gcTensor (version 1.0.0)

GCTF: Generalised Coupled Tensor Factorisation (GCTF)

Description

The input data is assumed to be a list containing multiple matrices. GCTF decomposes N matrices (Xs) to M low-dimensional factor matices (Zs).

Usage

GCTF(X, R, M=NULL, pseudocount=.Machine$double.eps, initZ=NULL, fix=NULL, Ranks, Beta=1,
    num.iter=30, thr=1E-10, verbose=FALSE)

Value

U : A matrix which has N-rows and J-columns (J < N, M). V : A matrix which has M-rows and J-columns (J < N, M). J : The number of dimension (J < N, M). RecError : The reconstruction error between data tensor and reconstructed tensor from U and V. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error. Trial : All the results of the trials to estimate the rank. Runtime : The number of the trials to estimate the rank. RankMethod : The rank estimation method.

Arguments

X

A list containing N data matrices.

R

Coupling matrix which has N-rows and M-columns. N is the number of data matrices and M is the number of factor matrices decomposed by GCTF algorithm. If i-th data (X_i) has j-th factor matrix (Z_j), 1 is filled in R[i,j], otherwise 0.

M

A list containing N mask matrices. If in n-th data matrix, i-th row/j-th column is missing value, 0 is filled, otherwise 0. Default value is NULL, which means all the values are filled with 1 (No missing value).

pseudocount

The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon).

initZ

A M-length list, which is the initial values of factor matrix Z. If not specified, random matrices are generated and used (Default: NULL).

fix

Whether each factor matrix Z is updated in each iteration step (Default: NULL, which means all Zs are updated).

Ranks

A M-length list, which is the correspondence between the dimension of data matrices and the lower dimension of factor matrices.

Beta

The parameter of Beta-divergence. Beta=0, 1, and 2 each mean Euclid Distance, KL-divergence, and Itakura-Saito divergence between the data matrices and reconstructed matrices by factor matrices (Default: 1).

num.iter

The number of interation step (Default: 30).

thr

When error change rate is lower than thr, the iteration is terminated (Default: 1E-10).

verbose

If verbose == TRUE, Error change rate is generated in console window (Default: FALSE).

Author

Koki Tsuyuzaki

References

Y. Kenan Yilmaz, et. al., (2011). Generalised Coupled Tensor Factorisation, NIPS

Beyza Ermis, et. al., (2015). Link prediction in heterogeneous data via generalized coupled tensor factorization, Data Mining and Knowledge Discovery

Examples

  if(interactive()){
  # Simulation Datasets
  set.seed(123)

  # I times J times K
  X1 <- rand_tensor(modes = c(4, 5, 6))
  X1 <- X1@data^2
  names(dim(X1)) <- c("I", "J", "K")

  # I times P
  X2 <- matrix(runif(4 * 7), nrow=4, ncol=7)
  names(dim(X2)) <- c("I", "M")

  # J times Q
  X3 <- matrix(runif(5 * 8), nrow=5, ncol=8)
  names(dim(X3)) <- c("J", "N")

  # Coupled Tensor/Matrix
  X <- list(X1 = X1, X2 = X2, X3 = X3)

  # Coupling matrix R (CP)
  R_CP <- rbind(
      c(1,1,1,0,0),
      c(1,0,0,1,0),
      c(0,1,0,0,1)
  )
  rownames(R_CP) <- paste0("X", seq(3))
  colnames(R_CP) <- LETTERS[seq(5)]

  # Size of Factor matrices (CP)
  Ranks_CP <- list(
      A=list(I=4, r=3),
      B=list(J=5, r=3),
      C=list(K=6, r=3),
      D=list(M=7, r=3),
      E=list(N=8, r=3))

  # Coupling matrix R (Tucker)
  R_Tucker <- rbind(
      c(1,1,1,1,0,0),
      c(1,0,0,0,1,0),
      c(0,1,0,0,0,1)
  )
  rownames(R_Tucker) <- paste0("X", seq(3))
  colnames(R_Tucker) <- LETTERS[seq(6)]

  # Size of Factor matrices (Tucker)
  Ranks_Tucker <- list(
      A=list(I=4, p=3),
      B=list(J=5, q=4),
      C=list(K=6, r=3),
      D=list(p=3, q=4, r=3),
      E=list(M=7, p=3),
      F=list(N=8, q=4))

  # CP
  out.CP_EUC <- GCTF(X, R_CP, Ranks=Ranks_CP, Beta=0, verbose=TRUE)
  out.CP_KL <- GCTF(X, R_CP, Ranks=Ranks_CP, Beta=1, verbose=TRUE)
  out.CP_IS <- GCTF(X, R_CP, Ranks=Ranks_CP, Beta=2, verbose=TRUE)

  # Tucker
  out.Tucker_EUC <- GCTF(X, R_Tucker, Ranks=Ranks_Tucker, Beta=0, verbose=TRUE)
  out.Tucker_KL <- GCTF(X, R_Tucker, Ranks=Ranks_Tucker, Beta=1, verbose=TRUE)
  out.Tucker_IS <- GCTF(X, R_Tucker, Ranks=Ranks_Tucker, Beta=2, verbose=TRUE)
  }