LCLV function

L-CLV for L-shaped data

Define clusters of X-variables aroud latent components. In each cluster, two latent components are extracted, the first one is a linear combination of the external information collected for the rows of X and the second one is a linear combination of the external information associated with the columns of X.

LCLV(X, Xr, Xu, ccX = FALSE, sX = TRUE, sXr = FALSE, sXu = FALSE, nmax = 20)

Arguments

• X: The matrix of variables to be clustered

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

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

• ccX: TRUE/FALSE : double centering of X (FALSE, by default) If FALSE this implies that cX = TRUE : column-centering of X

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

• 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)

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

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

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

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

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

• partition K: 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
  • compt: The latent components of the clusters (after consolidation) defined according to the Xr variables
  • compc: The latent components of the clusters (after consolidation) defined according to the Xu variables
  • loading_v: loadings of the external Xr variables (after consolidation)
  • loading_u: loadings of the external Xu variables (after consolidation)

References

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

Vigneau, E., Charles, M.,& Chen, M. (2014). External preference segmentation with additional information on consumers: A case study on apples. Food Quality and Preference, 32, 83-92.

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