View source: R/hausdInterval.R
hausdInterval | R Documentation |
hausdInterval
computes a confidence interval for the Hausdorff distance between a point cloud X
and the underlying manifold from which X
was sampled. See Details and References.
hausdInterval(
X, m, B = 30, alpha = 0.05, parallel = FALSE,
printProgress = FALSE)
X |
an |
m |
the size of the subsamples. |
B |
the number of subsampling iterations. The default value is |
alpha |
|
parallel |
logical: if |
printProgress |
if |
For B
times, the subsampling algorithm subsamples m
points of X
(without replacement) and computes the Hausdorff distance between the original sample X
and the subsample. The result is a sequence of B
values. Let q
be the (1-alpha
) quantile of these values and let c = 2 * q
. The interval [0, c]
is a valid (1-alpha
) confidence interval for the Hausdorff distance between X
and the underlying manifold, as proven in (Fasy, Lecci, Rinaldo, Wasserman, Balakrishnan, and Singh, 2013, Theorem 3).
The function hausdInterval
returns a number c
. The confidence interval is [0, c]
.
Fabrizio Lecci
Fasy BT, Lecci F, Rinaldo A, Wasserman L, Balakrishnan S, Singh A (2013). "Statistical Inference For Persistent Homology: Confidence Sets for Persistence Diagrams." (arXiv:1303.7117). Annals of Statistics.
bootstrapBand
X <- circleUnif(1000)
interval <- hausdInterval(X, m = 800)
print(interval)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.