Simultaneous Clustering and Factorial Decomposition of Three-Way Datasets.

simuclustfactor

The goal of simuclustfactor is to perform:

• tandem clustering and factor-decomposition procedures sequentially (TWCFTA and TWFCTA).
• simultaneous clustering and factor decomposition procedures simultaneously (T3Clus and 3FKMeans).
• combined T3Clus and 3FKMeans procedures simultaneously (CT3Clus).

Installation

You can install the development version of simuclustfactor from GitHub with:

# install.packages("devtools")
devtools::install_github("prablordeppey/simuclustfactor-r")

Implementations

Synthetic Dataset Generation (Additive noise)

library(simuclustfactor)

# Defining tensor dimensions in full and reduced spaces.
I=8; J=5; K=4 # number of objects, variables and occasions respectively.
G=3; Q=3; R=2 # number of clusters, factors for variable and factors for occasion respectively.
data = generate_dataset(I, J, K, G, Q, R, mean=0, stdev=0.5, random_state=0)  # generate synthetic dataset with noise level 0.5. 

# Extracting the data
Y_g_qr = data$Y_g_qr  # centroids matrix in the reduced space.
Z_i_jk = data$Z_i_jk  # score/centroid matrix in the full-space.
X_i_jk = data$X_i_jk  # dataset with noise.

# Ground-truth associations
U_i_g = data$U_i_g  # binary stochastic membership matrix
B_j_q = data$B_j_q  # variables factor matrix
C_k_r = data$C_k_r  # occasions factor matrix

# Folding generated data matrices into tensors
X_i_j_k = fold(X_i_jk, mode=1, shape=c(I,J,K))
Z_i_j_k = fold(Z_i_jk, mode=1, shape=c(I,J,K))
Y_g_q_r = fold(Y_g_qr, mode=1, shape=c(G,Q,R))

Tandem Models

# Initialize the tandem model
tandem_model = tandem(random_state=NULL, verbose=TRUE, init='svd', n_max_iter=10, n_loops=10, tol=1e-5, U_i_g=NULL, B_j_q=NULL, C_k_r=NULL)

TWCFTA

twcfta = fit.twcfta(tandem_model, X_i_jk, full_tensor_shape=c(I,J,K), reduced_tensor_shape=c(G,Q,R))

TWFCTA

twfcta = fit.twfcta(tandem_model, X_i_jk, full_tensor_shape=c(I,J,K), reduced_tensor_shape=c(G,Q,R))

# The following attributes are accessible for the tandem models via the '@' operator
twfcta@U_i_g0  # initial membership matrix
twfcta@B_j_q0  # initial variable-component matrix
twfcta@C_k_r0  # initial occasion-component matrix
twfcta@U_i_g  # final membership matrix
twfcta@B_j_q  # final variable-component matrix
twfcta@C_k_r  # final occasion-component matrix

twfcta@Y_g_qr  # The centroids in the reduced space (data matrix).
twfcta@X_i_jk_scaled  # Standardized data matrix.

twfcta@BestTimeElapsed  # Execution time for the best iterate.
twfcta@BestLoop  # Loop that obtained the best iterate.

twfcta@BestKmIteration  # Number of iterations until best iterate for the K-means.
twfcta@BestFaIteration  # Number of iterations until best iterate for the FA.
twfcta@FaConverged  # Flag to check if algorithm converged for the Factor decomposition.
twfcta@KmConverged  # Flag to check if algorithm converged for the K-means.
twfcta@nKmConverges  # Number of loops that converged for the K-means.
twfcta@nFaConverges  # Number of loops that converged for the Factor decomposition.

twfcta@TSS_full  # Total deviance in the full-space.
twfcta@BSS_full  # Between deviance in the reduced-space.
twfcta@RSS_full  # Residual deviance in the reduced-space.
twfcta@TSS_reduced  # Total deviance in the reduced-space.
twfcta@BSS_reduced  # Between deviance in the reduced-space.
twfcta@RSS_reduced  # Residual deviance in the reduced-space.

twfcta@PF_full  # PseudoF computed in the full-space.
twfcta@PF_reduced  # PseudoF computed in the reduced-space.
twfcta@PF  # Actual PseudoF score used to obtain the best loop. PF_reduced for twfcta and PF_full twcfta.

twfcta@Labels  # Object cluster assignments.
twfcta@FsKM  # Objective function values for the KM best iterate.
twfcta@FsFA  # Objective function values for the FA best iterate.
twfcta@Enorm  # Average l2norm of residual norm.

Simultaneous Models

# Initialize the model
simultaneous_model = simultaneous(random_state=NULL, verbose=TRUE, init='svd', n_max_iter=10, n_loops=10, tol=1e-5, U_i_g=NULL, B_j_q=NULL, C_k_r=NULL)

T3Clus & 3FKMeans

t3clus = fit.t3clus(simultaneous_model, X_i_jk, full_tensor_shape=c(I,J,K), reduced_tensor_shape=c(G,Q,R))
tfkmeans = fit.3fkmeans(simultaneous_model, X_i_jk, full_tensor_shape=c(I,J,K), reduced_tensor_shape=c(G,Q,R))

CT3Clus

t3clus = fit.ct3clus(simultaneous_model, X_i_jk, full_tensor_shape=c(I,J,K), reduced_tensor_shape=c(G,Q,R), alpha=1)
ct3clus = fit.ct3clus(simultaneous_model, X_i_jk, full_tensor_shape=c(I,J,K), reduced_tensor_shape=c(G,Q,R), alpha=0.5)
tfkmeans = fit.ct3clus(simultaneous_model, X_i_jk, full_tensor_shape=c(I,J,K), reduced_tensor_shape=c(G,Q,R), alpha=0)

# The following attributes are accessible for the simultaneous models via the '@' operator
ct3clus@U_i_g0  # initial membership matrix.
ct3clus@B_j_q0  # initial variable-component matrix.
ct3clus@C_k_r0  # initial occasion-component matrix.
ct3clus@U_i_g  # final membership matrix.
ct3clus@B_j_q  # final variable-component matrix.
ct3clus@C_k_r  # final occasion-component matrix.

ct3clus@Y_g_qr  # Centroids in the reduced space (data matrix).
ct3clus@X_i_jk_scaled  # Standardized data matrix.

ct3clus@BestTimeElapsed  # Execution time for the best iterate.
ct3clus@BestLoop  # Loop that obtained the best iterate.
ct3clus@BestIteration  # Number of iterations until best iterate found.
ct3clus@Converged  # Flag to check if the algorithm converged.
ct3clus@nConverges  # Number of loops that converged.

ct3clus@TSS_full  # Total deviance in the full-space.
ct3clus@BSS_full  # Between deviance in the reduced-space.
ct3clus@RSS_full  # Residual deviance in the reduced-space.
ct3clus@TSS_reduced  # Total deviance in the reduced-space.
ct3clus@BSS_reduced  # Between deviance in the reduced-space.
ct3clus@RSS_reduced  # Residual deviance in the reduced-space.

ct3clus@PF_full  # PseudoF computed in the full-space.
ct3clus@PF_reduced  # PseudoF computed in the reduced-space.
ct3clus@PF  # Weighted PseudoF score used to obtain the best loop.

ct3clus@Labels  # Object cluster assignments.
ct3clus@Fs  # Objective function values for the best iterate.
ct3clus@Enorm  # Average l2norm of residual norm.