# riem.scUL: Spectral Clustering with Unnormalized Laplacian In Riemann: Learning with Data on Riemannian Manifolds

## Description

The version of Shi and Malik first constructs the affinity matrix

A_{ij} = \exp(-d(x_i, d_j)^2 / σ^2)

where σ is a common bandwidth parameter and performs k-means clustering on the row-space of eigenvectors for the unnormalized graph laplacian matrix

L=D-A

.

## Usage

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

## Arguments

 riemobj a S3 "riemdata" class for N manifold-valued data. k the number of clusters (default: 2). sigma bandwidth parameter (default: 1). geometry (case-insensitive) name of geometry; either geodesic ("intrinsic") or embedded ("extrinsic") geometry.

## Value

a named list containing

cluster

a length-N vector of class labels (from 1:k).

eigval

eigenvalues of the graph laplacian's spectral decomposition.

embeds

an (N\times k) low-dimensional embedding.

## References

von Luxburg U (2007). “A Tutorial on Spectral Clustering.” Statistics and Computing, 17(4):395–416.

## 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 #------------------------------------------------------------------- # Example on Sphere : a dataset with three types # # class 1 : 10 perturbed data points near (1,0,0) on S^2 in R^3 # class 2 : 10 perturbed data points near (0,1,0) on S^2 in R^3 # class 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) lab = rep(c(1,2,3), each=10) ## CLUSTERING WITH DIFFERENT K VALUES cl2 = riem.scUL(myriem, k=2)$cluster cl3 = riem.scUL(myriem, k=3)$cluster cl4 = riem.scUL(myriem, k=4)$cluster ## MDS FOR VISUALIZATION mds2d = riem.mds(myriem, ndim=2)$embed ## VISUALIZE opar <- par(no.readonly=TRUE) par(mfrow=c(1,4), pty="s") plot(mds2d, col=lab, pch=19, main="true label") plot(mds2d, col=cl2, pch=19, main="riem.scUL: k=2") plot(mds2d, col=cl3, pch=19, main="riem.scUL: k=3") plot(mds2d, col=cl4, pch=19, main="riem.scUL: k=4") par(opar) 

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