CLV3W function

Hierarchical clustering of variables (associated with mode 2 three-way array) with consolidation

Hierarchical Cluster Analysis of a set of variables (mode 2) given a three-way array with a further consolidation step. Each group of variables is associated with a one-rank PARAFAC model (comp x loading x weight). Moreover, a Non Negativity (NN) constraint may be added to the model, so that the loading coefficients have positive values. Return an object of class clv3w.

CLV3W(X,mode.scale=0,NN=FALSE,moddendoinertie=TRUE,gmax=20,graph=TRUE,cp.rand=10)

Arguments

• X: : a three way array - variables of mode 2 will be clustered

• mode.scale: : scaling parameter applied to X, by default centering of X (for mode 2 x mode 3) is done. By default no scaling (mode.scale=0)

  0 : no scaling only centering - the default

  1 : scaling with standard deviation of (mode 2 x mode 3) elements

  2 : global scaling (each block i.e. each mode 2 slice will have the same inertia )

  3 : global scaling (each block i.e. each mode 3 slice will have the same inertia )

• NN: : non Negativity constraint to be added on the loading coefficients. By default no constraint (NN=FALSE)

  TRUE : a non negativity constrained is applied on the loading coefficients to set them as positive values

  FALSE : loading coefficients may be either positive or negative

• moddendoinertie: : dendrogram. By default it is based on the delta clustering criterion (moddendoinertie =TRUE)

  TRUE : dendrogram associated with the clustering criterion delta

  FALSE : dendrogram associated with the the height (cumulative delta)

• gmax: : maximum number of partitions for which the consolidation will be done (default : gmax=11)

• graph: : boolean, if TRUE, the graphs associated with the dendrogram and the evolution of the aggregation criterion are displayed (default : graph=TRUE)

• cp.rand: : number of random starts associated with the one rank Candecomp/Parafac model (By default cp.rand=10)

Returns

• tabres: Results of the hierarchical 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 (delta) : delta loss

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

  • Column 6: the percentage of explained inertia of the data array X

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

  • Column 8: the percentage of explained inertia of the data array X 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

• hclust: contains the results of the HCA

• partition K: contains a list for each number of clusters of the partition, K=1 to gmax 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 associated with the first mode (after consolidation)
  • loading: the vector of loadings associated with the second mode by cluster (after consolidation)
  • weigth: the vector of weights associated with the third mode by cluster (after consolidation)
  • criterion: vector of loss giving for each cluster the residual amount between the sub-array and its reconstitution associated with the cluster one rank PARAFAC model (after consolidation)

• param: contains the clustering parameters

  • gmax: maximum number of partitions for which the consolidation has been done
  • X: the scaled three-way array

call : call of the method

Examples

data(ciders)
## Cluster Analysis of cider sensory descriptors with block scaling
## to set the assessors to the same footing
res.cider<-CLV3W(ciders,mode.scale=3,NN=FALSE,moddendoinertie=FALSE,gmax=20,graph=FALSE,cp.rand=5)
plot(res.cider,type="delta")
plot(res.cider,type="dendrogram")
print(res.cider)
summary(res.cider,2)
get_comp(res.cider,2)
get_loading(res.cider,2)
get_weight(res.cider,2)

References

Wilderjans, T. F., & Cariou, V. (2016). CLV3W: A clustering around latent variables approach to detect panel disagreement in three-way conventional sensory profiling data. Food quality and preference, 47, 45-53.

Cariou, V., & Wilderjans, T. F. (2018). Consumer segmentation in multi-attribute product evaluation by means of non-negatively constrained CLV3W. Food Quality and Preference, 67, 18-26.

See Also

CLV3W_kmeans, get_comp, get_loading, get_partition, plot, plot_var.clv3w,

Author(s)

Veronique Cariou, veronique.cariou@oniris-nantes.fr