Package 'cardinalR'

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))

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)

Description

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

Usage

gen_clusteredspheres(
  n_vec = c(1000, 100),
  k_small = 3,
  r_vec = c(15, 3),
  sep = 10/sqrt(3)
)

Arguments

Value

A data containing small spheres within a big sphere.

Examples

set.seed(20240412)
clusteredspheres <- gen_clusteredspheres(n_vec = c(1000, 100), k_small = 3,
r_vec = c(15, 3), sep = 10 / sqrt(3))

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)

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 tibble 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)

Description

This function generates a dataset representing a conical spiral structure.

Usage

gen_conicspiral(n = 500, spins = 1)

Arguments

Value

A data containing a conical spiral structure.

Examples

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

Description

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

Usage

gen_crescent(n = 500)

Arguments

Value

A tibble containing a Crescent structure.

Examples

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

Description

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

Usage

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

Arguments

Value

A data containing a cubic structure.

Examples

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

Description

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

Usage

gen_curvybranches(n = 400, k = 4)

Arguments

Value

A data containing non-linear shaped branches.

Examples

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

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)

Description

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

Usage

gen_curvycylinder(n = 500, h = 10)

Arguments

Value

A data containing a curvy cylinder.

Examples

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

Description

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

Usage

gen_expbranches(n = 400, k = 4)

Arguments

Value

A tibble containing exponential shaped branches.

Examples

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

Description

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

Usage

gen_gaussian(n = 500, p = 4, m = rep(0, p), s = diag(p) * 0.01)

Arguments

Value

A tibble containing a multivariate Gaussian cloud dataset.

Examples

set.seed(20240412)
gaussian <- gen_gaussian(n = 500, p = 4, m = rep(0, 4), s = diag(4))

Description

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

Usage

gen_gridcube(n = 500, p = 4)

Arguments

Value

A tibble containing the cube with grid points.

Examples

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

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)

Description

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

Usage

gen_helicalspiral(n = 500)

Arguments

Value

A data containing a helical hyper spiral.

Examples

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

Description

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

Usage

gen_hemisphere(n = 500)

Arguments

Value

A data containing a hemisphere.

Examples

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

Description

Remove points within a spherical hole in the middle

Usage

gen_hole(df, anchor = NULL, r = 0.5)

Arguments

Value

A tibble with the hole removed.

Examples

set.seed(20240412)
df <- gen_scurve(n = 1000)
gen_hole(df, r = 0.5)

Description

This function generates a dataset representing a structure with a sphere with points on the surface.

Usage

gen_hollowsphere(n = 500, p = 4)

Arguments

Value

A data containing a hollow sphere.

Examples

set.seed(20240412)
hollowsphere <- gen_hollowsphere(n = 500)

Description

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

Usage

gen_linearbranches(n = 400, k = 4)

Arguments

Value

A data containing linear shaped branches.

Examples

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

Description

This function generates a dataset consisting of long linear data.

Usage

gen_longlinear(n = 500, p = 4)

Arguments

Value

A tibble containing the long linear data.

Examples

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

Description

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

Usage

gen_mobius(n = 500)

Arguments

Value

A tibble containing a mobius structure.

Examples

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

Description

This function generates a dataset with multiple clusters in high-dimensional space. Each cluster can have a different shape, scale, rotation, and centroid, allowing the construction of complex synthetic datasets.

Usage

gen_multicluster(
  n = c(200, 300, 500),
  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,
  add_bkg = FALSE,
  ...
)

Arguments

Value

A tibble containing all generated clusters, with columns x1, x2, ... for dimensions and a cluster label.

Examples

set.seed(20240412)

# Example rotation matrices for 4D space
rot1 <- gen_rotation(p = 4, planes_angles = list(list(plane = c(1, 2), angle = 60),
                                                list(plane = c(3, 4), angle = 90)))
rot2 <- gen_rotation(p = 4, planes_angles = list(list(plane = c(1, 3), angle = 30)))
rot3 <- gen_rotation(p = 4, planes_angles = list(list(plane = c(2, 4), angle = 45)))

clust_data <- gen_multicluster(
  n = c(200, 300, 500),
  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 = list(rot1, rot2, rot3),
  add_bkg = FALSE
)

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))

Description

This function generates a dataset representing a nonlinear hyperbola structure.

Usage

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

Arguments

Value

A data containing a nonlinear hyperbola structure.

Examples

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

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

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

Description

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

Usage

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

Arguments

Value

A data containing curvy shaped branches originated in one point.

Examples

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

Description

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

Usage

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

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)

Description

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

Usage

gen_pyrfrac(n = 500, p = 4)

Arguments

Value

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

Examples

set.seed(20240412)
pyrfrac <- gen_pyrfrac(n = 500, p = 3)

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 tibble 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)

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)

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)

Description

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

Usage

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

Arguments

Value

A tibble containing a quadratic structure.

Examples

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

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)

Description

This function generates S-curve data.

Usage

gen_scurve(n = 500)

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)

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, r_hole = 0.5)

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 = 1000)

Description

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

Usage

gen_sphericalspiral(n = 500, spins = 1)

Arguments

Value

A data containing a spherical spiral.

Examples

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

Description

This function generates swiss roll data.

Usage

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

Arguments

Value

A tibble 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)

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, steps = 5)

Arguments

Value

A data containing 3-D trefoil knot.

Examples

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

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, steps = 5)

Arguments

Value

A tibble containing 4-D trefoil knot.

Examples

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

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)

Description

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

Usage

gen_unifcubehole(n = 5000, p = 4, r_hole = 0.5)

Arguments

Value

A data containing the cube data with a hole.

Examples

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

Description

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

Usage

gen_unifsphere(n = 500, r = 1)

Arguments

Value

A data containing a uniform sphere.

Examples

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

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))

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)

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) |> as.matrix()
gen_wavydims3(n = 500, p = 3, data = df)

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()

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()

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()

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()

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()

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()

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()

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 tibble containing the mobius cluster and Gaussian cluster.

Examples

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

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))

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)

Arguments

Value

A tibble containing the generated dataset with columns:

• x1, x2, x3, x4 — 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()

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, shift = 1, shape = "crescent")

Arguments

Value

A tibble containing $\sum n$ rows and $p$ columns, with the generated features ('x1, x2, x3, x4') and a 'cluster' label.

Examples

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

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))

Arguments

Value

A tibble with n[1] + n[2] rows and 5 columns:

• x1,x2, x3, x4 — coordinates of the generated points.

• cluster — cluster membership label.

Examples

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

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))

Arguments

Value

A tibble with n[1] + n[2] rows and 5 columns:

• x1, x2, x3, x4: 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()

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)

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)

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)

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)

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)

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)

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)

Description

This function normalize the data by the largest absolute value found in the dataset.

Usage

normalize_data(data)

Arguments

Value

A normalized data.

Examples

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

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)

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)

Description

The 'three_clust_01' dataset contains three distinct clusters in a 4-D space.

Usage

data(three_clust_01)

Format

A data frame with 1500 rows and 5 columns:

cluster, x1, x2, x3, x4

High-dimensional coordinates

Source

This dataset is generated for example purposes.

Examples

# Load the mobiusgau dataset
data(three_clust_01)

# Display the first few rows of the dataset
head(three_clust_01)

Description

The 'three_clust_02' dataset contains three distinct clusters in a 4-D space.

Usage

data(three_clust_02)

Format

A data frame with 1500 rows and 5 columns:

cluster, x1, x2, x3, x4

High-dimensional coordinates

Source

This dataset is generated for example purposes.

Examples

# Load the mobiusgau dataset
data(three_clust_02)

# Display the first few rows of the dataset
head(three_clust_02)

Description

The 'three_clust_03' dataset contains three distinct clusters in a 4-D space.

Usage

data(three_clust_03)

Format

A data frame with 1500 rows and 5 columns:

cluster, x1, x2, x3, x4

High-dimensional coordinates

Source

This dataset is generated for example purposes.

Examples

# Load the mobiusgau dataset
data(three_clust_03)

# Display the first few rows of the dataset
head(three_clust_03)

Description

The 'three_clust_04' dataset contains three distinct clusters in a 4-D space.

Usage

data(three_clust_04)

Format

A data frame with 1500 rows and 5 columns:

cluster, x1, x2, x3, x4

High-dimensional coordinates

Source

This dataset is generated for example purposes.

Examples

# Load the mobiusgau dataset
data(three_clust_04)

# Display the first few rows of the dataset
head(three_clust_04)

Description

The 'three_clust_05' dataset contains three distinct clusters in a 4-D space.

Usage

data(three_clust_05)

Format

A data frame with 1500 rows and 5 columns:

cluster, x1, x2, x3, x4

High-dimensional coordinates

Source

This dataset is generated for example purposes.

Examples

# Load the mobiusgau dataset
data(three_clust_05)

# Display the first few rows of the dataset
head(three_clust_05)