rbase.median: Geometric Median of Manifold-valued Data

Description Usage Arguments Value Author(s) References Examples

View source: R/rbase.median.R

Description

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.

Usage

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rbase.median(input, maxiter = 496, eps = 1e-06, parallel = FALSE)

Arguments

input

a S3 object of riemdata class. See riemfactory for more details.

maxiter

maximum number of iterations for gradient descent algorithm.

eps

stopping criterion for the norm of gradient.

parallel

a flag for enabling parallel computation.

Value

a named list containing

x

an estimate geometric median.

iteration

number of iterations until convergence.

Author(s)

Kisung You

References

\insertRef

fletcher_geometric_2009RiemBase

\insertRef

aftab_generalized_2015RiemBase

Examples

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### 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

RiemBase documentation built on Aug. 21, 2021, 5:07 p.m.