count_smooth_maximal: Count local maximal of persistent landscape with smoothing

In hosscine/phacm: The R Package for Analyzing Persistent Homology and Cycles of Manifold

Description

Calculate fuzy betti number of the persistent diagram like human expert.

Usage

count_smooth_maximal(x, ...)

## S3 method for class 'pd'
count_smooth_maximal(x, exist.method = zero_threshold,
  cutoff.method = zero_hat_threshold, spar = seq(0, 1, 0.1),
  plot = TRUE, ...)

## S3 method for class 'pl'
count_smooth_maximal(x, exist.method = zero_threshold,
  cutoff.method = zero_hat_double_threshold, spar = seq(0, 1, 0.1),
  plot = TRUE, ...)

Arguments

x	pd or pl object.
...	other arguments passed to specific methods.
exist.method	the function to compute threshold for judging whther the cycle exists or not on each dimension.
cutoff.method	the function to compute threshold for taking out small persistence holes.
spar	smoothing parameters to be passed stats::smooth.spline().
plot	if TRUE, plot smoothing result.
x	pd object.
...	ignored.
x	pl object.

Details

The number of local maximal of persistent landscape is corresponding to the betti number of the data. However, the counting result is frequently larger than the true betti number because of some jaggies on the persistent landscape. Human experts who analyze persistent landscape calculate the betti number fuzzly to interpret the jaggies. count_smooth_maximal imitates the method of human expert's analysis by counting local maximal of multi resolutional smoothed persistent landscape and meaning it.

Value

counting result.

References

R.Futagami, N. Yamada, T. Shibuya. "Infering Underlying Manifold of Data by the Use of Persistent Homology Analysis." Proc. of 7th Workshop on Computational Topology in Image Context, The Spain, Jan. 2018.

See Also

count_local_maximal(), stats::smooth.spline()

hosscine/phacm documentation built on May 23, 2019, 1:46 p.m.