rbase.robust {RiemBase}

Robust Fréchet Mean of Manifold-valued Data

Description

Robust estimator for mean starts from dividing the data \{x_i\}_{i=1}^n into k equally sized sets. For each subset, it first estimates Fréchet mean. It then follows a step to aggregate k sample means by finding a geometric median.

Usage

rbase.robust(input, k = 5, maxiter = 496, eps = 1e-06, parallel = FALSE)

Arguments

input

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

k

number of subsets for which the data be divided into.

maxiter

maximum number of iterations for gradient descent algorithm and Weiszfeld 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

Lerasle M, Oliveira R~I (2011). “Robust empirical mean Estimators.” ArXiv e-prints. 1112.3914.

Minsker S (2013). “Geometric median and robust estimation in Banach spaces.” ArXiv e-prints. 1308.1334.

Feng J, Xu H, Mannor S (2014). “Distributed Robust Learning.” ArXiv e-prints. 1409.5937.

See Also

rbase.mean, rbase.median

Examples

### 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 Robust Fréchet Mean
out1 = rbase.robust(data)
out2 = rbase.robust(data,parallel=TRUE) # test parallel implementation