riem.rmml {Riemann} | R Documentation |
Riemannian Manifold Metric Learning
Description
Given N
observations X_1, X_2, \ldots, X_N \in \mathcal{M}
and
corresponding label information, riem.rmml
computes pairwise distance of data under Riemannian Manifold Metric Learning
(RMML) framework based on equivariant embedding. When the number of data points
is not sufficient, an inverse of scatter matrix does not exist analytically so
the small regularization parameter \lambda
is recommended with default value of \lambda=0.1
.
Usage
riem.rmml(riemobj, label, lambda = 0.1, as.dist = FALSE)
Arguments
riemobj |
a S3 |
label |
a length- |
lambda |
regularization parameter. If |
as.dist |
logical; if |
Value
a S3 dist
object or (N\times N)
symmetric matrix of pairwise distances according to as.dist
parameter.
References
Zhu P, Cheng H, Hu Q, Wang Q, Zhang C (2018). “Towards Generalized and Efficient Metric Learning on Riemannian Manifold.” In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, 3235–3241. ISBN 978-0-9992411-2-7.
Examples
#-------------------------------------------------------------------
# Distance between Two Classes of SPD Matrices
#
# Class 1 : Empirical Covariance from Standard Normal Distribution
# Class 2 : Empirical Covariance from Perturbed 'iris' dataset
#-------------------------------------------------------------------
## DATA GENERATION
data(iris)
ndata = 10
mydata = list()
for (i in 1:ndata){
mydata[[i]] = stats::cov(matrix(rnorm(100*4),ncol=4))
}
for (i in (ndata+1):(2*ndata)){
tmpdata = as.matrix(iris[,1:4]) + matrix(rnorm(150*4,sd=0.5),ncol=4)
mydata[[i]] = stats::cov(tmpdata)
}
myriem = wrap.spd(mydata)
mylabs = rep(c(1,2), each=ndata)
## COMPUTE GEODESIC AND RMML PAIRWISE DISTANCE
pdgeo = riem.pdist(myriem)
pdmdl = riem.rmml(myriem, label=mylabs)
## VISUALIZE
opar = par(no.readonly=TRUE)
par(mfrow=c(1,2), pty="s")
image(pdgeo[,(2*ndata):1], main="geodesic distance", axes=FALSE)
image(pdmdl[,(2*ndata):1], main="RMML distance", axes=FALSE)
par(opar)