KpartitionNJW {uHMM}

KpartitionNJW function

Description

Perform spectral classification on the similarity matrix of a dataset (Ng et al. (2001) algorithm), using kmeans algorithm on data projected in the space of its K first eigen vectors.

Usage

KpartitionNJW(similarity, K)

Arguments

similarity

matrix of similarity.

K

number of clusters.

Value

The function returns a list containing:

label

vector of cluster sequencing.

centres

matrix of cluster centers in the space of the K first normalised eigen vectors.

vecteursPropresProjK

matrix containing, in columns, the K first normalised eigen vectors of the similarity matrix.

valeursPropresK

vector containing the K first eigen values of the similarity matrix.

vecteursPropres

matrix containing, in columns, eigen vectors of the similarity matrix.

valeursPropres

vector containing eigen values of the similarity matrix.

inertieZ

vector of within-cluster sum of squares, one component per cluster.

References

Ng Andrew, Y., M. I. Jordan, and Y. Weiss. "On spectral clustering: analysis and an algorithm [C]." Advances in Neural Information Processing Systems (2001).

Examples

#####
x <- rbind(matrix(rnorm(100, mean = 0, sd = 0.3), ncol = 2), 
           matrix(rnorm(100, mean = 2, sd = 0.3), ncol = 2), 
           matrix(rnorm(100, mean = 4, sd = 0.3), ncol = 2))

similarity<-ZPGaussianSimilarity(x,7)
similarity=similarity%*%t(similarity)
sp<-KpartitionNJW(similarity,3)
plot(x,col=sp$label)

#####    
x <- rbind(data.frame(x=1:100+(runif(100)-0.5)*2,y=runif(100)/5), 
           data.frame(x=1:100+(runif(100)-0.5)*2,y=runif(100)/5+1),
           data.frame(x=1:100+(runif(100)-0.5)*2,y=runif(100)/5+2))

similarity<-ZPGaussianSimilarity(x,7)
similarity=similarity%*%t(similarity)
sp<-KpartitionNJW(similarity,3)
plot(x,col=sp$label)

#####
x=(runif(1000)*4)-2;y=(runif(1000)*4)-2
keep<-which((x**2+y**2<0.5)|(x**2+y**2>1.5**2 & x**2+y**2<2**2 ))
data<-data.frame(x,y)[keep,]

similarity=ZPGaussianSimilarity(data, 7)
similarity=similarity%*%t(similarity)
sp<-KpartitionNJW(similarity,2)

plot(data,col=sp$label)