ktaucenters: ktaucenters

In ktaucenters: Robust Clustering Procedures

Description

Robust Clustering algorithm based on centers, a robust and efficient version of KMeans.

Usage

ktaucenters(X, K, centers = NULL, tolmin = 1e-06, NiterMax = 100,
  nstart = 1, startWithKmeans = TRUE, startWithROBINPD = TRUE,
  cutoff = 0.999)

Arguments

X	numeric matrix of size n x p.
K	the number of cluster.
centers	a matrix of size K x p containing the K initial centers, one at each matrix-row. If centers is NULL a random set of (distinct) rows in X are chosen as the initial centres.
tolmin	a tolerance parameter used for the algorithm stopping rule
NiterMax	a maximun number of iterations used for the algorithm stopping rule
nstart	the number of trials that the base algorithm ktaucenters_aux is run. If it is greater than 1 and center is not set as NULL, a random set of (distinct) rows in X will be chosen as the initial centres.
startWithKmeans	TRUE if kmean centers values is included as starting point.
startWithROBINPD	TRUE if ROBINDEN estimator is included as starting point
cutoff	optional argument for outliers detection - quantiles of chi-square to be used as a threshold for outliers detection, defaults to 0.999

Value

A list including the estimated K centers and labels for the observations

• centers: matrix of size K x p, with the estimated K centers.

• cluster: array of size n x 1 integers labels between 1 and K.

• tauPath: sequence of tau scale values at each iterations.

• Wni: numeric array of size n x 1 indicating the weights associated to each observation.

• emptyClusterFlag: a boolean value. True means that in some iteration there were clusters totally empty

• niter: number of iterations untill convergence is achived or maximun number of iteration is reached

• di: distance of each observation to its assigned cluster-center

• outliers: indices observation that can be considered as outliers

References

Gonzalez, J. D., Yohai, V. J., & Zamar, R. H. (2019). Robust Clustering Using Tau-Scales. arXiv preprint arXiv:1906.08198.

Examples

# Generate Sintetic data (three cluster well separated)
Z <- rnorm(600);
mues <- rep(c(-3, 0, 3), 200)
X <-  matrix(Z + mues, ncol=2)

# Generate 60 sintetic outliers (contamination level 20%)
X[sample(1:300,60), ] <- matrix(runif( 40, 3 * min(X), 3 * max(X) ),
                                ncol = 2, nrow = 60)

### Applying the algortihm ####
sal <- ktaucenters(
     X, K=3, centers=X[sample(1:300,3), ],
     tolmin=1e-3, NiterMax=100)

#### plotting  the clusters####
par(mfrow = c(1,1));

par(mfrow = c(1,2))
plot(X,type = "n", main = "ktaucenters (Robust) \n outliers: solid black dots")
points(X[sal$cluster==1,],col=2);
points(X[sal$cluster==2,],col=3);
points(X[sal$cluster==3,],col=4)
points(X[sal$outliers,1], X[sal$outliers,2], pch=19)

### Applying a classical (non Robust) algortihm ###
sal <- kmeans(X, centers=3,nstart=100)

### plotting the clusters ###
plot(X, type ="n", main = "kmeans (Classical)")
points(X[sal$cluster==1,],col=2);
points(X[sal$cluster==2,],col=3);
points(X[sal$cluster==3,],col=4)

ktaucenters documentation built on Aug. 3, 2019, 9:03 a.m.