Clusterpath as hierarchical clustering

ggplot2 and ggraph function to plotting the results from the clusterpath algorithm.

Usage

gg_cluster(list_results, id_names = NULL)

average_hierarchy(replicates)

Arguments

list_results

A list of results optimization from HR_Clusterpath().

id_names

A liste of strings for the nodes label. If NULL (default), the labels are integer from \(1\) to \(d\), the number of variables.

replicates

A list of results optimization replicates from HR_Clusterpath().

Value

For gg_cluster(), the dendrogram obtained from the optimization results from HR_Clusterpath() for each lambda. For average_hierarchy(), the average dendrogram obtained from the several optimization results from HR_Clusterpath() for each lambda.

Details

During its development in \([1]\), the clusterpath algorithm was built from a convex relaxation of hierarchical clustering that allows us to produce this kind of graphs from the results of the algorithm with a enough thin and large grid for the penalty \(\lambda\).

References

\([1]\) Hocking, T. D., Joulin, A., Bach, F., and Vert, J.-P. (2011). Clusterpath: An Algorithm for Clustering using Convex Fusion Penalties. In Proceedings of the 28th International Conference on Machine Learning, Bellevue, Washington, USA,. Omnipress.

Examples

# Construction of clusters and R matrix
R <- matrix(c(1, -3, 0,
              -3, 2, -2,
              0, -2, 1), nc = 3)
clusters <- list(1:5, 6:10, 11:15)

# Construction of induced theta and corresponding variogram gamma
Theta <- build_theta(R, clusters)
Gamma <- graphicalExtremes::Theta2Gamma(Theta)

gr3_bal_sim_param_cluster <-
  list(
    R = R,
    clusters = clusters,
    Theta = Theta,
    Gamma = Gamma,
    chi = 1,
    n = 1e3,
    d = 15
  )

set.seed(804)
data <- graphicalExtremes::rmpareto(n = gr3_bal_sim_param_cluster$n,
                                    model = "HR",
                                    par = gr3_bal_sim_param_cluster$Gamma)

lambda <- seq(0, 2, 1e-3)

res <- HR_Clusterpath(data = data,
                      zeta = gr3_bal_sim_param_cluster$chi,
                      lambda = lambda,
                      eps_f = 1e-1)

gg_cluster(res)