PACBO (version 0.1.0)

PACBO: PACBO

Description

This function performs clustering on online datasets. The number of cells is data-driven and need not to be chosen in advance by the user.

Usage

PACBO(mydata, R, coeff = 2, K_max = 50, scaling = FALSE, var_ind = FALSE, N_iterations = 500, plot_ind = FALSE, axis_ind = c(1, 2))

Arguments

mydata

a matrix where each row corresponds to an observation of length d.

R

a positive real value that should be larger than the maximum Euclidean distance of all the observations in mydata. We recommend to set R equaling to this maximum Euclidean distance.

coeff

a positive real value, enforcing large number of cells. The default, 2, should be convenient for most users. A larger value brings more cells for the clustering.

K_max

a positive integer indicating the maximum number of cells allowed for the clustering.

scaling

logical indicating whether the matrix mydata should be centered and scaled. The centering is done by subtracting the column means of mydata from their corresponding columns; the scaling is done by dividing the (centered) columns of mydata by their standard deviations. We recommend to set it to TRUE only when the maximum Euclidean distance of all the observations in mydata is smaller than 1.

var_ind

logical indicating whether predicted centers of cells will be calculated sequentially. If TRUE, at each round, predicted centers of cells will be calculated on the basis of the past observations and past predicted centers. Setting this to FALSE will largely save execution time.

N_iterations

a positive integer indicating the number of iterations of algorithm.

plot_ind

logical indicating whether clusters should be plotted.

axis_ind

numeric indicating which axes are to be plotted if d >= 2. The default is the first two coordinates of observations.

Value

Returns a list including

predicted_centers

a matrix of predicted centers of cells, where each row corresponds to a center.

nb_of_clusters

positive integer indicating the estimation of the number of cells for the dataset.

labels

labels for observations in mydata.

Details

The PACBO algorithm is introduced and fully described in Le Li, Benjamin Guedj, Sebastien Loustau (2016), "PAC-Bayesian Online Clustering" (https://arxiv.org/abs/1602.00522). It relies on PAC-Bayesian approach, allowing for a dynamic (i.e., time-dependent) estimation of the number of clusters, up to K_max clusters. Its implementation is done via an RJMCMC-flavored algorithm.

References

Le Li, Benjamin Guedj and Sebastien Loustau (2016), PAC-Bayesian Online Clustering, arXiv preprint: https://arxiv.org/abs/1602.00522.

Examples

## generating 4 clusters of 100 points in \strong{R}^{5}.
set.seed(100)
Nb <- 4
d <- 5
T <- 100
proportion = rep(1/Nb, Nb)
Mean_vectors <- matrix(runif(d*Nb,min=-10, max=10),nrow=Nb,ncol=d, byrow=TRUE)
mydata <- matrix(replicate(T, rmnorm(1, mean= Mean_vectors[sample(1:Nb, 1, prob = proportion),],
varcov = diag(1,d))), nrow = T, byrow=T)
R <- max(sqrt(rowSums(mydata^2)))
##run the algorithm.
result <- PACBO(mydata, R, plot_ind = TRUE)