clusterpath_l1: Fit a fast version of the weighted l1-clusterpath algorithm

In jchiquet/fusedanova: Univariate hierarchical clustering

Description

The l1-clusterpath algorithm is a convex clustering algorithm with fused-LASSO (or Total Variation) penality, ie. a sum of weighted l1-norm on the difference of each coefficient.

Usage

clusterpath_l1(x, group, weighting = c("laplace", "gaussian",
  "adaptive"), gamma = 0, hclust = TRUE)

Arguments

x	a numeric vector of observation for n individuals.
group	an optional vector or factor giving the initial grouping. If missing, each individual are set in a single group.
weighting	character; which type of weights is supposed to be used. The supported weights are: "laplace", "gaussian" or "adaptive". See details below. "laplace" by default.
gamma	non-negative scalar ; the gamma parameter is needed for "laplace", "gaussian" and "adaptive" weights. Default is 0.
hclust	boolean: should the result be outputed as an hclust object? Default is TRUE.

Value

an S3 object with class hclust or a data frame of the succesive fusions.

The optimization problem solved is

β^hat _λ1 = argmin_β sum_k sum_i (Y_ik - &beta_k)² + λ sum_k,l w_k,l | β_k - β_l |,

where Y_ik is the intensity of a continuous random variable for sample i in condition k and beta_k is the mean parameter of condition k. We denote by K the total number of conditions and n_k the number of sample in each condition.

References

Chiquet J, Gutierrez P, Rigaill G: Fast tree inference with weighted fusion penalties, Journal of Computational and Graphical Statistics 205–216, 2017.

T. Hocking, J.-P. Vert, F. Bach, and A. Joulin. Clusterpath: an Algorithm for Clustering using Convex Fusion Penalties, ICML, 2011.

Examples

data(aves)
clpath <- clusterpath_l1(aves$weight, aves$family, gamma = 0)
plot(clpath)

jchiquet/fusedanova documentation built on July 19, 2019, 12:49 a.m.