# riem.knn: Find K-Nearest Neighbors In Riemann: Learning with Data on Riemannian Manifolds

## Description

Given N observations X_1, X_2, …, X_N \in \mathcal{M}, riem.knn constructs k-nearest neighbors.

## Usage

 1 riem.knn(riemobj, k = 2, geometry = c("intrinsic", "extrinsic")) 

## Arguments

 riemobj a S3 "riemdata" class for N manifold-valued data. k the number of neighbors to find. geometry (case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry.

## Value

a named list containing

nn.idx

an (N \times k) neighborhood index matrix.

nn.dists

an (N\times k) distances from a point to its neighbors.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 #------------------------------------------------------------------- # Example on Sphere : a dataset with three types # # * 10 perturbed data points near (1,0,0) on S^2 in R^3 # * 10 perturbed data points near (0,1,0) on S^2 in R^3 # * 10 perturbed data points near (0,0,1) on S^2 in R^3 #------------------------------------------------------------------- ## GENERATE DATA mydata = list() for (i in 1:10){ tgt = c(1, stats::rnorm(2, sd=0.1)) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } for (i in 11:20){ tgt = c(rnorm(1,sd=0.1),1,rnorm(1,sd=0.1)) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } for (i in 21:30){ tgt = c(stats::rnorm(2, sd=0.1), 1) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } myriem = wrap.sphere(mydata) mylabs = rep(c(2,3,4), each=10) ## K-NN CONSTRUCTION WITH K=5 & K=10 knn1 = riem.knn(myriem, k=5) knn2 = riem.knn(myriem, k=10) ## MDS FOR VISUALIZATION embed2 = riem.mds(myriem, ndim=2)$embed ## VISUALIZE opar <- par(no.readonly=TRUE) par(mfrow=c(1,2), pty="s") plot(embed2, pch=19, main="knn with k=4", col=mylabs) for (i in 1:30){ for (j in 1:5){ lines(embed2[c(i,knn1$nn.idx[i,j]),]) } } plot(embed2, pch=19, main="knn with k=8", col=mylabs) for (i in 1:30){ for (j in 1:10){ lines(embed2[c(i,knn2\$nn.idx[i,j]),]) } } par(opar) 

Riemann documentation built on June 20, 2021, 5:07 p.m.