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Type: Package
Title: CUR/CX Tensor Decomposition
Version: 1.0.2
Date: 2021-08-02
Depends: R (≥ 4.1.0)
Imports: methods, fields, MASS, igraph, rTensor
Suggests: testthat, nnTensor
Description: CUR/CX decomposition factorizes a matrix into two factor matrices and Multidimensional CX Decomposition factorizes a tensor into a core tensor and some factor matrices. See the reference section of GitHub README.md https://github.com/rikenbit/ccTensor, for details of the methods.
License: Artistic-2.0
URL: https://github.com/rikenbit/ccTensor
NeedsCompilation: no
Packaged: 2021-08-11 23:40:36 UTC; root
Author: Koki Tsuyuzaki [aut, cre], Itoshi Nikaido [aut]
Maintainer: Koki Tsuyuzaki <k.t.the-answer@hotmail.co.jp>
Repository: CRAN
Date/Publication: 2021-08-12 04:30:07 UTC

CUR/CX Tensor Decomposition

Description

CUR/CX decomposition factorizes a matrix into two factor matrices and Multidimensional CX Decomposition factorizes a tensor into a core tensor and some factor matrices. See the reference section of GitHub README.md <https://github.com/rikenbit/ccTensor>, for details of the methods.

Details

The DESCRIPTION file:

Package: ccTensor
Type: Package
Title: CUR/CX Tensor Decomposition
Version: 1.0.2
Date: 2021-08-02
Authors@R: c(person("Koki", "Tsuyuzaki", role = c("aut", "cre"), email = "k.t.the-answer@hotmail.co.jp"), person("Itoshi", "Nikaido", role = "aut"))
Depends: R (>= 4.1.0)
Imports: methods, fields, MASS, igraph, rTensor
Suggests: testthat, nnTensor
Description: CUR/CX decomposition factorizes a matrix into two factor matrices and Multidimensional CX Decomposition factorizes a tensor into a core tensor and some factor matrices. See the reference section of GitHub README.md <https://github.com/rikenbit/ccTensor>, for details of the methods.
License: Artistic-2.0
URL: https://github.com/rikenbit/ccTensor
Author: Koki Tsuyuzaki [aut, cre], Itoshi Nikaido [aut]
Maintainer: Koki Tsuyuzaki <k.t.the-answer@hotmail.co.jp>

Index of help topics: 

ccTensor-package        CUR/CX Tensor Decomposition
CUR                     CUR Matrix Decomposition
CX                      CX Matrix Decomposition
MultiCX                 MultiCX Tensor Decomposition

Author(s)

NA

Maintainer: NA

References

Michael W. Mahoney, et. al., (2009). CUR matrix decompositions for improved data analysis. PNAS

Petros Drineas et.al., (2008). Relative-error CUR Matrix Decompositions. SIAM J. Matrix Anal. Appl.

Maria F. K. B. et. al. (2019). Multidimensional CX Decomposition of Tensors. WCNPS

See Also

CX,CUR,MultiCX

Examples

ls("package:ccTensor")

CUR Matrix Decomposition

Description

The input data is assumed to be a matrix. CUR decomposes the matrix to three low-dimensional factor matices. C and R are not estimated values but the actual column and row vectors sampled from the matrix.

Usage

CUR(A, c.rank=NULL, r.rank=NULL, thr=0.9,
  c.method=c("best.match", "random", "exact.num.random", "top.scores"),
  u.method=c("invCR", "invW"),
  r.method=c("best.match", "random", "exact.num.random", "top.scores"))

Arguments

A

The input matrix which has N-rows and M-columns.

c.rank

The number of low-dimension of C (J1 < N,M). If this argument is not specified or specified as NULL, the low-dimension is estimated based on the cumulative singular value (Default: NULL).

r.rank

The number of low-dimension of R (J2 < N,M). If this argument is not specified or specified as NULL, the low-dimension is estimated based on the cumulative singular value (Default: NULL).

thr

The threshold to determine the low-dimension J1 and J2. The value must be range 0 to 1 (Default: 0.9).

c.method

The column sampling algorithm (Default: best.match).

u.method

The algorithm to calculate U (Default: invCR).

r.method

The row sampling algorithm (Default: best.match).

Value

C: A N-rows and J1-columns matrix contains the sampled column vectors from the input matrix A. U: A J1-rows and J2-columns matrix. R: A J2-rows and M-columns matrix contains the sampled row vectors from the input matrix A. indC: The sampled column indices. indC: The sampled row indices. RecError : The reconstruction error between data matrix and reconstructed matrix from C and X.

Author(s)

Koki Tsuyuzaki

References

Michael W. Mahoney, et. al., (2009). CUR matrix decompositions for improved data analysis. PNAS

Examples

    library("ccTensor")
    library("nnTensor")
    # Test data
    matdata <- toyModel(model = "NMF")
    # Simple usage
    out <- CUR(matdata, c.rank=3, r.rank=4)

CX Matrix Decomposition

Description

The input data is assumed to be a matrix. CX decomposes the matrix to two low-dimensional factor matices. C is not an estimated values but the actual column vectors sampled from the matrix.

Usage

CX(A, rank=NULL, thr=0.9,
  c.method=c("best.match", "random", "exact.num.random", "top.scores"))

Arguments

A

The input matrix which has N-rows and M-columns.

rank

The number of low-dimension (J < N,M). If this argument is not specified or specified as NULL, the low-dimension is estimated based on the cumulative singular value (Default: NULL).

thr

The threshold to determine the low-dimension J. The value must be range 0 to 1 (Default: 0.9).

c.method

The column sampling algorithm (Default: best.match).

Value

C: A N-rows and J-columns matrix contains the sampled column vectors from the input matrix A. X: A J-rows and M-columns matrix. indC: The sampled column indices. RecError : The reconstruction error between data matrix and reconstructed matrix from C and X.

Author(s)

Koki Tsuyuzaki

References

Petros Drineas et.al., (2008). Relative-error CUR Matrix Decompositions. SIAM J. Matrix Anal. Appl.

Examples

    library("ccTensor")
    library("nnTensor")
    # Test data
    matdata <- toyModel(model = "NMF")
    # Simple usage
    out <- CX(matdata, rank=5)

MultiCX Tensor Decomposition

Description

The input data is assumed to be a tensor. MultiCX decomposes the tensor into a core tensor and some factor matrices. The factor matrices are not estimated values but the actual column vectors sampled from the unfolded matrix in each mode.

Usage

MultiCX(Y, rank=NULL, modes=1:3, thr=0.9,
  c.method=c("best.match", "random", "exact.num.random", "top.scores"))

Arguments

Y

The input tensor (e.g. N times M times L).

rank

The number of low-dimension of factor matrices (e.g. J1, J2, and J3). If this argument is not specified or specified as NULL, the low-dimension is estimated based on the cumulative singular value (Default: NULL).

modes

The vector of the modes on whih to perform the decomposition (Default: 1:3 <all modes>).

thr

The threshold to determine the low-dimension of factor matrices. The value must be range 0 to 1 (Default: 0.9).

c.method

The column sampling algorithm (Default: best.match).

Value

U: Core tensor (e.g. J1 times J2 times J3). C: Factor matrices (e.g. C_1: ????????) RecError : The reconstruction error between data tensor and reconstructed tensor from C and X.

Author(s)

Koki Tsuyuzaki

References

Maria F. K. B. et. al. (2019). Multidimensional CX Decomposition of Tensors. WCNPS

Examples

    library("ccTensor")
    library("nnTensor")
    # Test data
    tensdata <- toyModel(model = "CP")
    # Simple usage
    out <- MultiCX(tensdata, rank=c(3,4,5))

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