CLV function

Hierarchical clustering of variables with consolidation

Hierarchical Cluster Analysis of a set of variables with consolidation. Directional or local groups may be defined. Each group of variables is associated with a latent component. Moreover, the latent component may be constrained using external information collected on the observations or on the variables.

CLV(
  X,
  Xu = NULL,
  Xr = NULL,
  method = NULL,
  sX = TRUE,
  sXr = FALSE,
  sXu = FALSE,
  nmax = 20,
  maxiter = 20,
  graph = TRUE
)

Arguments

• X: : The matrix of variables to be clustered

• Xu: : The external variables associated with the columns of X

• Xr: : The external variables associated with the rows of X

• method: : The criterion to be use in the cluster analysis.

  1 or "directional" : the squared covariance is used as a measure of proximity (directional groups).

  2 or "local" : the covariance is used as a measure of proximity (local groups)

• sX: ,TRUE/FALSE : standardization or not of the columns X (TRUE by default)

  (predefined -> cX = TRUE : column-centering of X)

• sXr: ,TRUE/FALSE : standardization or not of the columns Xr (FALSE by default)

  (predefined -> cXr = TRUE : column-centering of Xr)

• sXu: ,TRUE/FALSE : standardization or not of the columns Xu (FALSE by default)

  (predefined -> cXu= FALSE : no centering, Xu considered as a weight matrix)

• nmax: : maximum number of partitions for which the consolidation will be done (by default nmax=20)

• maxiter: : maximum number of iterations allowed for the consolidation/partitioning algorithm (by default maxiter=20)

• graph,: TRUE/FALSE (by default TRUE) : dendrogram and variation of the optimization criterion.

  These plots can also be obtained with "plot"

Returns

• tabres: Results of the clustering algorithm. In each line you find the results of one specific step of the hierarchical clustering.

  • Columns 1 and 2: The numbers of the two groups which are merged

  • Column 3: Name of the new cluster

  • Column 4: The value of the aggregation criterion for the Hierarchical Ascendant Clustering (HAC)

  • Column 5: The value of the clustering criterion for the HAC

  • Column 6: The percentage of the explained initial criterion value

    (method 1 => % var. expl. by the latent comp.)

  • Column 7: The value of the clustering criterion after consolidation

  • Column 8: The percentage of the explained initial criterion value after consolidation

  • Column 9: The number of iterations in the partitioning algorithm.

    Remark : A zero in columns 7 to 9 indicates that no consolidation was done

• partition K: contains a list for each number of clusters of the partition, K=2 to nmax with

  • clusters: in line 1, the groups membership before consolidation; in line 2 the groups membership after consolidation
  • comp: The latent components of the clusters (after consolidation)
  • loading: if there are external variables Xr or Xu : The loadings of the external variables (after consolidation)

Details

If external variables are used, define either Xr or Xu, but not both. Use the LCLV function when Xr and Xu are simultaneously provided.

Examples

data(apples_sh)
#directional groups
resclvX <- CLV(X = apples_sh$senso, method = "directional", sX = TRUE)
plot(resclvX,type="dendrogram")
plot(resclvX,type="delta")
#local groups with external variables Xr
resclvYX <- CLV(X = apples_sh$pref, Xr = apples_sh$senso, method = "local", sX = FALSE, sXr = TRUE)

References

Vigneau E., Qannari E.M. (2003). Clustering of variables around latents components. Comm. Stat, 32(4), 1131-1150.

Vigneau E., Chen M., Qannari E.M. (2015). ClustVarLV: An R Package for the clustering of Variables around Latent Variables. The R Journal, 7(2), 134-148

See Also

CLV_kmeans, LCLV