Package {ResistantProcrustes}

Title: Resistant Procrustes Methods for Multivariate Data
Version: 0.1.1
Imports: gllvm, fBasics, gtools
Description: Provides resistant alternatives to the standard Procrustes analysis for comparing multivariate datasets, including seven resistant Procrustean methods and their associated permutation tests, as well as the standard Procrustes analysis and its permutation tests. Methods are based on Tang and Jackson (2026) "Improving and evaluating resistant alternatives to Procrustes analysis for multivariate dataset matching" <doi:10.1002/env.70073>.
License: MIT + file LICENSE
Encoding: UTF-8
Config/roxygen2/version: 8.1.0
NeedsCompilation: no
Packaged: 2026-09-30 19:57:29 UTC; xiaozhuotang
Author: Xiaozhuo Tang [aut, cre]
Maintainer: Xiaozhuo Tang <xiaozhuot@mun.ca>
Repository: CRAN
Date/Publication: 2026-10-10 11:30:19 UTC

Biweight Method Permutation Test Performs a permutation test for the Biweight method.

Description

Biweight Method Permutation Test Performs a permutation test for the Biweight method.

Usage

Biweight_permute(P_mat, Q_mat, P_N, S0, verbose = FALSE)

Arguments

P_mat

A matrix representing the configuration to be transformed to best align with Q_mat.

Q_mat

A matrix representing the fixed configuration that remains unchanged during the transformation.

P_N

Number of permutations.

S0

Observed objective function value from the Biweight method.

verbose

Logical; if TRUE, displays progress messages during iterations. Defaults to FALSE.

Value

A list containing:

count_n

The number of permuted objective function values less than or equal to the observed value.

p_value

The permutation test p-value.

S

A vector of objective function values obtained from the permutations.

Huber Method Permutation Test Performs a permutation test for the Huber method.

Description

Huber Method Permutation Test Performs a permutation test for the Huber method.

Usage

Huber_permute(P_mat, Q_mat, P_N, S0, verbose = FALSE)

Arguments

P_mat

A matrix representing the configuration to be transformed to best align with Q_mat.

Q_mat

A matrix representing the fixed configuration that remains unchanged during the transformation.

P_N

Number of permutations.

S0

Observed objective function value from the Huber method.

verbose

Logical; if TRUE, displays progress messages during iterations. Defaults to FALSE.

Value

A list containing:

count_n

The number of permuted objective function values less than or equal to the observed value.

p_value

The permutation test p-value.

S

A vector of objective function values obtained from the permutations.

The Improved Least Median of Squares (ILMS) Permutation Test Performs a permutation test for the ILMS method.

Description

The Improved Least Median of Squares (ILMS) Permutation Test Performs a permutation test for the ILMS method.

Usage

ILMS_permute(
  P_mat,
  Q_mat,
  P_N,
  S0,
  nR = 0,
  s_l_LMS = 1e-09,
  s_u_LMS = 10,
  verbose = FALSE
)

Arguments

P_mat

A matrix representing the configuration to be transformed to best align with Q_mat.

Q_mat

A matrix representing the fixed configuration that remains unchanged during the transformation.

P_N

Number of permutations.

S0

Observed objective function value from the ILMS method.

nR

Number of randomly sampled subsets. If nR <= 0, all possible subsets are used.

s_l_LMS

Lower bound for the scale s.

s_u_LMS

Upper bound for the scale s.

verbose

Logical; if TRUE, displays progress messages during iterations. Defaults to FALSE.

Value

A list containing:

count_n

The number of permuted objective function values less than or equal to the observed value.

p_value

The permutation test p-value.

S

A vector of objective function values obtained from the permutations.

Examples

P_mat <- matrix(c(
  0.3068822, -1.24752606,
  -2.1150143, 4.24520347,
  0.5271354, 1.64468795,
  -0.1264126, -0.08113392,
  -1.4749896, -2.26016700,
  -0.2347269, -1.27047483,
  -0.4833630, 1.43158341,
  -2.3499156, 0.85892382,
  -2.1021129, 0.40267502,
  0.5812934, -0.57210742,
  0.7397990, 1.54898604,
  -1.2173015, -0.65486036,
  -0.6093984, -1.16937177,
  0.3833907, -0.72611343,
  -0.8423056, 1.22427834
), ncol = 2, byrow = TRUE)

Q_mat <- matrix(c(
  1.96990726, -1.67860936,
  1.16952104, -3.19996198,
  -1.64680983, 3.40009837,
  1.51340633, 0.90762220,
  6.02678651, -1.29463718,
  2.56525182, -0.70441947,
  0.08388971, 3.87254957,
  4.11361309, 4.77780158,
  -0.91329668, 0.01870814,
  0.73714253, -0.50391759,
  -1.60842305, 3.07780435,
  3.90039741, 1.29926458,
  3.31127451, -0.28114418,
  0.85909201, -0.86365691,
  1.52112556, 4.02668249
), ncol = 2, byrow = TRUE)
result_ILMS <- LMS_LTS_estimator(P_mat,Q_mat,nR=0,s_l_LMS=0.000000001,s_u_LMS=10)
S0 <- result_ILMS$s
P_N <- 10
permute_fit <- ILMS_permute(P_mat,Q_mat,P_N,S0,nR=0,s_l_LMS=0.000000001,s_u_LMS=10)

Improved Least median of squares (ILMS) method Align two matrices using the ILMS.

Description

Improved Least median of squares (ILMS) method Align two matrices using the ILMS.

Usage

LMS_LTS_estimator(X1, X2, nR = 0, s_l_LMS = 1e-09, s_u_LMS = 10)

Arguments

X1

A matrix representing the configuration to be transformed to best align with X2.

X2

A matrix representing the fixed configuration that remains unchanged during the transformation.

nR

Number of randomly sampled subsets.

s_l_LMS

Lower bound for the scale s.

s_u_LMS

Upper bound for the scale s.

Value

A list containing the estimated rotation matrix, scaling factor,translation vectors for X1,and scale s.

Examples

X1 <- matrix(c(
  0.3068822, -1.24752606,
  -2.1150143, 4.24520347,
  0.5271354, 1.64468795,
  -0.1264126, -0.08113392,
  -1.4749896, -2.26016700,
  -0.2347269, -1.27047483,
  -0.4833630, 1.43158341,
  -2.3499156, 0.85892382,
  -2.1021129, 0.40267502,
  0.5812934, -0.57210742,
  0.7397990, 1.54898604,
  -1.2173015, -0.65486036,
  -0.6093984, -1.16937177,
  0.3833907, -0.72611343,
  -0.8423056, 1.22427834
), ncol = 2, byrow = TRUE)

X2 <- matrix(c(
  1.96990726, -1.67860936,
  1.16952104, -3.19996198,
  -1.64680983, 3.40009837,
  1.51340633, 0.90762220,
  6.02678651, -1.29463718,
  2.56525182, -0.70441947,
  0.08388971, 3.87254957,
  4.11361309, 4.77780158,
  -0.91329668, 0.01870814,
  0.73714253, -0.50391759,
  -1.60842305, 3.07780435,
  3.90039741, 1.29926458,
  3.31127451, -0.28114418,
  0.85909201, -0.86365691,
  1.52112556, 4.02668249
), ncol = 2, byrow = TRUE)
fit <- LMS_LTS_estimator(X1,X2,nR=0,s_l_LMS=0.000000001,s_u_LMS=10)

Least median of squares (LMS) method Align two matrices using the LMS.

Description

Least median of squares (LMS) method Align two matrices using the LMS.

Usage

LMS_estimator(X1, X2, nR, s_l_LMS = 1e-09, s_u_LMS = 10)

Arguments

X1

A matrix representing the configuration to be transformed to best align with X2.

X2

A matrix representing the fixed configuration that remains unchanged during the transformation.

nR

Number of randomly sampled subsets.

s_l_LMS

Lower bound for the scale s.

s_u_LMS

Upper bound for the scale s.

Value

A list containing the estimated rotation matrix, scaling factor,translation vectors for X1,and scale s.

The Least Median of Squares (LMS) Permutation Test Performs a permutation test for the LMS method.

Description

The Least Median of Squares (LMS) Permutation Test Performs a permutation test for the LMS method.

Usage

LMS_permute(
  P_mat,
  Q_mat,
  P_N,
  S0,
  nR = 0,
  s_l_LMS = 1e-09,
  s_u_LMS = 10,
  verbose = FALSE
)

Arguments

P_mat

A matrix representing the configuration to be transformed to best align with Q_mat.

Q_mat

A matrix representing the fixed configuration that remains unchanged during the transformation.

P_N

Number of permutations.

S0

Observed objective function value from the LMS method.

nR

Number of randomly sampled subsets. If nR <= 0, all possible subsets are used.

s_l_LMS

Lower bound for the scale s.

s_u_LMS

Upper bound for the scale s.

verbose

Logical; if TRUE, displays progress messages during iterations. Defaults to FALSE.

Value

A list containing:

count_n

The number of permuted objective function values less than or equal to the observed value.

p_value

The permutation test p-value.

S

A vector of objective function values obtained from the permutations.

Least trimmed squares (LTS) method Align two matrices using the ILMS.

Description

Least trimmed squares (LTS) method Align two matrices using the ILMS.

Usage

LTS_estimator(X1, X2, nR)

Arguments

X1

A matrix representing the configuration to be transformed to best align with X2.

X2

A matrix representing the fixed configuration that remains unchanged during the transformation.

nR

Number of randomly sampled subsets.

Value

A list containing the estimated rotation matrix, scaling factor,translation vectors for X1, and least trimmed squares.

The Least Trimmed Squares (LTS) Permutation Test Performs a permutation test for the LTS method.

Description

The Least Trimmed Squares (LTS) Permutation Test Performs a permutation test for the LTS method.

Usage

LTS_permute(P_mat, Q_mat, P_N, S0, nR = 0, verbose = FALSE)

Arguments

P_mat

A matrix representing the configuration to be transformed to best align with Q_mat.

Q_mat

A matrix representing the fixed configuration that remains unchanged during the transformation.

P_N

Number of permutations.

S0

Observed objective function value from the LTS method.

nR

Number of randomly sampled subsets. If nR <= 0, all possible subsets are used.

verbose

Logical; if TRUE, displays progress messages during iterations. Defaults to FALSE.

Value

A list containing:

count_n

The number of permuted objective function values less than or equal to the observed value.

p_value

The permutation test p-value.

S

A vector of objective function values obtained from the permutations.

Repeated Median Method without reflection Align two matrices using repeated median method that cannot deal with reflection

Description

Repeated Median Method without reflection Align two matrices using repeated median method that cannot deal with reflection

Usage

MM2_estimator_no_reflection(X1, X2)

Arguments

X1

This matrix is fixed during the transformation

X2

This matrix is transformed to fit the other matrix

Value

A list containing rotation matrix,scaling,translation of matrix X1, translation of matrix X2, objective function, and sum of square value

Repeated Median Method with reflection Align two matrices using the repeated median method while allowing for reflection. This method is recommended for practical applications where reflected configurations may occur.

Description

Repeated Median Method with reflection Align two matrices using the repeated median method while allowing for reflection. This method is recommended for practical applications where reflected configurations may occur.

Usage

MM2_estimator_with_reflection(X1, X2)

Arguments

X1

A matrix representing the fixed configuration that remains unchanged during the transformation.

X2

A matrix representing the configuration to be transformed to best align with X1.

Value

A list containing the estimated rotation matrix, scaling factor,translation vectors for X1 and X2, objective function value, and the sum of squared errors.

Repeated Median Method Permutation Test Performs a permutation test for the repeated median method.

Description

Repeated Median Method Permutation Test Performs a permutation test for the repeated median method.

Usage

MM2_permute(P_mat, Q_mat, P_N, S0, verbose = FALSE)

Arguments

P_mat

A matrix representing the fixed configuration that remains unchanged during the transformation.

Q_mat

A matrix representing the configuration to be transformed to best align with P_mat.

P_N

Number of permutations.

S0

Observed objective function value from the repeated median method.

verbose

Logical; if TRUE, displays progress messages during iterations. Defaults to FALSE.

Value

A list containing:

count_n

The number of permuted objective function values less than or equal to the observed value.

p_value

The permutation test p-value.

S

A vector of objective function values obtained from the permutations.

The standard Procrustes analysis Align two matrices using Procrustes analysis

Description

The standard Procrustes analysis Align two matrices using Procrustes analysis

Usage

Procrustes_fun(X1, X2)

Arguments

X1

A matrix representing the configuration to be transformed to best align with X2.

X2

A matrix representing the fixed configuration that remains unchanged during the transformation.

Value

A list containing the estimated rotation matrix, scaling factor,translation vectors for X1, and the sum of square values.

Examples

X1 <- matrix(c(
  0.3068822, -1.24752606,
  -2.1150143, 4.24520347,
  0.5271354, 1.64468795,
  -0.1264126, -0.08113392,
  -1.4749896, -2.26016700,
  -0.2347269, -1.27047483,
  -0.4833630, 1.43158341,
  -2.3499156, 0.85892382,
  -2.1021129, 0.40267502,
  0.5812934, -0.57210742,
  0.7397990, 1.54898604,
  -1.2173015, -0.65486036,
  -0.6093984, -1.16937177,
  0.3833907, -0.72611343,
  -0.8423056, 1.22427834
), ncol = 2, byrow = TRUE)

X2 <- matrix(c(
  1.96990726, -1.67860936,
  1.16952104, -3.19996198,
  -1.64680983, 3.40009837,
  1.51340633, 0.90762220,
  6.02678651, -1.29463718,
  2.56525182, -0.70441947,
  0.08388971, 3.87254957,
  4.11361309, 4.77780158,
  -0.91329668, 0.01870814,
  0.73714253, -0.50391759,
  -1.60842305, 3.07780435,
  3.90039741, 1.29926458,
  3.31127451, -0.28114418,
  0.85909201, -0.86365691,
  1.52112556, 4.02668249
), ncol = 2, byrow = TRUE)
fit <- Procrustes_fun(X1,X2)

Standard Procrustes Analysis Permutation Test Performs a permutation test for the standard Procrustes analysis.

Description

Standard Procrustes Analysis Permutation Test Performs a permutation test for the standard Procrustes analysis.

Usage

Procrustes_permute(P_mat, Q_mat, P_N, S0, verbose = FALSE)

Arguments

P_mat

A matrix representing the configuration to be transformed to best align with Q_mat.

Q_mat

A matrix representing the fixed configuration that remains unchanged during the transformation.

P_N

Number of permutations.

S0

Observed objective function value from the Procrustes analysis.

verbose

Logical; if TRUE, displays progress messages during iterations. Defaults to FALSE.

Value

A list containing:

count_n

The number of permuted objective function values less than or equal to the observed value.

p_value

The permutation test p-value.

S

A vector of objective function values obtained from the permutations.

Examples

P_mat <- matrix(c(
  0.3068822, -1.24752606,
  -2.1150143, 4.24520347,
  0.5271354, 1.64468795,
  -0.1264126, -0.08113392,
  -1.4749896, -2.26016700,
  -0.2347269, -1.27047483,
  -0.4833630, 1.43158341,
  -2.3499156, 0.85892382,
  -2.1021129, 0.40267502,
  0.5812934, -0.57210742,
  0.7397990, 1.54898604,
  -1.2173015, -0.65486036,
  -0.6093984, -1.16937177,
  0.3833907, -0.72611343,
  -0.8423056, 1.22427834
), ncol = 2, byrow = TRUE)

Q_mat <- matrix(c(
  1.96990726, -1.67860936,
  1.16952104, -3.19996198,
  -1.64680983, 3.40009837,
  1.51340633, 0.90762220,
  6.02678651, -1.29463718,
  2.56525182, -0.70441947,
  0.08388971, 3.87254957,
  4.11361309, 4.77780158,
  -0.91329668, 0.01870814,
  0.73714253, -0.50391759,
  -1.60842305, 3.07780435,
  3.90039741, 1.29926458,
  3.31127451, -0.28114418,
  0.85909201, -0.86365691,
  1.52112556, 4.02668249
), ncol = 2, byrow = TRUE)
result_Procrustes <- Procrustes_fun(P_mat,Q_mat)
S0 <- result_Procrustes$s
P_N <- 10
permute_fit <- Procrustes_permute(P_mat,Q_mat,P_N,S0)

S-estimator method Align two matrices using the S-estimator.

Description

S-estimator method Align two matrices using the S-estimator.

Usage

S_estimator(X1, X2, c_value, A_value, nR, s_l = 1e-09, s_u = 10)

Arguments

X1

A matrix representing the configuration to be transformed to best align with X2.

X2

A matrix representing the fixed configuration that remains unchanged during the transformation.

c_value

It controls where the loss function begins to flatten.

A_value

It is a normalization constant used in the S-estimator defining equation.

nR

Number of randomly sampled subsets.

s_l

Lower bound for the scale s.

s_u

Upper bound for the scale s.

Value

A list containing the estimated rotation matrix, scaling factor,translation vectors for X1,and scale s.

S-estimator Permutation Test Performs a permutation test for the S-estimator method.

Description

S-estimator Permutation Test Performs a permutation test for the S-estimator method.

Usage

S_permute(
  P_mat,
  Q_mat,
  P_N,
  S0,
  nR = 0,
  s_l = 1e-09,
  s_u = 10,
  verbose = FALSE
)

Arguments

P_mat

A matrix representing the configuration to be transformed to best align with Q_mat.

Q_mat

A matrix representing the fixed configuration that remains unchanged during the transformation.

P_N

Number of permutations.

S0

Observed objective function value from the S-estimator method.

nR

Number of randomly sampled subsets. If nR <= 0, all possible subsets are used.

s_l

Lower bound for the scale s.

s_u

Upper bound for the scale s.

verbose

Logical; if TRUE, displays progress messages during iterations. Defaults to FALSE.

Value

A list containing:

count_n

The number of permuted objective function values less than or equal to the observed value.

p_value

The permutation test p-value.

S

A vector of objective function values obtained from the permutations.

Huber and Biweight methods Align two matrices using the Huber and Biweight loss functions via iterative majorization.

Description

Huber and Biweight methods Align two matrices using the Huber and Biweight loss functions via iterative majorization.

Usage

majorization(X1, X2, tuning_con, loss)

Arguments

X1

A matrix representing the configuration to be transformed to best align with X2.

X2

A matrix representing the fixed configuration that remains unchanged during the transformation.

tuning_con

Tuning constant beyond which the resistant loss functions become flat.

loss

Specifies the loss function to use: "Huber" or "Biweight".

Value

A list containing the estimated rotation matrix, scaling factor,translation vectors for X1, weight matrix, objective function value, and convergence.

Huber and Biweight Methods with Automatic Tuning Constant Selection Align two matrices using Huber or biweight loss functions via iterative majorization, with automatic selection of the tuning constant.

Description

Huber and Biweight Methods with Automatic Tuning Constant Selection Align two matrices using Huber or biweight loss functions via iterative majorization, with automatic selection of the tuning constant.

Usage

majorization_tuned(X1, X2, loss)

Arguments

X1

A matrix representing the configuration to be transformed to best align with X2.

X2

A matrix representing the fixed configuration that remains unchanged during the transformation.

loss

Specifies the loss function to use: "Huber" or "Biweight".

Value

A list containing the estimated rotation matrix, scaling factor,translation vectors for X1, weight matrix, objective function value, and convergence.