gr.pdist: Pairwise Distance for Data on Grassmann Manifold

In RiemGrassmann: Inference, Learning, and Optimization on Grassmann Manifold

Description

For data on grassmann manifold x_1,x_2,…,x_N \in Gr(k,n), compute pairwise distances d(x_i,x_j) via several metrics. The distance type "intrinsic" corresponds to geodesic distance while "extrinsic" is equivalent to "chordal" distance.

Usage

gr.pdist(
  input,
  type = c("Intrinsic", "Extrinsic", "Asimov", "Binet-Cauchy", "Chordal",
    "Fubini-Study", "Martin", "Procrustes", "Projection", "Spectral"),
  as.dist = TRUE,
  useR = FALSE
)

Arguments

input	either an array of size (n\times k\times N) or a list of length N whose elements are (n\times k) orthonormal basis (ONB) on Grassmann manifold.
type	type of distance measure. Name of each type is Case Insensitive and hyphen can be omitted.
as.dist	a logical; TRUE to return a dist object or FALSE to return an (N\times N) symmetric matrix.
useR	a logical; TRUE to use R computations while FALSE goes everything in C++.

Value

a dist object or (N\times N) symmetric matrix depending on as.dist.

Author(s)

Kisung You

Examples

## generate a dataset with two types of Grassmann elements
#  group1 : first four columns of (8x8) identity matrix + noise
#  group2 : last  four columns of (8x8) identity matrix + noise

mydata = list()
sdval  = 0.25
diag8  = diag(8)
for (i in 1:10){
  mydata[[i]] = qr.Q(qr(diag8[,1:4] + matrix(rnorm(8*4,sd=sdval),ncol=4)))
}
for (i in 11:20){
  mydata[[i]] = qr.Q(qr(diag8[,5:8] + matrix(rnorm(8*4,sd=sdval),ncol=4)))
}

## try 'intrinsic' distance using C++ implementation
dmat = gr.pdist(mydata, type="intrinsic", as.dist=FALSE)
opar = par(no.readonly=TRUE)
par(pty="s")
image(dmat, main="intrinsic distance")
par(opar)


## compute and visualize distances for all types
#  we will iterate over all measures
alltypes = c("intrinsic","extrinsic","asimov","binet-cauchy",
"chordal","fubini-study","martin","procrustes","projection","spectral")
ntypes   = length(alltypes)

opar <- par(no.readonly=TRUE)
par(mfrow=c(2,5), pty="s")
for (i in 1:ntypes){
  dmat = gr.pdist(mydata, type=alltypes[i], as.dist=FALSE)
  image(dmat[,20:1], main=alltypes[i])
}
par(opar)

RiemGrassmann documentation built on March 25, 2020, 5:07 p.m.