Help for package simuclustfactor

Type:

Package

Title:

Simultaneous Clustering and Factorial Decomposition of Three-Way Datasets

Version:

0.0.3

Maintainer:

Prosper Ablordeppey <pablordeppey@ua.pt>

Description:

Implements two iterative techniques called T3Clus and 3Fkmeans, aimed at simultaneously clustering objects and a factorial dimensionality reduction of variables and occasions on three-mode datasets developed by Vichi et al. (2007) <doi:10.1007/s00357-007-0006-x>. Also, we provide a convex combination of these two simultaneous procedures called CT3Clus and based on a hyperparameter alpha (alpha in [0,1], with 3FKMeans for alpha=0 and T3Clus for alpha= 1) also developed by Vichi et al. (2007) <doi:10.1007/s00357-007-0006-x>. Furthermore, we implemented the traditional tandem procedures of T3Clus (TWCFTA) and 3FKMeans (TWFCTA) for sequential clustering-factorial decomposition (TWCFTA), and vice-versa (TWFCTA) proposed by P. Arabie and L. Hubert (1996) <doi:10.1007/978-3-642-79999-0_1>.

License:

GPL-3

Encoding:

UTF-8

RoxygenNote:

7.2.1

Depends:

R (≥ 2.10)

Imports:

methods, stats, Rdpack

RdMacros:

Rdpack

Suggests:

testthat (≥ 3.0.0)

Config/testthat/edition:

NeedsCompilation:

Packaged:

2022-10-17 16:54:46 UTC; iCETEE

Author:

Prosper Ablordeppey

[aut, cre], Adelaide Freitas

[ctb], Giorgia Zaccaria

[ctb]

Repository:

CRAN

Date/Publication:

2022-10-18 06:40:05 UTC

Simultaneous results attributes

Description

Simultaneous results attributes

Slots

U_i_g0: matrix. Initial object membership function matrix
B_j_q0: matrix. Initial factor/component matrix for the variables
C_k_r0: matrix. Initial factor/component matrix for the occasions
U_i_g: matrix. Final/updated object membership function matrix
B_j_q: matrix. Final/updated factor/component matrix for the variables
C_k_r: matrix. Final/updated factor/component matrix for the occasions
Y_g_qr: matrix. Derived centroids in the reduced space (data matrix)
X_i_jk_scaled: matrix. Standardized dataset matrix
BestTimeElapsed: numeric. Execution time for the best iterate
BestLoop: numeric. Loop that obtained the best iterate
BestIteration: numeric. Iteration yielding the best results
Converged: numeric. Flag to check if algorithm converged for the K-means
nConverges: numeric. Number of loops that converged for the K-means
TSS_full: numeric. Total deviance in the full-space
BSS_full: numeric. Between deviance in the reduced-space
RSS_full: numeric. Residual deviance in the reduced-space
PF_full: numeric. PseudoF in the full-space
TSS_reduced: numeric. Total deviance in the reduced-space
BSS_reduced: numeric. Between deviance in the reduced-space
RSS_reduced: numeric. Residual deviance in the reduced-space
PF_reduced: numeric. PseudoF in the reduced-space
PF: numeric. Weighted PseudoF score
Labels: integer. Object cluster assignments
Fs: numeric. Objective function values for the KM best iterate
Enorm: numeric. Average l2 norm of the residual norm.

Tandem results attributes

Description

Tandem results attributes

Slots

U_i_g0: matrix. Initial object membership function matrix.
B_j_q0: matrix. Initial factor/component matrix for the variables.
C_k_r0: matrix. Initial factor/component matrix for the occasions.
U_i_g: matrix. Final/updated object membership function matrix.
B_j_q: matrix. Final/updated factor/component matrix for the variables.
C_k_r: matrix. Final/updated factor/component matrix for the occasions.
Y_g_qr: matrix. Derived centroids in the reduced space (data matrix).
X_i_jk_scaled: matrix. Standardized dataset matrix.
BestTimeElapsed: numeric. Execution time for the best iterate.
BestLoop: numeric. Loop that obtained the best iterate.
BestKmIteration: numeric. Number of iteration until best iterate for the K-means.
BestFaIteration: numeric. Number of iteration until best iterate for the FA.
FaConverged: numeric. Flag to check if algorithm converged for the K-means.
KmConverged: numeric. Flag to check if algorithm converged for the Factor Decomposition.
nKmConverges: numeric. Number of loops that converged for the K-means.
nFaConverges: numeric. Number of loops that converged for the Factor decomposition.
TSS_full: numeric. Total deviance in the full-space.
BSS_full: numeric. Between deviance in the reduced-space.
RSS_full: numeric. Residual deviance in the reduced-space.
PF_full: numeric. PseudoF in the full-space.
TSS_reduced: numeric. Total deviance in the reduced-space.
BSS_reduced: numeric. Between deviance in the reduced-space.
RSS_reduced: numeric. Residual deviance in the reduced-space.
PF_reduced: numeric. PseudoF in the reduced-space.
PF: numeric. Actual PseudoF value to obtain best loop.
Labels: integer. Object cluster assignments.
FsKM: numeric. Objective function values for the KM best iterate.
FsFA: numeric. Objective function values for the FA best iterate.
Enorm: numeric. Average l2 norm of the residual norm.

3FKMeans Model

Description

Implements simultaneous version of TWFCTA

Usage

fit.3fkmeans(model, X_i_jk, full_tensor_shape, reduced_tensor_shape)

## S4 method for signature 'simultaneous'
fit.3fkmeans(model, X_i_jk, full_tensor_shape, reduced_tensor_shape)

Arguments

model

Initialized simultaneous 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 performs simultaneously the sequential TWFCTA model. The model finds B_j_q and C_k_r such that the within-clusters deviance of the component scores is minimized.

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
BestIteration - Iteration yielding the best results
Converged - Flag to check if algorithm converged for the K-means
nConverges - Number of loops that converged for the K-means
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 - Weighted PseudoF score
Labels - Object cluster assignments
Fs - Objective function values for the KM best iterate
Enorm - Average l2 norm of the residual norm.

References

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. Vichi M, Kiers HAL (2001). “Factorial k-means analysis for two-way data.” Computational Statistics and Data Analysis, 37(1), 49-64. https://EconPapers.repec.org/RePEc:eee:csdana:v:37:y:2001:i:1:p:49-64. Vichi M, Rocci R, Kiers H (2007). “Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches.” Journal of Classification, 24, 71-98. doi:10.1007/s00357-007-0006-x.

Examples

X_i_jk = generate_dataset()$X_i_jk
model = simultaneous()
tfkmeans = fit.3fkmeans(model, X_i_jk, c(8,5,4), c(3,3,2))

CT3Clus Model

Description

Implements simultaneous T3Clus and 3FKMeans integrating an alpha value between 0 and 1 inclusive for a weighted result.

Usage

fit.ct3clus(
  model,
  X_i_jk,
  full_tensor_shape,
  reduced_tensor_shape,
  alpha = 0.5
)

## S4 method for signature 'simultaneous'
fit.ct3clus(
  model,
  X_i_jk,
  full_tensor_shape,
  reduced_tensor_shape,
  alpha = 0.5
)

Arguments

model

Initialized simultaneous 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.

alpha

0<alpha>1 hyper parameter. Model is T3Clus when alpha=1 and 3FKMeans when alpha=0.

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
BestIteration - Iteration yielding the best results
Converged - Flag to check if algorithm converged for the K-means
nConverges - Number of loops that converged for the K-means
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 - Weighted PseudoF score
Labels - Object cluster assignments
Fs - Objective function values for the KM best iterate
Enorm - Average l2 norm of the residual norm.

References

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. Rocci R, Vichi M (2005). “Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units.” Psychometrika, 70, 715-736. doi:10.1007/s11336-001-0926-z. Vichi M, Kiers HAL (2001). “Factorial k-means analysis for two-way data.” Computational Statistics and Data Analysis, 37(1), 49-64. https://EconPapers.repec.org/RePEc:eee:csdana:v:37:y:2001:i:1:p:49-64. Vichi M, Rocci R, Kiers H (2007). “Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches.” Journal of Classification, 24, 71-98. doi:10.1007/s00357-007-0006-x.

Examples

X_i_jk = generate_dataset()$X_i_jk
model = simultaneous()
ct3clus = fit.ct3clus(model, X_i_jk, c(8,5,4), c(3,3,2), alpha=0.5)

T3Clus Model

Description

Implements simultaneous version of TWCFTA

Usage

fit.t3clus(model, X_i_jk, full_tensor_shape, reduced_tensor_shape)

## S4 method for signature 'simultaneous'
fit.t3clus(model, X_i_jk, full_tensor_shape, reduced_tensor_shape)

Arguments

model

Initialized simultaneous 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 performs simultaneously the sequential TWCFTA model. The model finds B_j_q and C_k_r such that the between-clusters deviance of the component scores is maximized.

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
BestIteration - Iteration yielding the best results
Converged - Flag to check if algorithm converged for the K-means
nConverges - Number of loops that converged for the K-means
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 - Weighted PseudoF score
Labels - Object cluster assignments
Fs - Objective function values for the KM best iterate
Enorm - Average l2 norm of the residual norm.

References

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. Rocci R, Vichi M (2005). “Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units.” Psychometrika, 70, 715-736. doi:10.1007/s11336-001-0926-z. Vichi M, Rocci R, Kiers H (2007). “Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches.” Journal of Classification, 24, 71-98. doi:10.1007/s00357-007-0006-x.

Examples

X_i_jk = generate_dataset()$X_i_jk
model = simultaneous()
t3clus = fit.t3clus(model, X_i_jk, c(8,5,4), c(3,3,2))

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.

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))

TWFCTA model

Description

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

Usage

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

## S4 method for signature 'tandem'
fit.twfcta(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 implements sequential factorial decomposition and clustering.

The technique performs Tucker2 decomposition on the X_i_jk matrix to obtain the matrix of component scores Y_i_qr with component weights matrices B_j_q and C_k_r.
The K-means clustering algorithm is then applied to the component scores matrix Y_i_qr to obtain the desired core centroids matrix Y_g_qr and its associated stochastic membership function matrix U_i_g.

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

The technique helps interpret the within clusters variability of the data. The Tucker2 tends to explain most of the total variation in the dataset. Hence, the variance of variables that do not contribute to the clustering structure in the dataset is also included.
The Tucker2 dimensions may still mask some essential clustering structures in the dataset.

References

Examples

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

Folding Matrix to Tensor by Mode.

Description

X_i_jk => X_i_j_k, X_j_ki => X_i_j_k, X_k_ij => X_i_j_k

Usage

fold(X, mode, shape)

Arguments

X

Data matrix to fold.

mode

Mode of operation.

shape

Dimension of original tensor.

Value

X_i_j_k Three-mode tensor.

Examples

X_i_jk = generate_dataset()$X_i_jk
X_i_j_k = fold(X_i_jk, mode=1, shape=c(I=8,J=5,K=4)) # X_i_j_k

Three-Mode Dataset Generator for Simulations

Description

Generate G clustered synthetic dataset of I objects measured on J variables for K occasions with additive noise.

Usage

generate_dataset(
  I = 8,
  J = 5,
  K = 4,
  G = 3,
  Q = 3,
  R = 2,
  centroids_spread = c(0, 1),
  noise_mean = 0,
  noise_stdev = 0.5,
  seed = NULL
)

Arguments

I

Number of objects.

J

Number of variables per occasion.

K

Number of occasions.

G

Number of clusters.

Q

Number of factors for the variables.

R

Number of factors for the occasions.

centroids_spread

interval from which to uniformly pick the centroids.

noise_mean

Mean of noise to generate.

noise_stdev

Noise effect level/spread/standard deviation.

seed

Seed for random sequence generation.

Value

Z_i_jk: Component scores in the full space.

E_i_jk: Generated noise at the given noise level.

X_i_jk: Dataset with noise level set to noise_stdev specified.

Y_g_qr: Centroids matrix in the reduced space.

U_i_g: Stochastic membership function matrix.

B_j_q: Objects component scores matrix.

C_k_r: Occasions component scores matrix.

Examples

generate_dataset(seed=0)

Random Membership Function Matrix Generator

Description

Generates random binary stochastic membership function matrix for the I objects.

Usage

generate_rmfm(I, G, seed = NULL)

Arguments

I

Number of objects.

G

Number of groups/clusters.

seed

Seed for random number generation.

Value

U_i_g, binary stochastic membership matrix.

Examples

generate_rmfm(I=8,G=3)

One-run of the K-means clustering technique

Description

Initializes centroids based on a given membership function matrix or randomly. Iterate once over the input data to update the membership function matrix assigning objects to the closest centroids.

Usage

onekmeans(Y_i_qr, G, U_i_g = NULL, seed = NULL)

Arguments

Y_i_qr

Input data to group/cluster.

G

Number of clusters to find.

U_i_g

Initial membership matrix for the I objects.

seed

Seed for random values generation.

Value

updated membership matrix U_i_g.

References

Oti EU, Olusola MO, Eze FC, Enogwe SU (2021). “Comprehensive Review of K-Means Clustering Algorithms.” International Journal of Advances in Scientific Research and Engineering (IJASRE), ISSN:2454-8006, DOI: 10.31695/IJASRE, 7(8), 64–69. doi:10.31695/IJASRE.2021.34050, https://ijasre.net/index.php/ijasre/article/view/1301.

Examples

X_i_jk = generate_dataset(seed=0)$X_i_jk
onekmeans(X_i_jk, G=5)

PseudoF Score in the Full-Space

Description

Computes the PseudoF score in the full space.

Usage

pseudof.full(bss, wss, full_tensor_shape, reduced_tensor_shape)

Arguments

bss

Between sums of squared deviations between clusters.

wss

Within sums of squared deviations within clusters.

full_tensor_shape

Dimensions of the tensor in the original space.

reduced_tensor_shape

Dimension of the tensor in the reduced space.

Value

PseudoF score

References

Caliński T, Harabasz J (1974). “A dendrite method for cluster analysis.” Communications in Statistics, 3(1), 1-27. doi:10.1080/03610927408827101, https://www.tandfonline.com/doi/pdf/10.1080/03610927408827101 , https://www.tandfonline.com/doi/abs/10.1080/03610927408827101. Rocci R, Vichi M (2005). “Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units.” Psychometrika, 70, 715-736. doi:10.1007/s11336-001-0926-z.

Examples

pseudof.full(12,6,c(8,5,4),c(3,3,2))

PseudoF Score in the Reduced-Space

Description

Computes the PseudoF score in the reduced space.

Usage

pseudof.reduced(bss, wss, full_tensor_shape, reduced_tensor_shape)

Arguments

bss

Between sums of squared deviations between clusters.

wss

Within sums of squared deviations within clusters.

full_tensor_shape

Dimensions of the tensor in the original space.

reduced_tensor_shape

Dimension of the tensor in the reduced space.

Value

PseudoF score

References

Examples

pseudof.reduced(12,6,c(8,5,4),c(3,3,2))

Simultaneous Model Constructor

Description

Initialize model object required by the simultaneous methods.

Usage

simultaneous(
  seed = NULL,
  verbose = TRUE,
  init = "svd",
  n_max_iter = 10,
  n_loops = 10,
  tol = 1e-05,
  U_i_g = NULL,
  B_j_q = NULL,
  C_k_r = NULL
)

Arguments

seed

Seed for random sequence generation.

verbose

Flag to display output result for each loop.

init

The initialization method for the model parameters. Values could be 'svd','random','twcfta' or 'twfcta' Defaults to svd.

n_max_iter

Maximum number of iterations to optimize objective function.

n_loops

Number of runs/loops in search of the global result.

tol

Acceptable tolerance level.

U_i_g

Membership function matrix for the objects.

B_j_q

Component matrix for the variables.

C_k_r

Component matrix for the occasions.

Details

Two simultaneous models T3Clus and 3FKMeans are the implemented methods.

T3Clus finds B_j_q and C_k_r such that the between-clusters deviance of the component scores is maximized.
3FKMeans finds B_j_q and C_k_r such that the within-clusters deviance of the component scores is minimized.

Value

An object of class "simultaneous".

Note

The model finds the best partition described by the best orthogonal linear combinations of the variables and orthogonal linear combinations of the occasions.

References

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. Vichi M, Rocci R, Kiers H (2007). “Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches.” Journal of Classification, 24, 71-98. doi:10.1007/s00357-007-0006-x.

Examples

simultaneous()

Simultaneous Model

Description

Simultaneous Model

Slots

seed: numeric. Seed for random sequence generation. Defaults to None.
verbose: logical. Whether to display executions output or not. Defaults to False.
init: character. The parameter initialization method. Defaults to 'svd'.
n_max_iter: numeric. Maximum number of iterations. Defaults to 10.
n_loops: numeric. Number of initialization to guarantee global results. Defaults to 10.
tol: numeric. Tolerance level/acceptable error. Defaults to 1e-5.
U_i_g: numeric. (I,G) initial stochastic membership function matrix.
B_j_q: numeric. (J,Q) initial component weight matrix for variables.
C_k_r: numeric. (K,R) initial component weight matrix for occasions.

Split Member of Largest cluster with An Empty cluster.

Description

If there is an empty cluster share members of largest cluster with empty cluster via the k-means clustering technique

Usage

split_update(LC, LC_members, LC_scores, EC, U_i_g, C_g, seed)

Arguments

LC

Largest cluster index.

LC_members

Members of largest cluster.

LC_scores

Scores of largest cluster.

EC

Empty cluster index to share members of LC with.

U_i_g

Current membership function matrix with empty cluster to update.

C_g

Number of members in each cluster.

seed

Seed for random number generation.

Value

U_i_g, the updated membership matrix.

Initializes an instance of the tandem model required by the tandem methods.

Description

Initializes an instance of the tandem model required by the tandem methods.

Usage

tandem(
  seed = NULL,
  verbose = TRUE,
  init = "svd",
  n_max_iter = 10,
  n_loops = 10,
  tol = 1e-05,
  U_i_g = NULL,
  B_j_q = NULL,
  C_k_r = NULL
)

Arguments

seed

Seed for random sequence generation.

verbose

Flag to display iteration outputs for each loop.

init

Parameter initialization method, 'svd' or 'random'.

n_max_iter

Maximum number of iteration to optimize the objective function.

n_loops

Maximum number of loops/runs for global results.

tol

Allowable tolerance to check convergence.

U_i_g

Initial membership function matrix for the objects.

B_j_q

Initial component scores matrix for the variables.

C_k_r

Initial component sores matrix for the occasions.

Value

An object of class "tandem".

References

Tandem Class

Description

Tandem Class

Slots

seed: Seed for random sequence generation. Defaults to None.
verbose: logical. Whether to display executions output or not. Defaults to False.
init: character. The parameter initialization method. Defaults to 'svd'.
n_max_iter: numeric. Maximum number of iterations. Defaults to 10.
n_loops: numeric. Number of initialization to guarantee global results. Defaults to 10.
tol: numeric. Tolerance level/acceptable error. Defaults to 1e-5.
U_i_g: matrix. (I,G) initial stochastic membership function matrix.
B_j_q: matrix. (J,Q) initial component weight matrix for variables.
C_k_r: matrix. (K,R) initial component weight matrix for occasions.

Tensor Matricization

Description

Unfold/Matricize tensor. convert matrix to tensor by mode.

Usage

unfold(tensor, mode)

Arguments

tensor

Three-mode tensor array.

mode

Mode of operation.

Value

Matrix

Examples

X_i_jk = generate_dataset()$X_i_jk
X_i_j_k = fold(X_i_jk, mode=1, shape=c(I=8,J=5,K=4))
unfold(X_i_j_k, mode=1) # X_i_jk

Simultaneous results attributes

Description

Slots

Tandem results attributes

Description

Slots

3FKMeans Model

Description

Usage

Arguments

Details

Value

References

Examples

CT3Clus Model

Description

Usage

Arguments

Value

References

See Also

Examples

T3Clus Model

Description

Usage

Arguments

Details

Value

References

Examples

TWCFTA model

Description

Usage

Arguments

Details

Value

Note

References

See Also

Examples

TWFCTA model

Description

Usage

Arguments

Details

Value

Note

References

See Also

Examples

Folding Matrix to Tensor by Mode.

Description

Usage

Arguments

Value

Examples

Three-Mode Dataset Generator for Simulations

Description

Usage

Arguments

Value

Examples

Random Membership Function Matrix Generator

Description

Usage

Arguments

Value

Examples

One-run of the K-means clustering technique

Description

Usage

Arguments

Value

References

Examples

PseudoF Score in the Full-Space

Description

Usage

Arguments

Value