Type: Package
Title: Clustering and Simulation of Spherical Cauchy and PKBD Models
Version: 0.0.2
Description: Provides tools for estimation and clustering of spherical data, seamlessly integrated with the 'flexmix' package. Includes the necessary M-step implementations for both Poisson Kernel-Based Distribution (PKBD) and spherical Cauchy distribution. Additionally, the package provides random number generators for PKBD and spherical Cauchy distribution. Methods are based on Golzy M., Markatou M. (2020) <doi:10.1080/10618600.2020.1740713>, Kato S., McCullagh P. (2020) <doi:10.3150/20-bej1222> and Sablica L., Hornik K., Leydold J. (2023) <doi:10.1214/23-ejs2149>.
License: GPL-3
Encoding: UTF-8
Imports: Rcpp (≥ 0.12.18), Tinflex (≥ 1.8), flexmix, torch, methods
LinkingTo: Rcpp, RcppArmadillo
URL: https://github.com/lsablica/circlus
BugReports: https://github.com/lsablica/circlus/issues
RoxygenNote: 7.3.2
Depends: R (≥ 3.1.0)
LazyData: true
NeedsCompilation: yes
Packaged: 2025-02-19 16:33:16 UTC; lukas
Author: Lukas Sablica ORCID iD [aut, cre], Kurt Hornik ORCID iD [aut], Bettina Gruen ORCID iD [aut], Josef Leydold ORCID iD [aut]
Maintainer: Lukas Sablica <lsablica@wu.ac.at>
Repository: CRAN
Date/Publication: 2025-02-19 17:00:07 UTC

Abstracts of Papers Co-Authored by Friedrich Leisch

Description

A dataset containing the abstracts of papers co-authored by Friedrich Leisch together with obtained metadata and embeddings generated using GMT and OpenAI embeddings models.

Usage

Abstracts

Format

A data frame with 129 rows and 282 variables.

PKB distribution Driver for FlexMix

Description

This model driver for flexmix implements model-based clustering of PKB distributions.

Usage

FLXMCpkb(formula = . ~ .)

Arguments

formula

A formula.

Value

Returns an object of class FLXMC.

Examples

mix <- rbind(rpkb(30, 0.95, c(1, 0, 0)), rpkb(30, 0.9, c(-1, 0, 0)))
m1 <- flexmix::flexmix(mix ~ 1, k = 2, model = FLXMCpkb())

Spherical Cauchy Driver for FlexMix

Description

This model driver for flexmix implements model-based clustering of spherical Cauchy distributions.

Usage

FLXMCspcauchy(formula = . ~ .)

Arguments

formula

A formula.

Value

Returns an object of class FLXMC.

Examples

mix <- rbind(rpkb(30, 0.95, c(1, 0, 0)), rpkb(30, 0.9, c(-1, 0, 0)))
m1 <- flexmix::flexmix(mix ~ 1, k = 2, model = FLXMCspcauchy())

PKB distribution Driver for FlexMix Using Neural Networks

Description

This model driver for flexmix implements model-based clustering of PKB distributions using neural network in the M-step.

Usage

FLXMRpkb(
  formula = . ~ .,
  EPOCHS = 100,
  LR = 0.1,
  max_iter = 200,
  adam_iter = 5,
  free_iter = adam_iter,
  line_search_fn = "strong_wolfe"
)

Arguments

formula

A formula.

EPOCHS

The number of epochs in the M-step estimation (default: 100).

LR

The learning rate used in the M-step estimation (default: 0.1).

max_iter

The maximum number of iterations of the LBFGS optimizer (default: 200).

adam_iter

The number of iteration for which the adam optimizer is used before the algorithm switches to L-BFGS (default: 5).

free_iter

The number of initial iterations for which the model in M-step is fully reseted (default: adam_iter).

line_search_fn

The method used for line search in LBFGS (default: "strong_wolfe").

Value

Returns an object of class FLXMC.

Examples


if(torch::torch_is_installed()){
mix <- rbind(rpkb(30, 0.95, c(1, 0, 0)), rpkb(30, 0.9, c(-1, 0, 0)))
m1 <- flexmix::flexmix(mix ~ 1, k = 2, model = FLXMRpkb())
}

Spherical Cauchy Driver for FlexMix Using Neural Networks

Description

This model driver for flexmix implements model-based clustering of spherical Cauchy distributions using neural networks in the M-step.

Usage

FLXMRspcauchy(
  formula = . ~ .,
  EPOCHS = 100,
  LR = 0.1,
  max_iter = 200,
  adam_iter = 5,
  free_iter = adam_iter,
  line_search_fn = "strong_wolfe"
)

Arguments

formula

A formula.

EPOCHS

EPOCHS The number of epochs in the M-step estimation (default: 100).

LR

The learning rate used in the M-steo estimation (default: 0.1).

max_iter

The maximum number of iterations of the LBFGS optimizer (default: 200).

adam_iter

The number of iteration for which the adam optimizer is used before the algorithm switches to L-BFGS (default: 5).

free_iter

The number of initial iterations for which the model in M-step is fully reseted (default: adam_iter).

line_search_fn

The method used for line search in LBFGS (default: "strong_wolfe").

Value

Returns an object of class FLXMC.

Examples


if(torch::torch_is_installed()){
mix <- rbind(rpkb(30, 0.95, c(1, 0, 0)), rpkb(30, 0.9, c(-1, 0, 0)))
m1 <- flexmix::flexmix(mix ~ 1, k = 2, model = FLXMRspcauchy())
}

Density Function for PKB distribution

Description

Calculates the density of the PKB distribution for given data points.

Usage

dpkb(y, mu, rho, log = FALSE)

Arguments

y

A matrix or data frame where each row represents a data point on the unit hypersphere.

mu

A vector or matrix representing the mean direction parameter(s). If a vector, it must be normalized (unit length) and is applied to all data points. If a matrix, it must have the same number of rows as y, and each row must be normalized.

rho

A scalar or a vector representing the concentration parameter. If a vector, its length must match the number of rows in y. Each rho[i] is used to evaluate the density for y[i, ]. Must be between 0 (inclusive) and 1 (exclusive).

log

Logical; if TRUE, the log-density is returned. Default is FALSE.

Details

This function calculates the density of the PKB distribution for each data point in y, given the parameters mu and rho.

Value

A vector of density values (or log-density if log = TRUE) for each row in y.

Examples

y <- matrix(c(1, 0, 0, 0, 0, 1), ncol = 3, byrow = TRUE)
mu <- c(1, 0, 0)
rho <- 0.5
dpkb(y, mu, rho)

Density Function for Spherical Cauchy Distribution

Description

Calculates the density of the spherical Cauchy distribution for given data points.

Usage

dspcauchy(y, mu, rho, log = FALSE)

Arguments

y

A matrix or data frame where each row represents a data point on the unit hypersphere.

mu

A vector or matrix representing the mean direction parameter(s). If a vector, it must be normalized (unit length) and is applied to all data points. If a matrix, it must have the same number of rows as y, and each row must be normalized.

rho

A scalar or a vector representing the concentration parameter. If a vector, its length must match the number of rows in y. Each rho[i] is used to evaluate the density for y[i, ]. Must be between 0 (inclusive) and 1 (exclusive).

log

Logical; if TRUE, the log-density is returned. Default is FALSE.

Details

This function calculates the density of the spherical Cauchy distribution for each data point in y, given the parameters mu and rho.

Value

A vector of density values (or log-density if log = TRUE) for each row in y.

Examples

y <- matrix(c(1, 0, 0, 0, 0, 1), ncol = 3, byrow = TRUE)
mu <- c(1, 0, 0)
rho <- 0.5
dspcauchy(y, mu, rho)

Random Sampling from PKBD Distributions using ACG Envelopes

Description

Generates a random sample from PKBD distributions.

Usage

rPKBD_ACG(n, rho, mu)

Arguments

n

The number of random draws.

rho

A numeric giving the concentration parameter.

mu

A numeric vector giving the mean direction parameter.

Value

A matrix with the generated values.

Random Sampling from PKB Distributions using Projected Saw Distribution

Description

Generates a random sample from PKB distributions.

Usage

rPKBD_Saw(n, rho, mu)

Arguments

n

The number of random draws.

rho

A numeric giving the concentration parameter.

mu

A numeric vector giving the mean direction parameter.

Value

A matrix with the generated values.

Random Sampling from PKB Distributions using ACG or Projected Saw Distributions

Description

Generates a random sample from PKB distributions.

Usage

rpkb(n, rho, mu, method = "ACG")

Arguments

n

The number of random draws.

rho

A numeric giving the concentration parameter.

mu

A numeric vector giving the mean direction parameter.

method

A character indicating the method to use, "ACG" for angular central Gaussian distribution envelopes and "Saw" for the use of projected Saw distributions.

Value

A matrix with the generated values.

Examples

rpkb(10, 0.95, c(1, 0, 0))

Random Sampling from Spherical Cauchy Distributions

Description

Generates a random sample from spherical Cauchy distributions.

Usage

rspcauchy(n, rho, mu)

Arguments

n

The number of random draws.

rho

A numeric value giving the rho parameter.

mu

A numeric vector giving the mu direction parameter.

Value

A matrix with the generated values.

Examples

rspcauchy(10, 0.95, c(1, 0, 0))