Description Usage Arguments Value Author(s) References Examples
For manifold-valued data, geometric median is the solution of following cost function,
\textrm{min}_x ∑_{i=1}^n ρ (x, x_i) = ∑_{i=1}^n \| \log_x (x_i) \|,\quad x\in\mathcal{M}
for a given data \{x_i\}_{i=1}^n, ρ(x,y) the geodesic distance between two points on manifold \mathcal{M}, and \| \log_x (y) \| a logarithmic mapping onto the tangent space T_x \mathcal{M}. Weiszfeld's algorithms is employed.
1 | rbase.median(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 geometric median.
number of iterations until convergence.
Kisung You
fletcher_geometric_2009RiemBase
\insertRefaftab_generalized_2015RiemBase
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 Geodesic Median
out1 = rbase.median(data)
out2 = rbase.median(data,parallel=TRUE) # test parallel implementation
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.