riem.coreset18B: Build Lightweight Coreset In Riemann: Learning with Data on Riemannian Manifolds

Description

Given manifold-valued data X_1,X_2,…,X_N \in \mathcal{M}, this algorithm finds the coreset of size M that can be considered as a compressed representation according to the lightweight coreset construction scheme proposed by the reference below.

 1 2 3 4 5 6 riem.coreset18B( riemobj, M = length(riemobj$data)/2, geometry = c("intrinsic", "extrinsic"), ... )  Arguments  riemobj a S3 "riemdata" class for N manifold-valued data. M the size of coreset (default: N/2). geometry (case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry. ... extra parameters including maxitermaximum number of iterations to be run (default:50). epstolerance level for stopping criterion (default: 1e-5). Value a named list containing coreid a length-M index vector of the coreset. weight a length-M vector of weights for each element. References \insertRef bachem_scalable_2018aRiemann Examples   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 #------------------------------------------------------------------- # Example on Sphere : a dataset with three types # # * 10 perturbed data points near (1,0,0) on S^2 in R^3 # * 10 perturbed data points near (0,1,0) on S^2 in R^3 # * 10 perturbed data points near (0,0,1) on S^2 in R^3 #------------------------------------------------------------------- ## GENERATE DATA mydata = list() for (i in 1:10){ tgt = c(1, stats::rnorm(2, sd=0.1)) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } for (i in 11:20){ tgt = c(rnorm(1,sd=0.1),1,rnorm(1,sd=0.1)) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } for (i in 21:30){ tgt = c(stats::rnorm(2, sd=0.1), 1) mydata[[i]] = tgt/sqrt(sum(tgt^2)) } myriem = wrap.sphere(mydata) ## MDS FOR VISUALIZATION embed2 = riem.mds(myriem, ndim=2)$embed ## FIND CORESET OF SIZES 3, 6, 9 core1 = riem.coreset18B(myriem, M=3) core2 = riem.coreset18B(myriem, M=6) core3 = riem.coreset18B(myriem, M=9) col1 = rep(1,30); col1[core1$coreid] = 2 col2 = rep(1,30); col2[core2$coreid] = 2 col3 = rep(1,30); col3[core3\$coreid] = 2 ## VISUALIZE opar <- par(no.readonly=TRUE) par(mfrow=c(1,3), pty="s") plot(embed2, pch=19, col=col1, main="coreset size=3") plot(embed2, pch=19, col=col2, main="coreset size=6") plot(embed2, pch=19, col=col3, main="coreset size=9") par(opar) 

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