Additional functions
In cardinalR: Collection of Data Structures

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  message = FALSE
)

library(cardinalR)

These are helper functions included in the package.

Generating background noise

The gen_bkgnoise() function allows users to generate multivariate Gaussian noise to serve as background data in high-dimensional spaces.

# Example: Generate 4D background noise
bkg_data <- gen_bkgnoise(n = 500, p = 4, 
                         m = c(0, 0, 0, 0), s = c(2, 2, 2, 2))
head(bkg_data)

The generated data has independent dimensions with specified means (m) and standard deviations (s).

Randomizing rows

randomize_rows() ensures the rows of the input data is randomized.

randomized_data <- randomize_rows(bkg_data)
head(randomized_data)

Relocating clusters

relocate_clusters() allows users to translate clusters in any dimension(s). This is achieved by centering each cluster (subtracting its mean) and then adding a translation vector from a provided matrix (vert_mat).

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

vert_mat <- matrix(c(
  5, 0, 0, 0,
  0, 5, 0, 0,
  0, 0, 5, 0
), nrow = 3, byrow = TRUE)

relocated_df <- relocate_clusters(df, vert_mat)
head(relocated_df)

Generating Rotation Matrices

The gen_rotation() function creates a rotation matrix in high-dimensional space for given planes and angles.

rotations_4d <- list(
  list(plane = c(1, 2), angle = 60),
  list(plane = c(3, 4), angle = 90)
)

rot_mat <- gen_rotation(p = 4, planes_angles = rotations_4d)
rot_mat

Normalize data

When combining clusters or transforming data geometrically, magnitudes can differ drastically. The normalize_data() function rescales the entire dataset to fit within ([-1, 1]) based on its maximum absolute value.

norm_data <- normalize_data(bkg_data)
head(norm_data)

Generating cluster locations

To place clusters in different positions, gen_clustloc() generates points forming a simplex-like arrangement ensuring each cluster center is equidistant from others as much as possible.

centers <- gen_clustloc(p = 4, k = 5)
head(centers)

Numeric generators

Two helper functions, gen_nproduct() and gen_nsum(), generate numeric vectors of positive integers that approximately satisfy a user-specified target product or sum, respectively.

The function gen_nsum(n, k) divides a total sum n into k positive integers. It first assigns an equal base value to each element and then randomly distributes any remainder, ensuring the elements sum exactly to n.

gen_nsum(n = 100, k = 3)

The function gen_nproduct(n, p) aims to produce p positive integers whose product is approximately n. It starts with all elements equal to the rounded $p^{th}$ root of n and iteratively adjusts elements up or down in a randomized manner until the product is within a small tolerance of n. This accommodates the fact that exact integer solutions for a given product are often impossible.