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Directional (version 6.8)

A Collection of Functions for Directional Data Analysis

Description

A collection of functions for directional data (including massive data, with millions of observations) analysis. Hypothesis testing, discriminant and regression analysis, MLE of distributions and more are included. The standard textbook for such data is the "Directional Statistics" by Mardia, K. V. and Jupp, P. E. (2000). Other references include a) Phillip J. Paine, Simon P. Preston Michail Tsagris and Andrew T. A. Wood (2018). "An elliptically symmetric angular Gaussian distribution". Statistics and Computing 28(3): 689-697. . b) Tsagris M. and Alenazi A. (2019). "Comparison of discriminant analysis methods on the sphere". Communications in Statistics: Case Studies, Data Analysis and Applications 5(4):467--491. . c) P. J. Paine, S. P. Preston, M. Tsagris and Andrew T. A. Wood (2020). "Spherical regression models with general covariates and anisotropic errors". Statistics and Computing 30(1): 153--165. . d) Tsagris M. and Alenazi A. (2024). "An investigation of hypothesis testing procedures for circular and spherical mean vectors". Communications in Statistics-Simulation and Computation, 53(3): 1387--1408. . e) Tsagris M. and Alzeley O. (2023). "Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling". . f) Zehao Yu and Xianzheng Huang (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension. Electronic Journal of Statistics, 18(1): 301--334. . g) Tsagris M. (2024). "Directional data analysis using the spherical Cauchy and the Poisson-kernel based distribution". .

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Install

install.packages('Directional')

Monthly Downloads

1,274

Version

6.8

License

GPL (>= 2)

Maintainer

Michail Tsagris

Last Published

September 9th, 2024

Functions in Directional (6.8)

Conversion of cosines to azimuth and plunge

Conversion of cosines to azimuth and plunge
Cross validation for estimating the classification rate

Cross validation for estimating the classification rate
Density of the SESPC distribution

Density of the SESPC distribution
Tuning of the k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance. Tuning the k neigbours
Transform unit vectors to angular data

Transform unit vectors to angular data
Euclidean transformation

Euclidean transformation
Density of the Wood bimodal distribution on the sphere

Density of the Wood bimodal distribution on the sphere
Contour plot (on the plane) of the ESAG and Kent distributions without any data

Contour plot (on the plane) of the ESAG and Kent and ESAG distributions without any data
Inverse of the Euclidean transformation

Inverse of the Euclidean transformation
Rotation matrix on SO(3) from three Euler angles

Construct a rotation matrix on SO(3) from the Euler angles.
MLE of the ESAG distribution in arbitrary dimensions

MLE of the ESAG distribution
Spherical regression using the ESAG distribution

Spherical regression using the ESAG distribution
Bootstrap 2-sample mean test for (hyper-)spherical data

Bootstrap 2-sample mean test for (hyper-)spherical data
Anova for circular data

Analysis of variance for circular data
Habeck's rotation matrix generation

Generation of three-dimensional random rotations using Habeck's algorithm.
Summary statistics for grouped circular data

Summary statistics for grouped circular data
Haversine distance matrix

Harvesine distance matrix
Anova for (hyper-)spherical data

Analysis of variance for (hyper-)spherical data
Goodness of fit test for grouped data

Goodness of fit test for grouped data
Density of some circular distributions

Density of some circular distributions
Hypothesis test for von Mises-Fisher distribution over Kent distribution

Hypothesis test for von Mises-Fisher distribution over Kent distribution
Permutation based 2-sample mean test for (hyper-)spherical data

Permutation based 2-sample mean test for (hyper-)spherical data
Density of some (hyper-)spherical distributions

Density of some (hyper-)spherical distributions
Bootstrap ANOVA for circular data

Bootstrap ANOVA for circular data
MLE of the Kent distribution

MLe of the Kent distribution
Saddlepoint approximations of the Fisher-Bingham distributions

Saddlepoint approximations of the Fisher-Bingham distributions
Simulation of random values from a Bingham distribution

Simulating from a Bingham distribution
Permutation based 2-sample mean test for circular data

Permutation based 2-sample mean test for circular data
Bootstrap 2-sample mean test for circular data

Bootstrap 2-sample mean test for circular data
Bootstrap ANOVA for (hyper-)spherical data

Bootstrap ANOVA for (hyper-)spherical data
Lambert's equal area projection

Lambert's equal area projection
k-NN regression

k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Contour plot of a mixture of von Mises-Fisher distributions model

Contour plot of a mixture of von Mises-Fisher distributions model for spherical data only.
Spherical regression using rotationally symmetric distributions

Spherical regression using rotationally symmetric distributions
Tuning of the k-NN regression

Tuning of the k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Uniformity test for circular data

Uniformity tests for circular data.
Mixtures of Von Mises-Fisher distributions

Mixtures of Von Mises-Fisher distributions
Maps of the world and the continents

maps of the world and the continents
Hypothesis test for IAG distribution over the ESAG distribution

Hypothesis test for IAG distribution over the ESAG distribution
Normalised spatial median for directional data

Normalised spatial median for directional data
MLE of some circular distributions with multiple samples

MLE of some circular distributions with multiple samples
Test for a given mean direction

Test for a given mean direction
Inverse of Lambert's equal area projection

Inverse of Lambert's equal area projection
Hypothesis test for SIPC distribution over the SESPC distribution

Hypothesis test for SIPC distribution over the SESPC distribution
MLE of the Purkayashta distribution

MLE of the Purkayashta distribution
Projections based test of uniformity

Projections based test of uniformity
Converting an unsigned unit quaternion to rotation matrix on SO(3)

Converting an unsigned unit quaternion to rotation matrix on SO(3)
Spherical and hyperspherical median

Fast calculation of the spherical and hyperspherical median
Cumulative distribution function of circular distributions

Cumulative distribution function of circular distributions
Simulation of random values from a mixture of von Mises-Fisher distributions

Simulation of random values from a mixture of von Mises-Fisher distributions
Logarithm of the Kent distribution normalizing constant

Logarithm of the Kent distribution normalizing constant
Simulation of random values from a spherical Kent distribution

Simulation of random values from a spherical Kent distribution
Generate random folds for cross-validation

Generate random folds for cross-validation
Angular central Gaussian random values simulation

Angular central Gaussian random values simulation
Rayleigh's test of uniformity

Rayleigh's test of uniformity
Simulation from a Matrix Fisher distribution on SO(3)

Simulation from a Matrix Fisher distribution on SO(3)
MLE of the Matrix Fisher distribution on SO(3)

MLE of the Matrix Fisher distribution on SO(3)
Spherical and hyper-spherical distance correlation

Spherical and hyper-spherical distance correlation
Spherical-spherical correlation

Spherical-spherical correlation
Simulation of random values from the ESAG distribution

Simulation of random values from the ESAG distribution
Simulation from a Bingham distribution using any symmetric matrix A

Simulation from a Bingham distribution using any symmetric matrix A
Rotation matrix from a rotation axis and angle of rotation

Rotation matrix from a rotation axis and angle of rotation
Euler angles from a rotation matrix on SO(3)

Compute the Euler angles from a rotation matrix on SO(3).
Converting a rotation matrix on SO(3) to an unsigned unit quaternion

Converting a rotation matrix on SO(3) to an unsigned unit quaternion
Spherical regression using the SESPC distribution

Spherical regression using the SESPC distribution
Circular or angular regression

Circular or angular regression
MLE of some circular distributions

MLE of some circular distributions
Read a file as a Filebacked Big Matrix

Read a file as a Filebacked Big Matrix
Simulation of random values from some circular distributions

Simulation of random values from some circular distributions
MLE of the SESPC distribution

MLE of the SESPC distribution
Random sample of matrices in SO(p)

Random sample of matrices in SO(p)
Simulation of random values from rotationally symmetric distributions

Simulation of random values from rotationally symmetric distributions
Two sample location test for (hyper-)spherical data

Analysis of variance for (hyper-)spherical data
Contour plot (on the sphere) of the ESAG and Kent distributions

Contour plot (on the sphere) of the ESAG and Kent distributions
Spherical-spherical regression

Spherical-Spherical regression
Interactive 3D plot of spherical data

Interactive 3D plot of spherical data
Contour plot of spherical data using a von Mises-Fisher kernel density estimate

Contour plot of spherical data using a von Mises-Fisher kernel density estimate
Contour plot (on the sphere) of the SESPC distribution

Contour plot (on the sphere) of the SESPC distribution
Contour plot (on the sphere) of a mixture of von Mises-Fisher distributions

Contour plot (on the sphere) of a mixture of von Mises-Fisher distributions
von Mises kernel density estimation

Kernel density estimation of circular data with a von Mises kernel
Many simple circular or angular regressions

Many simple circular or angular regressions
Forward Backward Early Dropping selection for circular data using the SPML regression

Forward Backward Early Dropping selection for circular data using the SPML regression
Generation of unit vector(s) with a given angle

Generation of unit vector(s) with a given angle
Simulation of random values from a spherical Fisher-Bingham distribution

Simulation of random values from a spherical Fisher-Bingham distribution
MLE of (hyper-)spherical rotationally symmetric distributions

MLE of (hyper-)spherical rotationally symmetric distributions
Rotation matrix to rotate a spherical vector along the direction of another

Rotation matrix to rotate a spherical vector along the direction of another
Check visually whether matrix Fisher samples is correctly generated or not

Check visually whether matrix Fisher samples is correctly generated or not.
A test for testing the equality of the concentration parameters for ciruclar data

A test for testing the equality of the concentration parameter among g samples, where g >= 2 for ciruclar data
Tuning of the bandwidth parameter in the von Mises kernel

Tuning of the bandwidth parameter in the von Mises kernel for circular data
Simulation of random values from the SESPC distribution

Simulation of random values from the SESPC distribution
Contour plot (on the sphere) of some spherical rotationally symmetric distributions

Contour plot (on the sphere) of some spherical rotationally symmetric distributions
Test for equality of concentration parameters for spherical data

Test for equality of concentration parameters for spherical data
Naive Bayes classifiers for circular data

Naive Bayes classifiers for directional data
Prediction with some naive Bayes classifiers for circular data

Prediction with some naive Bayes classifiers for circular data
MLE of the Wood bimodal distribution on the sphere

MLE of the Wood bimodal distribution on the sphere
Contour plots of some rotationally symmetric distributions

Contour plots of some rotationally symmetric distributions
Tuning of the bandwidth parameter in the von Mises-Fisher kernel

Tuning of the bandwidth parameter in the von Mises-Fisher kernel for (hyper-)spherical data
(Hyper-)spherical regression using rotational symmetric distributions

(Hyper-)spherical regression using the rotational symmetric distributions
von Mises-Fisher kernel density estimation for (hyper-)spherical data

Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel
BIC for the model based clustering using mixtures of von Mises-Fisher distributions

BIC to choose the number of components in a model based clustering using mixtures of von Mises-Fisher distributions
Column-wise uniformity Watson test for circular data

Column-wise uniformity tests for circular data
Column-wise MLE of the angular Gaussian and the von Mises Fisher distributions

Column-wise MLE of the angular Gaussian and the von Mises Fisher distributions
Circular-linear correlation

Circular-linear correlation
Circular correlations between two circular variables

Circular correlations between two circular variables
Summary statistics for circular data

Summary statistics for circular data
Test of equality of the concentration parameters for circular data

A test for testing the equality of the concentration parameter among g samples, where g >= 2 for ciruclar data
Circular correlations between one and many circular variables

Circular correlations between two circular variables
Circular distance correlation between two circular variables

Circular distance correlation between two circular variables
Density of a mixture of von Mises-Fisher distributions

Density of a mixture of von Mises-Fisher distributions
The k-nearest neighbours using the cosinus distance

The k-nearest neighbours using the cosinus distance
Prediction in discriminant analysis based on some distributions

Prediction of a new observation using discriminant analysis based on some distributions
Rotation axis and angle of rotation given a rotation matrix

Rotation axis and angle of rotation given a rotation matrix
Density of the spherical ESAG and Kent distributions and of the ESAG distribution in arbitrary dimensions

Density of the spherical ESAG and Kent distributions
Directional-package

This is an R package that provides methods for the statistical analysis of directional data, including massive (very large scale) directional data.
k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance