why using a 4d array in cp?

[ccshao]

Dear scTenifoldNet dev,

Thanks very much for the interesting method. That is the first time I learn something about tensor low approximation, ane I would like to try it on my work.

As I am new to the idea of tensor, I was confused on the 4d array used in the rTensor::cp steps. As the N * N * T (N is the number of genes, T is the sampling times) is 3d array, why a 4d array is used in the implementations (example codes taken from CRAN 1.0.0)?

Her are codes used In the script of tensorDecomposition.R,

#- init a 4d array with the 3rd dim is 1
  tensorX <- array(data = 0, dim = c(nGenes,nGenes,1,nNet))
  if(!is.null(yList)){
    tensorY <- array(data = 0, dim = c(nGenes,nGenes,1,nNet))
  }
  

#- Here only the last dim is filled with correlation matrix.
  for(i in seq_len(nNet)){
    tempX <- matrix(0, nGenes, nGenes)
    rownames(tempX) <- colnames(tempX) <- sGenes
    temp <- as.matrix(xList[[i]])
    tGenes <- sGenes[sGenes %in% rownames(temp)]
    tempX[tGenes,tGenes] <- temp[tGenes,tGenes]
    tensorX[,,,i] <- tempX
    
    if(!is.null(yList)){
      tempY <- matrix(0, nGenes, nGenes)
      rownames(tempY) <- colnames(tempY) <- sGenes
      temp <- as.matrix(yList[[i]])
      tGenes <- sGenes[sGenes %in% rownames(temp)]
      tempY[tGenes,tGenes] <- temp[tGenes,tGenes]
      tensorY[,,,i] <- tempY
    }
    
  }

  tensorX <- rTensor::as.tensor(tensorX)
  set.seed(1)
  tensorX <- rTensor::cp(tnsr = tensorX, num_components = K, max_iter = maxIter, tol = maxError)
  tX <- tensorX$est@data[,,,1]
  for(i in seq_len(nNet)[-1]){
    tX <- tX +  tensorX$est@data[,,,i]
  }
  tX <- tX/nNet
  tX <- tX/max(abs(tX))
  tX <- round(tX,1)
  tX <- as(tX, 'dgCMatrix')
  rownames(tX) <- colnames(tX) <- sGenes

Actually I have tried tensorDecomposition with 3d array, i.e., simly remove the 3rd dim; and replace the "1" in the 3rd to other values. In the former senario I got different results compared to your codes, and the latter case there was an error:

Error in as(tX, "dgCMatrix") : no method or default for coercing “array” to “dgCMatrix”

Thanks in advance.