fit.twcfta {simuclustfactor}

TWCFTA model

Description

Implements K-means clustering and afterwards factorial reduction in a sequential fashion.

Usage

fit.twcfta(model, X_i_jk, full_tensor_shape, reduced_tensor_shape)

## S4 method for signature 'tandem'
fit.twcfta(model, X_i_jk, full_tensor_shape, reduced_tensor_shape)

Arguments

model

Initialized tandem model.

X_i_jk

Matricized tensor along mode-1 (I objects).

full_tensor_shape

Dimensions of the tensor in full space.

reduced_tensor_shape

Dimensions of tensor in the reduced space.

Details

The procedure requires sequential clustering and factorial decomposition.

• The K-means clustering algorithm is initially applied to the matricized tensor X_i_jk to obtain the centroids matrix X_g_jk and the membership matrix U_i_g.

• The Tucker2 decomposition technique is then implemented on the centroids matrix X_g_jk to yield the core centroids matrix Y_g_qr and the component weights matrices B_j_q and C_k_r.

Value

Output attributes accessible via the '@' operator.

• U_i_g0 - Initial object membership function matrix.

• B_j_q0 - Initial factor/component matrix for the variables.

• C_k_r0 - Initial factor/component matrix for the occasions.

• U_i_g - Final/updated object membership function matrix.

• B_j_q - Final/updated factor/component matrix for the variables.

• C_k_r - Final/updated factor/component matrix for the occasions.

• Y_g_qr - Derived centroids in the reduced space (data matrix).

• X_i_jk_scaled - Standardized dataset matrix.

• BestTimeElapsed - Execution time for the best iterate.

• BestLoop - Loop that obtained the best iterate.

• BestKmIteration - Number of iteration until best iterate for the K-means.

• BestFaIteration - Number of iteration until best iterate for the FA.

• FaConverged - Flag to check if algorithm converged for the K-means.

• KmConverged - Flag to check if algorithm converged for the Factor Decomposition.

• nKmConverges - Number of loops that converged for the K-means.

• nFaConverges - Number of loops that converged for the Factor decomposition.

• TSS_full - Total deviance in the full-space.

• BSS_full - Between deviance in the reduced-space.

• RSS_full - Residual deviance in the reduced-space.

• PF_full - PseudoF in the full-space.

• TSS_reduced - Total deviance in the reduced-space.

• BSS_reduced - Between deviance in the reduced-space.

• RSS_reduced - Residual deviance in the reduced-space.

• PF_reduced - PseudoF in the reduced-space.

• PF - Actual PseudoF value to obtain best loop.

• Labels - Object cluster assignments.

• FsKM - Objective function values for the KM best iterate.

• FsFA - Objective function values for the FA best iterate.

• Enorm - Average l2 norm of the residual norm.

Note

• This procedure is useful to further interpret the between clusters variability of the data and to understand the variables and/or occasions that most contribute to discriminate the clusters. However, the application of this technique could lead to the masking of variables that are not informative of the clustering structure.

• since the Tucker2 model is applied after the clustering, this cannot help select the most relevant information for the clustering in the dataset.

References

Arabie P, Hubert L (1996). “Advances in Cluster Analysis Relevant to Marketing Research.” In Gaul W, Pfeifer D (eds.), From Data to Knowledge, 3–19. Tucker L (1966). “Some mathematical notes on three-mode factor analysis.” Psychometrika, 31(3), 279-311. doi:10.1007/BF02289464, https://ideas.repec.org/a/spr/psycho/v31y1966i3p279-311.html.

See Also

fit.twfcta tandem

Examples

X_i_jk = generate_dataset()$X_i_jk
model = tandem()
twcfta = fit.twcfta(model, X_i_jk, c(8,5,4), c(3,3,2))