])) {
lines(
DiagAlphaShape[["cycleLocation"]][[one[i]]][j, , 1:2], pch = 19,
cex = 1, col = i)
}
}
par(mfrow = c(1, 1))
``` |

TDA documentation built on April 29, 2018, 1:04 a.m.

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