Title:	Invertible Transforms for Matrices
Version:	0.1.1
Description:	Provides composable invertible transforms for (sparse) matrices.
License:	MIT + file LICENSE
URL:	https://rohelab.github.io/invertiforms/, https://github.com/RoheLab/invertiforms
BugReports:	https://github.com/RoheLab/invertiforms/issues
Depends:	Matrix, methods
Imports:	sparseLRMatrix (≥ 0.1.0), glue
Suggests:	covr, testthat (≥ 3.0.0), igraph, igraphdata
Encoding:	UTF-8
RoxygenNote:	7.2.1.9000
Collate:	's4-generics.R' 'DoubleCenter.R' 'NormalizedLaplacian.R' 'PerturbedLaplacian.R' 'RegularizedLaplacian.R' 'invertiforms-package.R' 'utils.R'
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2022-11-12 22:09:18 UTC; alex
Author:	Alex Hayes [aut, cre, cph]
Maintainer:	Alex Hayes <alexpghayes@gmail.com>
Repository:	CRAN
Date/Publication:	2022-11-25 12:40:10 UTC

invertiforms: Invertible Transforms for Matrices

Description

Provides composable invertible transforms for (sparse) matrices.

Author(s)

Maintainer: Alex Hayes alexpghayes@gmail.com (ORCID) [copyright holder]

See Also

Useful links:

• https://rohelab.github.io/invertiforms/

• https://github.com/RoheLab/invertiforms

• Report bugs at https://github.com/RoheLab/invertiforms/issues

Construct and use DoubleCenter transformations

Description

A convenience function to create DoubleCenter S4 objects, which are useful for simultaneously row and column centering a matrix.

Usage

DoubleCenter(A)

## S4 method for signature 'DoubleCenter,sparseMatrix'
transform(iform, A)

## S4 method for signature 'DoubleCenter,sparseLRMatrix'
inverse_transform(iform, A)

## S4 method for signature 'DoubleCenter,vsp_fa'
inverse_transform(iform, A)

Arguments

Value

• DoubleCenter() creates a DoubleCenter object.

• transform() returns the transformed matrix, typically as a sparseLRMatrix::sparseLRMatrix.

• inverse_transform() returns the inverse transformed matrix, typically as a sparseLRMatrix::sparseLRMatrix in most cases. When possible reduces the sparseLRMatrix::sparseLRMatrix to a Matrix::sparseMatrix().

Examples

library(igraph)
library(igraphdata)

data("karate", package = "igraphdata")

A <- get.adjacency(karate)

iform <- DoubleCenter(A)

A_tilde <- transform(iform, A)
A_recovered <- inverse_transform(iform, A_tilde)

all.equal(A, A_recovered)

Row and column centering transformation

Description

Row and column centering transformation

Slots

row_means

numeric.

col_means

numeric.

overall_mean

numeric.

An abstract S4 class representing an invertible transformation

Description

An abstract S4 class representing an invertible transformation

Construct and use the Normalized Laplacian

Description

A convenience function to create NormalizedLaplacian S4 objects, which are useful for finding the normalized Laplacian of the adjacency matrix of a graph.

Usage

NormalizedLaplacian(A)

## S4 method for signature 'NormalizedLaplacian,sparseMatrix'
transform(iform, A)

## S4 method for signature 'NormalizedLaplacian,sparseMatrix'
inverse_transform(iform, A)

Arguments

Details

We define the normalized Laplacian L(A) of an n \times n graph adjacency matrix A as

L(A)_{ij} = \frac{A_{ij}}{\sqrt{d^{out}_i} \sqrt{d^{in}_j}}

where

d^{out}_i = \sum_{j=1}^n \| A_{ij} \|

and

d^{in}_j = \sum_{i=1}^n \| A_{ij} \|.

When A_{ij} denotes the present of an edge from node i to node j, which is fairly standard notation, d^{out}_i denotes the (absolute) out-degree of node i and d^{in}_j denotes the (absolute) in-degree of node j.

Note that this documentation renders most clearly at https://rohelab.github.io/invertiforms/.

Value

• NormalizedLaplacian() creates a NormalizedLaplacian object.

• transform() returns the transformed matrix, typically as a Matrix.

• inverse_transform() returns the inverse transformed matrix, typically as a Matrix.

Examples

library(igraph)
library(igraphdata)

data("karate", package = "igraphdata")

A <- get.adjacency(karate)

iform <- NormalizedLaplacian(A)

L <- transform(iform, A)
A_recovered <- inverse_transform(iform, L)

all.equal(A, A_recovered)

Normalized graph Laplacian transformation

Description

Normalized graph Laplacian transformation

Slots

rsA

numeric.

csA

numeric.

Construct and use the Perturbed Laplacian

Description

Construct and use the Perturbed Laplacian

Usage

PerturbedLaplacian(A, tau = NULL)

## S4 method for signature 'PerturbedLaplacian,sparseMatrix'
transform(iform, A)

## S4 method for signature 'PerturbedLaplacian,sparseLRMatrix'
inverse_transform(iform, A)

Arguments

Details

We define the perturbed Laplacian L^\tau(A) of an n \times n graph adjacency matrix A as

L^\tau(A)_{ij} = \frac{A_{ij} + \frac{\tau}{n}}{\sqrt{d^{out}_i + \tau} \sqrt{d^{in}_j + \tau}}

where

d^{out}_i = \sum_{j=1}^n \|A_{ij} \|

and

d^{in}_j = \sum_{i=1}^n \|A_{ij} \|.

When A_{ij} denotes the present of an edge from node i to node j, which is fairly standard notation, d^{out}_i denotes the (absolute) out-degree of node i and d^{in}_j denotes the (absolute) in-degree of node j.

Note that this documentation renders more clearly at https://rohelab.github.io/invertiforms/.

Value

• PerturbedLaplacian() creates a PerturbedLaplacian object.

• transform() returns the transformed matrix, typically as a Matrix.

• inverse_transform() returns the inverse transformed matrix, typically as a Matrix.

Examples

library(igraph)
library(igraphdata)

data("karate", package = "igraphdata")

A <- get.adjacency(karate)

iform <- PerturbedLaplacian(A)

L <- transform(iform, A)
L

## Not run: 
A_recovered <- inverse_transform(iform, L)
all.equal(A, A_recovered)

## End(Not run)

Perturbed graph Laplacian transformation

Description

Perturbed graph Laplacian transformation

Slots

tau

numeric.

rsA

numeric.

csA

numeric.

tau_choice

character.

Construct and use the Regularized Laplacian

Description

Construct and use the Regularized Laplacian

Usage

RegularizedLaplacian(A, tau_row = NULL, tau_col = NULL)

## S4 method for signature 'RegularizedLaplacian,Matrix'
transform(iform, A)

## S4 method for signature 'RegularizedLaplacian,matrix'
transform(iform, A)

## S4 method for signature 'RegularizedLaplacian,sparseLRMatrix'
transform(iform, A)

## S4 method for signature 'RegularizedLaplacian,Matrix'
inverse_transform(iform, A)

## S4 method for signature 'RegularizedLaplacian,matrix'
inverse_transform(iform, A)

## S4 method for signature 'RegularizedLaplacian,vsp_fa'
inverse_transform(iform, A)

Arguments

Details

We define the regularized Laplacian L^\tau(A) of an n \times n graph adjacency matrix A as

L^\tau(A)_{ij} = \frac{A_{ij}}{\sqrt{d^{out}_i + \tau_{row}} \sqrt{d^{in}_j + \tau_{col}}}

where

d^{out}_i = \sum_{j=1}^n \| A_{ij} \|

and

d^{in}_j = \sum_{i=1}^n \| A_{ij} \|.

When A_{ij} denotes the present of an edge from node i to node j, which is fairly standard notation, d^{out}_i denotes the (absolute) out-degree of node i and d^{in}_j denotes the (absolute) in-degree of node j. Then \tau_{row} is an additive out-degree regularizer and \tau_{col} is an additive in-degree regularizer.

Note that this documentation renders more clearly at https://rohelab.github.io/invertiforms/.

Value

• RegularizedLaplacian() creates a RegularizedLaplacian object.

• transform() returns the transformed matrix, typically as a Matrix.

• inverse_transform() returns the inverse transformed matrix, typically as a Matrix.

Examples

library(igraph)
library(igraphdata)

data("karate", package = "igraphdata")

A <- get.adjacency(karate)

iform <- RegularizedLaplacian(A)

L <- transform(iform, A)
L

A_recovered <- inverse_transform(iform, L)

all.equal(A, A_recovered)

Regularized graph Laplacian transformation

Description

Regularized graph Laplacian transformation

Slots

tau_row

numeric.

tau_col

numeric.

rsA

numeric.

csA

numeric.

tau_choice_row

character.

tau_choice_col

character.

Apply the inverse of an invertible transformation

Description

Apply the inverse of an invertible transformation

Usage

inverse_transform(iform, A)

Arguments

Value

The inverse transformed matrix.

Apply an invertible transformation

Description

Apply an invertible transformation

Usage

transform(iform, A)

Arguments

Value

The transformed matrix.