Description Usage Arguments Value Author(s) References Examples
For manifold-valued data, Fréchet mean is the solution of following cost function,
\textrm{min}_x ∑_{i=1}^n ρ^2 (x, x_i),\quad x\in\mathcal{M}
for a given data \{x_i\}_{i=1}^n and ρ(x,y) is the geodesic distance between two points on manifold \mathcal{M}. It uses a gradient descent method with a backtracking search rule for updating.
1 | rbase.mean(input, maxiter = 496, eps = 1e-06, parallel = FALSE)
|
input |
a S3 object of |
maxiter |
maximum number of iterations for gradient descent algorithm. |
eps |
stopping criterion for the norm of gradient. |
parallel |
a flag for enabling parallel computation. |
a named list containing
an estimate Fréchet mean.
number of iterations until convergence.
Kisung You
karcher_riemannian_1977RiemBase
\insertRefkendall_probability_1990RiemBase
\insertRefafsari_convergence_2013RiemBase
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ### Generate 100 data points on Sphere S^2 near (0,0,1).
ndata = 100
theta = seq(from=-0.99,to=0.99,length.out=ndata)*pi
tmpx = cos(theta) + rnorm(ndata,sd=0.1)
tmpy = sin(theta) + rnorm(ndata,sd=0.1)
### Wrap it as 'riemdata' class
data = list()
for (i in 1:ndata){
tgt = c(tmpx[i],tmpy[i],1)
data[[i]] = tgt/sqrt(sum(tgt^2)) # project onto Sphere
}
data = riemfactory(data, name="sphere")
### Compute Fréchet Mean
out1 = rbase.mean(data)
out2 = rbase.mean(data,parallel=TRUE) # test parallel implementation
|
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