Type:	Package
Title:	Collection of Data Structures
Version:	0.1.10
Description:	A collection of functions to generate a large variety of structures in high dimensions. These data structures are useful for testing, validating, and improving algorithms used in dimensionality reduction, clustering, machine learning, and visualization.
License:	MIT + file LICENSE
URL:	https://jayanilakshika.github.io/cardinalR/
BugReports:	https://github.com/JayaniLakshika/cardinalR/issues
Depends:	R (≥ 4.1.0)
Imports:	cli, dplyr, geozoo, gtools, MASS, mvtnorm, purrr, stats, tibble, tidyr
Suggests:	knitr, langevitour, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
Config/testthat/edition:	3
Encoding:	UTF-8
Language:	en-GB
LazyData:	true
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-08-21 02:47:45 UTC; jpiy0001
Author:	Jayani P. Gamage [aut, cre], Dianne Cook [aut], Paul Harrison [aut], Michael Lydeamore [aut], Thiyanga S. Talagala [aut]
Maintainer:	Jayani P. Gamage <jayanilakshika76@gmail.com>
Repository:	CRAN
Date/Publication:	2025-08-21 07:10:07 UTC

Generate Background Noise Data

Description

This function generates background noise data with specified parameters such as the number of samples, number of dimensions, mean, and standard deviation.

Usage

gen_bkgnoise(n = 500, p = 4, m = rep(0, p), s = rep(2, p))

Arguments

Value

A data containing the generated background noise data.

Examples

# Generate background noise with custom mean and standard deviation
set.seed(20240412)
gen_bkgnoise(n = 500, p = 4, m = c(0, 0, 0, 0), s = c(2, 2, 2, 2))

Generate Circle in p-d

Description

This function generates a dataset representing a structure with a circle.

Usage

gen_circle(n = 500, p = 4)

Arguments

Value

A data containing a circle.

Examples

set.seed(20240412)
circle <- gen_circle(n = 500, p = 4)

Generate Small Spheres Within a Big Sphere

Description

This function generates a dataset representing a structure with a small and big spheres.

Usage

gen_clusteredspheres(
  n = c(1000, 100),
  k = 3,
  p = 4,
  r = c(15, 3),
  loc = 10/sqrt(3)
)

Arguments

Value

A data containing small spheres within a big sphere.

Examples

set.seed(20240412)
clusteredspheres <- gen_clusteredspheres(n = c(1000, 100), k = 3, p = 4,
r = c(15, 3), loc = 10 / sqrt(3))

Generate Cluster Locations

Description

This function generate locations for any number of clusters in any dimensions.

Usage

gen_clustloc(p = 4, k = 3)

Arguments

Value

A matrix of the locations.

Examples

set.seed(20240412)
gen_clustloc(p = 4, k = 3)

Generate Blunted Cone

Description

This function generates a dataset representing a cone with the option of a sharp or blunted apex.

Usage

gen_cone(n = 500, p = 4, h = 5, ratio = 0.5)

Arguments

Value

A data containing the cone with the option of a sharp or blunted apex.

Examples

set.seed(20240412)
cone <- gen_cone(n = 500, p = 4, h = 5, ratio = 0.5)

Generate Conical Spiral

Description

This function generates a dataset representing a conical spiral structure.

Usage

gen_conicspiral(n = 500, p = 4, spins = 1)

Arguments

Value

A data containing a conical spiral structure.

Examples

set.seed(20240412)
conicspiral <- gen_conicspiral(n = 500, p = 4, spins = 1)

Generate Crescent

Description

This function generates a dataset representing a structure with a Crescent pattern.

Usage

gen_crescent(n = 500, p = 4)

Arguments

Value

A data containing a Crescent structure.

Examples

set.seed(20240412)
crescent <- gen_crescent(n = 500, p = 4)

Generate Cube with Hole

Description

This function generates a dataset representing a cube with a hole.

Usage

gen_cubehole(n = 500, p = 4)

Arguments

Value

A data containing the cube data with a hole.

Examples

set.seed(20240412)
cubehole <- gen_cubehole(n = 1000, p = 4)

Generate Cubic

Description

This function generates a dataset representing a structure with a cubic pattern.

Usage

gen_cubic(n = 500, p = 4, range = c(-1, 2))

Arguments

Value

A data containing a cubic structure.

Examples

set.seed(20240412)
cubic <- gen_cubic(n = 500, p = 4)

Generate data with curvy shaped branches

Description

This function generates a dataset representing a structure with non-linear shaped branches.

Usage

gen_curvybranches(n = 400, p = 4, k = 4)

Arguments

Value

A data containing non-linear shaped branches.

Examples

set.seed(20240412)
curvybranches <- gen_curvybranches(n = 400, p = 4, k = 4)

Generate Curvy Cell Cycle in p-d

Description

This function generates a dataset representing a structure with a curvy cell cycle.

Usage

gen_curvycycle(n = 500, p = 4)

Arguments

Value

A data containing a curvy cell cycle.

Examples

set.seed(20240412)
curvycycle <- gen_curvycycle(n = 500, p = 4)

Generate Curvy Cylinder

Description

This function generates a dataset representing a structure with a curvy cylinder.

Usage

gen_curvycylinder(n = 500, p = 4, h = 10)

Arguments

Value

A data containing a curvy cylinder.

Examples

set.seed(20240412)
curvycylinder <- gen_curvycylinder(n = 500, p = 4, h = 10)

Generate data with exponential shaped branches

Description

This function generates a dataset representing a structure with exponential shaped branches.

Usage

gen_expbranches(n = 400, p = 4, k = 4)

Arguments

Value

A data containing exponential shaped branches.

Examples

set.seed(20240412)
expbranches <- gen_expbranches(n = 400, p = 4, k = 4)

Generate Gaussian

Description

This function generates a dataset representing a structure with a Gaussian.

Usage

gen_gaussian(n = 500, p = 4, s = diag(p) * 0.01)

Arguments

Value

A data containing a Gaussian.

Examples

set.seed(20240412)
gaussian <- gen_gaussian(n = 500, p = 4, s = diag(4))

Generate Cube with grid points

Description

This function generates a grid dataset with specified grid points along each axes.

Usage

gen_gridcube(n = 500, p = 4)

Arguments

Value

A data containing the cube with grid points.

Examples

set.seed(20240412)
gridcube <- gen_gridcube(n = 500, p = 4)

Generate Grided Sphere

Description

This function generates a dataset representing a structure with a grided sphere.

Usage

gen_gridedsphere(n = 500, p = 4)

Arguments

Value

A data containing a grided sphere.

Examples

set.seed(20240412)
gridedsphere <- gen_gridedsphere(n = 500, p = 4)

Generate Helical Hyper Spiral

Description

This function generates a dataset representing a structure with a helical hyper spiral.

Usage

gen_helicalspiral(n = 500, p = 4)

Arguments

Value

A data containing a helical hyper spiral.

Examples

set.seed(20240412)
helicalspiral <- gen_helicalspiral(n = 500, p = 4)

Generate Hemisphere

Description

This function generates a dataset representing a structure with a hemisphere.

Usage

gen_hemisphere(n = 500, p = 4)

Arguments

Value

A data containing a hemisphere.

Examples

set.seed(20240412)
hemisphere <- gen_hemisphere(n = 500, p = 4)

Generate data with linear shaped branches

Description

This function generates a dataset representing a structure with linear shaped branches.

Usage

gen_linearbranches(n = 400, p = 4, k = 4)

Arguments

Value

A data containing linear shaped branches.

Examples

set.seed(20240412)
linearbranches <- gen_linearbranches(n = 400, p = 4, k = 4)

Generate Long Linear Data

Description

This function generates a dataset consisting of long linear data.

Usage

gen_longlinear(n = 500, p = 4)

Arguments

Value

A data containing the long linear data.

Examples

set.seed(20240412)
longlinear <- gen_longlinear(n = 500, p = 4)

Generate a 3-D Mobius in High Dimensions

Description

This function generates a dataset representing a structure with a mobius.

Usage

gen_mobius(n = 500, p = 4)

Arguments

Value

A data containing a mobius structure.

Examples

set.seed(20240412)
mobius <- gen_mobius(n = 500, p = 4)

Generate Multiple Clusters

Description

This function generates a dataset with multiple clusters.

Usage

gen_multicluster(
  n = c(200, 300, 500),
  p = 4,
  k = 3,
  loc = matrix(c(0, 0, 0, 0, 5, 9, 0, 0, 3, 4, 10, 7), nrow = 3, byrow = TRUE),
  scale = c(3, 1, 2),
  shape = c("gaussian", "bluntedcorn", "unifcube"),
  rotation = NULL,
  is_bkg = FALSE
)

Arguments

Value

A data containing same/different shaped clusters.

Examples

set.seed(20240412)
rotations_4d <- list(
cluster1 = list(
  list(plane = c(1, 2), angle = 60), # Rotation in the (1, 2) plane
  list(plane = c(3, 4), angle = 90)  # Rotation in the (3, 4) plane
  ),
cluster2 = list(
  list(plane = c(1, 3), angle = 30) # Rotation in the (1, 3) plane
  ),
cluster3 = list(
  list(plane = c(2, 4), angle = 45) # Rotation in the (2, 4) plane
  )
)
clust_data <- gen_multicluster(n = c(200, 300, 500), p = 4, k = 3,
loc = matrix(c(
  0, 0, 0, 0,
  5, 9, 0, 0,
  3, 4, 10, 7
), nrow = 3, byrow = TRUE),
scale = c(3, 1, 2),
shape = c("gaussian", "cone", "unifcube"),
rotation = rotations_4d,
is_bkg = FALSE)

Generate Random Noise Dimensions

Description

This function generates random noise dimensions to be added to the coordinates of a data structure.

Usage

gen_noisedims(n = 500, p = 4, m = rep(0, p), s = rep(2, p))

Arguments

Value

A data containing the generated random noise dimensions.

Examples

set.seed(20240412)
gen_noisedims(n = 500, p = 4, m = c(0, 0, 0, 0), s = c(2, 2, 2, 2))

Generate Nonlinear Hyperbola

Description

This function generates a dataset representing a nonlinear hyperbola structure.

Usage

gen_nonlinear(n = 500, p = 4, hc = 1, non_fac = 0.5)

Arguments

Value

A data containing a nonlinear hyperbola structure.

Examples

set.seed(20240412)
nonlinear <- gen_nonlinear(n = 500, p = 4, hc = 1, non_fac = 0.5)

Generates a vector of positive integers whose product is approximately equal to a target value.

Description

This function takes a target integer 'n' and the number of dimensions 'p', and returns a vector 'n_vec' of length 'p' containing positive integers. The goal is to have the product of the elements in 'n_vec' be as close as possible to 'n', especially when 'n' is not a perfect p-th power.

Usage

gen_nproduct(n = 500, p = 4)

Arguments

Value

A sorted vector of positive integers of length 'p'. The product of the elements in this vector will be approximately equal to 'n'. If 'n' is a perfect p-th power, the elements will be equal.

Examples

gen_nproduct(500, 6) # Example with n=500, p=6
gen_nproduct(700, 4) # Example with n=700, p=4
gen_nproduct(625, 4) # Example with n=625 (perfect power)
gen_nproduct(30, 3)  # Example with n=30, p=3
gen_nproduct(7, 2)   # Example where exact product might be hard

Generates a vector of positive integers whose summation is approximately equal to a target value.

Description

This function takes a target integer 'n' and the number of clusters 'k', and returns a vector 'n_vec' of length 'k' containing positive integers. The goal is to have the summation of the elements in 'n_vec' be as close as possible to 'n', especially when 'n' is not a perfect multiplier of 'k'.

Usage

gen_nsum(n = 500, k = 4)

Arguments

Value

A sorted vector of positive integers of length 'k'. The summation of the elements in this vector will be approximately equal to 'n'. If 'n' is a perfectly divisible by 'k', the elements will be equal.

Examples

gen_nsum(500, 6) # Example with n=500, p=6
gen_nsum(700, 4) # Example with n=700, p=4
gen_nsum(625, 5) # Example with n=625 (perfect division)
gen_nsum(30, 3)  # Example with n=30, p=3

Generate data with curvy shaped branches in a initial point

Description

This function generates a dataset representing a structure with curvy shaped branches.

Usage

gen_orgcurvybranches(n = 400, p = 4, k = 4)

Arguments

Value

A data containing curvy shaped branches originated in one point.

Examples

set.seed(20240412)
orgcurvybranches <- gen_orgcurvybranches(n = 400, p = 4, k = 4)

Generate data with linear shaped branches in a initial point

Description

This function generates a dataset representing a structure with linear shaped branches.

Usage

gen_orglinearbranches(n = 400, p = 4, k = 4)

Arguments

Value

A data containing linear shaped branches originated in one point.

Examples

set.seed(20240412)
orglinearbranches <- gen_orglinearbranches(n = 400, p = 4, k = 4)

Generate p-D Triangular Pyramid With Triangular Pyramid shaped holes

Description

This function generates p-D triangular pyramid with triangular pyramid shaped holes.

Usage

gen_pyrholes(n = 500, p = 4)

Arguments

Value

A data containing a triangular pyramid with triangular pyramid shaped holes.

Examples

set.seed(20240412)
pyrholes <- gen_pyrholes(n = 500, p = 3)

Generate Rectangular Based Pyramid

Description

This function generates a dataset representing a rectangular based pyramid.

Usage

gen_pyrrect(n = 500, p = 4, h = 5, l_vec = c(3, 2), rt = 0.5)

Arguments

Value

A data containing the rectangular based pyramid.

Examples

set.seed(20240412)
pyrrect <- gen_pyrrect(n = 500, p = 4, h = 5, l_vec = c(3, 2), rt = 0.5)

Generate Star Based Pyramid

Description

This function generates a dataset representing a star based pyramid.

Usage

gen_pyrstar(n = 500, p = 4, h = 5, rb = 3)

Arguments

Value

A data containing the star based pyramid.

Examples

set.seed(20240412)
pyrstar <- gen_pyrstar(n = 500, p = 4, h = 5, rb = 3)

Generate Triangular Based Pyramid

Description

This function generates a dataset representing a triangular based pyramid.

Usage

gen_pyrtri(n = 500, p = 4, h = 5, l = 3, rt = 0.5)

Arguments

Value

A data containing the triangular based pyramid.

Examples

set.seed(20240412)
pyrtri <- gen_pyrtri(n = 500, p = 4, h = 5, l = 3, rt = 0.5)

Generate Quadratic

Description

This function generates a dataset representing a structure with a quadratic pattern.

Usage

gen_quadratic(n = 500, p = 4, range = c(-1, 1))

Arguments

Value

A data containing a quadratic structure.

Examples

set.seed(20240412)
quadratic <- gen_quadratic(n = 500, p = 4)

Generate Rotations

Description

This function generates a rotation matrix.

Usage

gen_rotation(p = 4, planes_angles)

Arguments

Value

A matrix containing the rotations.

Examples

set.seed(20240412)
rotations_4d <- list(
  list(plane = c(1, 2), angle = 60), # Rotation in the (1, 2) plane
  list(plane = c(3, 4), angle = 90)  # Rotation in the (3, 4) plane
)
gen_rotation(p = 4, planes_angles = rotations_4d)

Generate S-curve Data

Description

This function generates S-curve data.

Usage

gen_scurve(n = 500, p = 4)

Arguments

Value

A data containing the generated S-curve data.

References

Buitinck, L., Louppe, G., Blondel, M., Pedregosa, F., Mueller, A., Grisel, O., ... & Varoquaux, G. (2013). API design for machine learning software: experiences from the scikit-learn project. arXiv preprint arXiv:1309.0238.

Examples

set.seed(20240412)
scurve <- gen_scurve(n = 500, p = 4)

Generate S-curve Data with a Hole

Description

This function generates S-curve data with a hole by filtering out samples that are not close to a specified anchor point.

Usage

gen_scurvehole(n = 500, p = 4)

Arguments

Value

A data containing the generated S-curve data with a hole.

References

Wang, Y., Huang, H., Rudin, C., & Shaposhnik, Y. (2021). Understanding how dimension reduction tools work: an empirical approach to deciphering t-SNE, UMAP, TriMAP, and PaCMAP for data visualization. J Mach. Learn. Res, 22, 1-73.

See Also

the PaCMAP homepage.

Examples

set.seed(20240412)
scurvehole <- gen_scurvehole(n = 500, p = 4)

Generate Spherical Spiral

Description

This function generates a dataset representing a structure with a spherical spiral.

Usage

gen_sphericalspiral(n = 500, p = 4, spins = 1)

Arguments

Value

A data containing a spherical spiral.

Examples

set.seed(20240412)
sphericalspiral <- gen_sphericalspiral(n = 500, p = 4, spins = 1)

Generate Swiss Roll Data

Description

This function generates swiss roll data.

Usage

gen_swissroll(n = 500, p = 4, w = c(-1, 1))

Arguments

Value

A data containing the generated swiss roll data.

References

Agrafiotis, D. K., & Xu, H. (2002). A self-organizing principle for learning nonlinear manifolds. Proceedings of the National Academy of Sciences, 99(25), 15869-15872.

Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323-2326.

Examples

set.seed(20240412)
swissroll <- gen_swissroll(n = 500, p = 4)

Generate 3-D Trefoil Knot Coordinates (Stereographic Projection)

Description

This function generates coordinates for a 3-D trefoil knot by applying a stereographic projection from 4-D space.

Usage

gen_trefoil3d(n = 500, p = 4, steps = 5)

Arguments

Value

A data containing 3-D trefoil knot.

Examples

set.seed(20240412)
trefoil3d <- gen_trefoil3d(n = 500, p = 4, steps = 5)

Generate 4-D Trefoil Knot Coordinates

Description

This function generates coordinates for a 4-D trefoil knot. The number of points is determined by the length of the theta and phi sequences.

Usage

gen_trefoil4d(n = 500, p = 4, steps = 5)

Arguments

Value

A data containing 4-D trefoil knot.

Examples

set.seed(20240412)
trefoil4d <- gen_trefoil4d(n = 500, p = 4, steps = 5)

Generate Cube with uniform points

Description

This function generates a grid dataset with specified uniform points along each axes..

Usage

gen_unifcube(n = 500, p = 4)

Arguments

Value

A data containing the cube with uniform points.

Examples

set.seed(20240412)
unifcube <- gen_unifcube(n = 500, p = 4)

Generate Uniform Sphere

Description

This function generates a dataset representing a structure with a uniform sphere.

Usage

gen_unifsphere(n = 500, p = 4, r = 1)

Arguments

Value

A data containing a uniform sphere.

Examples

set.seed(20240412)
unifsphere <- gen_unifsphere(n = 500, p = 4)

Generate Random Noise Dimensions With Wavy Pattern

Description

This function generates random noise dimensions by adding wavy patterns.

Usage

gen_wavydims1(n = 500, p = 4, theta = seq(pi/6, 12 * pi/6, length.out = 500))

Arguments

Value

A data containing the generated random noise dimensions.

Examples

set.seed(20240412)
gen_wavydims1(n = 500, p = 4, theta = seq(pi / 6, 12 * pi / 6, length.out = 500))

Generate Random Noise Dimensions With Wavy Pattern

Description

This function generates random noise dimensions by adding wavy patterns.

Usage

gen_wavydims2(n = 500, p = 4, x1_vec)

Arguments

Value

A data containing the generated random noise dimensions.

Examples

set.seed(20240412)
theta <- seq(0, 2 * pi, length.out = 500)
x1 <- sin(pi) * cos(theta)
gen_wavydims2(n = 500, p = 4, x1_vec = x1)

Generate Random Noise Dimensions With Wavy Pattern

Description

This function generates random noise dimensions by adding wavy patterns.

Usage

gen_wavydims3(n = 500, p = 4, data)

Arguments

Value

A data containing the generated random noise dimensions.

Examples

set.seed(20240412)
df <- gen_scurve(n = 500, p = 4) |> as.matrix()
gen_wavydims3(n = 500, p = 4, data = df)

Generate a Chain of Interlocked Circles in High-Dimensional Space

Description

This function generates k interlocked circular clusters in a p-dimensional space. Unlike make_klink_circles(), the circles are arranged in a **chain-like structure**, where each circle interlocks only with its immediate neighbor, resembling links in a chain.

Usage

make_chain_circles(n = c(200, 100), p = 4, k = 2, offset = 0.5, angle = 90)

Arguments

Value

A data frame (or tibble, depending on gen_multicluster()) containing the generated points and cluster assignments.

Examples

# Generate two chain-linked circles in 4-D
twochain_circles <- make_chain_circles()

Generate a Chain of Interlocked curvycycle in High-Dimensional Space

Description

This function generates k interlocked circular clusters in a p-dimensional space. Unlike make_klink_curvycycle(), the curvycycle are arranged in a **chain-like structure**, where each curvycycle interlocks only with its immediate neighbor, resembling links in a chain.

Usage

make_chain_curvycycle(n = c(200, 100), p = 4, k = 2, offset = 0.5, angle = 90)

Arguments

Value

A data frame (or tibble, depending on gen_multicluster()) containing the generated points and cluster assignments.

Examples

# Generate two chain-linked curvycycle in 4-D
twochain_curvycycle <- make_chain_curvycycle()

Generate Curvy Quadratic and Gaussian Clusters

Description

This function generates synthetic high-dimensional data containing two clusters: one quadratic-shaped cluster and one Gaussian-shaped cluster. The clusters are positioned apart in feature space with different scaling factors.

Usage

make_curvygau(n = c(200, 100), p = 4)

Arguments

Value

A tibble containing n[1] + n[2] rows and p columns, with generated features (x1, x2, ..., xp) and a cluster label.

Examples

# Generate 2 clusters in 4D: one quadratic, one Gaussian
curvygau <- make_curvygau()

Generate Concentric Circles with a Gaussian Cluster in High Dimensions

Description

This function generates a dataset consisting of multiple circular clusters together with a single Gaussian cluster in a p-dimensional space. The circles are placed concentrically at the origin with varying scales, while the Gaussian cluster serves as an additional background or center cluster.

Usage

make_gaucircles(
  n = c(200, 100, 100),
  p = 4,
  num_circles = 2,
  scale_circles = c(1, 2)
)

Arguments

Value

A data frame (or tibble, depending on gen_multicluster()) containing the generated dataset with cluster assignments.

Examples

# Two circles (radii 1 and 2) plus one Gaussian cluster in 4-D
gaucircles <- make_gaucircles()

Generate Concentric Curvycycles with a Gaussian Cluster in High Dimensions

Description

This function generates a dataset consisting of multiple circular clusters together with a single Gaussian cluster in a p-dimensional space. The curvycycle are placed concentrically at the origin with varying scales, while the Gaussian cluster serves as an additional background or center cluster.

Usage

make_gaucurvycycle(
  n = c(200, 100, 100),
  p = 4,
  num_curvycycle = 2,
  scale_curvycycle = c(1, 2)
)

Arguments

Value

A data frame (or tibble, depending on gen_multicluster()) containing the generated dataset with cluster assignments.

Examples

# Two curvycycle (radii 1 and 2) plus one Gaussian cluster in 4-D
gaucurvycycle <- make_gaucurvycycle()

Generate Multiple Interlocked Circles in High-Dimensional Space

Description

This function generates k interlocked circular clusters in a p-dimensional space. The circles are constructed using gen_multicluster(), with each circle positioned in a different coordinate plane and slightly offset so that they interlock with a central circle (hub-like structure).

Usage

make_klink_circles(n = c(200, 100), p = 4, k = 2, offset = 0.5)

Arguments

Value

A data frame (or tibble, depending on gen_multicluster()) containing the generated points and cluster assignments.

Examples

# Generate two interlocked circles in 4-D
twolink_circles <- make_klink_circles()

Generate Multiple Interlocked curvycycle in High-Dimensional Space

Description

This function generates k interlocked circular clusters in a p-dimensional space. The curvycycle are constructed using gen_multicluster(), with each curvycycle positioned in a different coordinate plane and slightly offset so that they interlock with a central curvycycle (hub-like structure).

Usage

make_klink_curvycycle(n = c(200, 100), p = 4, k = 2, offset = 0.5)

Arguments

Value

A data frame (or tibble, depending on gen_multicluster()) containing the generated points and cluster assignments.

Examples

# Generate two interlocked curvycycle in 4-D
twolink_curvycycle <- make_klink_curvycycle()

Generate Gaussian cluster with the Mobius Cluster

Description

This function generates a dataset consisting of a mobius cluster and Gaussian cluster.

Usage

make_mobiusgau(n = c(200, 100), p = 4)

Arguments

Value

A data containing the mobius cluster and Gaussian cluster.

Examples

mobgau <- make_mobiusgau(n = c(200, 100), p = 4)

Generate Multiple Gaussian Clusters

Description

This function generates a dataset consisting of multiple Gaussian clusters.

Usage

make_multigau(n = c(300, 200, 500), p = 4, k = 3, loc = NULL, scale = NULL)

Arguments

Value

A data containing the Gaussian clusters.

Examples

loc_matrix <- matrix(c(0, 0, 0, 0,
5, 9, 0, 0,
3, 4, 10, 7
), nrow = 3, byrow = TRUE)
multigau <- make_multigau(n = c(300, 200, 500),
p = 4, k = 3,
loc = loc_matrix, scale = c(0.2, 1.5, 0.5))

Generate a Single Grid Cluster in High Dimensions

Description

This function generates a dataset consisting of one grid-like cluster (a structured cube grid) in 2D, with optional Gaussian noise dimensions added to extend the dataset into higher dimensions.

Usage

make_onegrid(n = 500, p = 4)

Arguments

Value

A tibble containing the generated dataset with columns:

• x1, x2, ..., xp — coordinates of the data points.

• cluster — cluster assignment (always 1 for the grid).

Examples

# Default: 500 points, 4D space (grid in 2D + 2 noise dimensions)
onegrid <- make_onegrid()

Generate Parallel Multi-Shape Clusters

Description

This function generates synthetic high-dimensional data consisting of k clusters of a specified shape (e.g., crescents), arranged in parallel along alternating dimensions. The first cluster is shifted along the first dimension, the second along the third dimension, the third along the first dimension again, and so on.

Usage

make_shape_para(n = c(500, 300), k = 2, p = 4, shift = 0.4, shape = "crescent")

Arguments

Value

A tibble containing \sum n rows and p columns, with the generated features ('x1, x2, ..., xp') and a 'cluster' label.

Examples

# Generate 2 crescent-shaped clusters in 4D
twocrescent <- make_shape_para(n = c(500, 300), k = 2, p = 4, shape = "crescent")

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_01(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_01 <- make_three_clust_01()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_02(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_02 <- make_three_clust_02()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_03(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_03 <- make_three_clust_03()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_04(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_04 <- make_three_clust_04()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_05(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_05 <- make_three_clust_05()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_06(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_06 <- make_three_clust_06()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_07(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_07 <- make_three_clust_07()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_08(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_08 <- make_three_clust_08()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_09(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_09 <- make_three_clust_09()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_10(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_10 <- make_three_clust_10()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_11(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_11 <- make_three_clust_11()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_12(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_12 <- make_three_clust_12()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_13(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_13 <- make_three_clust_13()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_14(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_14 <- make_three_clust_14()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_15(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_15 <- make_three_clust_15()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_16(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_16 <- make_three_clust_16()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_17(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_17 <- make_three_clust_17()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_18(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_18 <- make_three_clust_18()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_19(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_19 <- make_three_clust_19()

Generate a Three-Cluster Dataset in High Dimensions

Description

This function generates a dataset consisting of three distinct clusters in a p-dimensional space. Each cluster is generated with a specified shape and location using the underlying 'gen_multicluster()' function.

Usage

make_three_clust_20(n = c(700, 300, 500), p = 4)

Arguments

Value

A data frame (or tibble, depending on 'gen_multicluster()') containing the generated dataset with cluster assignments.

Examples

# Generate default three clusters in 4-D
three_clust_20 <- make_three_clust_20()

Generate Two Overlapping Grid Clusters in High Dimensions

Description

This function generates a dataset consisting of two overlapping grid-like clusters in a 2D space, with optional noise dimensions added to reach higher-dimensional spaces. The overlap is controlled by scaling factors for the grids.

Usage

make_twogrid_overlap(n = c(500, 500), p = 4)

Arguments

Value

A tibble with n[1] + n[2] rows and p + 1 columns:

• x1, ..., xp — coordinates of the generated points.

• cluster — cluster membership label.

Examples

# Generate two overlapping grid clusters in 4-D
df <- make_twogrid_overlap()

Generate Two Shifted Grid Clusters in High Dimensions

Description

This function generates two grid-shaped clusters in a 2D space, where one grid is shifted relative to the other. Optionally, additional noise dimensions can be added to embed the structure in a higher-dimensional space.

Usage

make_twogrid_shift(n = c(500, 500), p = 4)

Arguments

Value

A tibble with n[1] + n[2] rows and p + 1 columns:

• x1, x2, ..., xp: Numeric coordinates of the points.

• cluster: Cluster membership label (factor with 2 levels).

Examples

# Generate 2 shifted grid clusters in 4-D
make_twogrid_shift <- make_twogrid_shift()

Mobius clust dataset with a noise dimension

Description

The 'mobiusgau' dataset contains a 3-dimensional Mobius and Gaussian cluster with added noise dimension. Each data point is represented by five dimensions (x1 to x4).

Usage

data(mobiusgau)

Format

A data frame with 1000 rows and 4 columns:

x1, x2, x3, x4

High-dimensional coordinates

Source

This dataset is generated for illustrative purposes.

Examples

# Load the mobiusgau dataset
data(mobiusgau)

# Display the first few rows of the dataset
head(mobiusgau)

tSNE embedding for mobiusgau dataset which with noise dimensions tSNE parameters set to perplexity: 15.

Description

The 'mobiusgau_tsne1' dataset contains the tSNE (t-distributed Stochastic Neighbor Embedding) embeddings of a five-dimensional mobiusgau. Each data point is represented by two tSNE coordinates (emb1 and emb2).

Usage

data(mobiusgau_tsne1)

Format

## 'mobiusgau_tsne1' A data frame with 1000 rows and 4 columns:

emb1

Numeric, first tSNE 2D embeddings.

emb2

Numeric, second tSNE 2D embeddings.

Source

This dataset is generated for illustrative purposes.

Examples

# Load the mobiusgau_tsne1 dataset
data(mobiusgau_tsne1)

# Display the first few rows of the dataset
head(mobiusgau_tsne1)

tSNE embedding for mobiusgau dataset which with noise dimensions tSNE parameters set to perplexity: 30.

Description

The 'mobiusgau_tsne2' dataset contains the tSNE (t-distributed Stochastic Neighbor Embedding) embeddings of a five-dimensional mobiusgau. Each data point is represented by two tSNE coordinates (emb1 and emb2).

Usage

data(mobiusgau_tsne2)

Format

## 'mobiusgau_tsne2' A data frame with 1000 rows and 4 columns:

emb1

Numeric, first tSNE 2D embeddings.

emb2

Numeric, second tSNE 2D embeddings.

Source

This dataset is generated for illustrative purposes.

Examples

# Load the mobiusgau_tsne2 dataset
data(mobiusgau_tsne2)

# Display the first few rows of the dataset
head(mobiusgau_tsne2)

tSNE embedding for mobiusgau dataset which with noise dimensions tSNE parameters set to perplexity: 5.

Description

The 'mobiusgau_tsne3' dataset contains the tSNE (t-distributed Stochastic Neighbor Embedding) embeddings of a five-dimensional mobiusgau. Each data point is represented by two tSNE coordinates (emb1 and emb2).

Usage

data(mobiusgau_tsne3)

Format

## 'mobiusgau_tsne3' A data frame with 1000 rows and 4 columns:

emb1

Numeric, first tSNE 2D embeddings.

emb2

Numeric, second tSNE 2D embeddings.

Source

This dataset is generated for illustrative purposes.

Examples

# Load the mobiusgau_tsne1 dataset
data(mobiusgau_tsne3)

# Display the first few rows of the dataset
head(mobiusgau_tsne3)

UMAP embedding for mobiusgau dataset which with noise dimensions UMAP parameters set to n-neigbors: 15 and min-dist: 0.1.

Description

The 'mobiusgau_umap1' dataset contains the UMAP (Uniform Manifold Approximation and Projection) embeddings of a five-dimensional mobiusgau. Each data point is represented by two UMAP coordinates (emb1 and emb2).

Usage

data(mobiusgau_umap1)

Format

## 'mobiusgau_umap1' A data frame with 1000 rows and 4 columns:

emb1

Numeric, first UMAP 2D embeddings.

emb2

Numeric, second UMAP 2D embeddings.

Source

This dataset is generated for illustrative purposes.

Examples

# Load the mobiusgau_umap1 dataset
data(mobiusgau_umap1)

# Display the first few rows of the dataset
head(mobiusgau_umap1)

UMAP embedding for mobiusgau dataset which with noise dimensions UMAP parameters set to n-neigbors: 30 and min-dist: 0.08.

Description

The 'mobiusgau_umap2' dataset contains the UMAP (Uniform Manifold Approximation and Projection) embeddings of a five-dimensional mobiusgau. Each data point is represented by two UMAP coordinates (emb1 and emb2).

Usage

data(mobiusgau_umap2)

Format

## 'mobiusgau_umap2' A data frame with 1000 rows and 4 columns:

emb1

Numeric, first UMAP 2D embeddings.

emb2

Numeric, second UMAP 2D embeddings.

Source

This dataset is generated for illustrative purposes.

Examples

# Load the mobiusgau_umap2 dataset
data(mobiusgau_umap2)

# Display the first few rows of the dataset
head(mobiusgau_umap2)

UMAP embedding for mobiusgau dataset which with noise dimensions UMAP parameters set to n-neigbors: 5 and min-dist: 0.9.

Description

The 'mobiusgau_umap3' dataset contains the UMAP (Uniform Manifold Approximation and Projection) embeddings of a five-dimensional mobiusgau. Each data point is represented by two UMAP coordinates (emb1 and emb2).

Usage

data(mobiusgau_umap3)

Format

## 'mobiusgau_umap3' A data frame with 1000 rows and 4 columns:

emb1

Numeric, first UMAP 2D embeddings.

emb2

Numeric, second UMAP 2D embeddings.

Source

This dataset is generated for illustrative purposes.

Examples

# Load the mobiusgau_umap3 dataset
data(mobiusgau_umap3)

# Display the first few rows of the dataset
head(mobiusgau_umap3)

Generate Normalized data

Description

This function normalize the data by absolute value

Usage

normalize_data(data)

Arguments

Value

A normalized data.

Examples

set.seed(20240412)
data1 <- gen_gaussian(n= 500, p = 4)
normalize_data(data = data1)

Randomize Rows of a Data Frame

Description

This function randomly shuffles the rows of a given data frame.

Usage

randomize_rows(data)

Arguments

Value

A data frame with rows randomly shuffled.

Examples

randomize_rows(mobiusgau)

Relocate Clusters in High-Dimensional Space

Description

This function relocates clusters in a dataset by centering each cluster and shifting it based on a given transformation matrix.

Usage

relocate_clusters(data, vert_mat)

Arguments

Value

A tibble containing the relocated clusters with randomized row order.

Examples

set.seed(20240412)
df <- tibble::tibble(
x1 = rnorm(12),
x2 = rnorm(12),
x3 = rnorm(12),
x4 = rnorm(12),
cluster = rep(1:3, each = 4)
)

# Create a 3x4 matrix to define new cluster centers
vert_mat <- matrix(c(
  5, 0, 0, 0,   # Shift cluster 1
  0, 5, 0, 0,   # Shift cluster 2
  0, 0, 5, 0    # Shift cluster 3
), nrow = 3, byrow = TRUE)
# Apply relocation
relocated_df <- relocate_clusters(df, vert_mat)