PSDTF: Positive Semidefinite Tensor Factorization with LogDet...

In nnTensor: Non-Negative Tensor Decomposition

Positive Semidefinite Tensor Factorization with LogDet Divergence (PSDTF)

Description

The input data is assumed to be a three-dimensional array (M x M x N), where each frontal slice is a positive semidefinite (PSD) matrix. PSDTF approximates each PSD matrix as a weighted sum of K PSD basis matrices using the LogDet divergence.

Usage

PSDTF(X, rank=3, initH=NULL, initV=NULL,
  thr=1e-10, num.iter=100, verbose=FALSE)

Arguments

X	A three-dimensional array of size M x M x N, where each frontal slice X[,,n] is a positive semidefinite matrix.
rank	The number of PSD basis matrices (Default: 3).
initH	The initial values of activation matrix H (K x N non-negative matrix) (Default: NULL).
initV	The initial values of PSD basis matrices, a list of K matrices each of size M x M (Default: NULL).
thr	The threshold for convergence based on relative change of LogDet divergence (Default: 1e-10).
num.iter	The number of maximum iterations (Default: 100).
verbose	If verbose is TRUE, the iteration number and error are printed (Default: FALSE).

Value

H : The activation coefficient matrix (K-rows and N-columns)

V : A list of K PSD basis matrices, each of size M x M

RecError : The LogDet divergence values at each iteration

RelChange : The relative change of error at each iteration

Author(s)

Koki Tsuyuzaki

References

K. Yoshii, R. Tomioka, D. Mochihashi, and M. Goto, "Beyond NMF: Time-domain audio source separation without phase reconstruction", ISMIR, pp.369-374, 2013.

Examples

if(interactive()){
  # Generate toy PSD tensor
  M <- 4
  N <- 10
  K <- 2
  V_true <- list()
  for(k in 1:K){
    A <- matrix(runif(M*M), M, M)
    V_true[[k]] <- A %*% t(A)
  }
  H_true <- matrix(runif(K*N), K, N)
  X <- array(0, dim=c(M, M, N))
  for(n in 1:N){
    for(k in 1:K){
      X[,,n] <- X[,,n] + H_true[k,n] * V_true[[k]]
    }
  }

  # Run PSDTF
  out <- PSDTF(X, rank=K, num.iter=20, verbose=TRUE)
}

nnTensor documentation built on May 8, 2026, 5:07 p.m.