FindNbrClusters {l1spectral}

Find the optimal number of clusters

Description

This internal function of the l1-spectral algorithm finds the optimal number of clusters to build.

Usage

FindNbrClusters(A, structure, k = NULL, k_max = NULL)

Arguments

A

The adjacency matrix

structure

Output of the function FindStructure().

k

True number of clusters (not necessarily needed). If not provided, k is chosen by spectral eigengap.

k_max

Maximal number of clusters to form (not necessarily needed). If not provided, k_max is set to the number of nodes.

Value

A list with the following elements:

• nbr_clusters Optimal number of clusters by component,

• nbr_clusters_total Optimal total number of clusters.

Author(s)

Camille Champion, Magali Champion

See Also

l1_spectralclustering, l1spectral.

Examples

 #########################################
 # Finding the optimal number of clusters
 #########################################

 # 1st example: non-perturbed graph
 Data <- CreateDataSet(k=3, n=20, p=list(p_inside=0,p_outside=0))

 Structure <- FindStructure(Data$A_hat)

 Clusters <- FindNbrClusters(A = Data$A_hat, structure = Structure, k=3)
 # The number of clusters is provided (3): each of the 3 components will be divided into 1 cluster

 Clusters <- FindNbrClusters(A = Data$A_hat, structure = Structure, k=5)
 # The number of clusters is provided (5) and larger than the number of components (3),
 # the spectral eigengap method is used to find the optimal number of clusters of each component.

 # 2nd example: perturbed graph
 Data <- CreateDataSet(k=3, n=20, p=list(p_inside=0.1,p_outside=0.1))

 Structure <- FindStructure(Data$A_hat) # there are less than 3 components

 Clusters <- FindNbrClusters(A = Data$A_hat, structure = Structure)
 # The number of clusters is optimized using the spectral eigengap method