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Directional (version 5.6)

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. (2022). An investigation of hypothesis testing procedures for circular and spherical mean vectors. Communications in Statistics-Simulation and Computation (Accepted for publication). .

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Install

install.packages('Directional')

Monthly Downloads

935

Version

5.6

License

GPL-2

Maintainer

Michail Tsagris

Last Published

September 22nd, 2022

Functions in Directional (5.6)

Directional-package

This is an R package that provides methods for the statistical analysis of directional data, including massive (very large scale) directional data.
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 correlations between one and many circular variables

Circular correlations between two circular variables
Circular-linear correlation

Circular-linear correlation
Rotation axis and angle of rotation given a rotation matrix

Rotation axis and angle of rotation given a rotation matrix
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
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 two circular variables

Circular correlations between two circular variables
Density of the spherical Kent and ESAG distributions

Density of the spherical Kent and ESAG distributions
Density of some (hyper-)spherical distributions

Density of some (hyper-)spherical distributions
Tuning of the k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance. Tuning the k neigbours
The k-nearest neighbours using the cosinus distance

The k-nearest neighbours using the cosinus distance
Density of some circular distributions

Density of some circular distributions
k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance
Cross validation for estimating the classification rate

Cross validation for estimating the classification rate
Cross validation with ESAG discrminant analysis

Cross validation for estimating the classification rate of a discrminant analysis for directional data assuming an ESAG distribution
MLE of the ESAG distribution

MLE of the ESAG distribution
Conversion of cosines to azimuth and plunge

Conversion of cosines to azimuth and plunge
Rotation matrix on SO(3) from three Euler angles

Construct a rotation matrix on SO(3) from the Euler angles.
Simulation of random values from a Bingham distribution

Simulating from a Bingham distribution
Goodness of fit test for grouped data

Goodness of fit test for grouped data
Transform unit vectors to angular data

Transform unit vectors to angular data
Summary statistics for grouped circular data

Summary statistics for grouped circular data
Prediction in discriminant analysis based on ESAG distribution

Prediction of a new observation using discriminant analysis based on ESAGdistribution
Saddlepoint approximations of the Fisher-Bingham distributions

Saddlepoint approximations of the Fisher-Bingham distributions
Hypothesis test for von Mises-Fisher distribution over Kent distribution

Hypothesis test for von Mises-Fisher distribution over Kent distribution
Anova for circular data

Analysis of variance for circular data
Permutation based 2-sample mean test for (hyper-)spherical data

Permutation based 2-sample mean test for (hyper-)spherical data
Anova for (hyper-)spherical data

Analysis of variance for (hyper-)spherical data
Bootstrap 2-sample mean test for (hyper-)spherical data

Bootstrap 2-sample mean test for (hyper-)spherical data
Euclidean transformation

Euclidean transformation
Spherical regression using the projected normal or the von Mises-Fisher distribution

Spherical regression using the projected normal or the von Mises-Fisher distribution
Inverse of the Euclidean transformation

Inverse of the Euclidean transformation
Logarithm of the Kent distribution normalizing constant

Logarithm of the Kent distribution normalizing constant
Hypothesis test for IAG distribution over the ESAG distribution

Hypothesis test for IAG distribution over the ESAG distribution
Contour plot of the Kent distribution without any data

Contour plot of the Kent distribution without any data
Contour plot of the Kent distribution for some data

Contour plot of the Kent distribution for some data
Uniformity test for circular data

Uniformity tests for circular data.
Habeck's rotation matrix generation

Generation of three-dimensional random rotations using Habeck's algorithm.
MLE of the Kent distribution

MLe of the Kent distribution
Lambert's equal area projection

Lambert's equal area projection
Haversine distance matrix

Harvesine distance matrix
Inverse of Lambert's equal area projection

Inverse of Lambert's equal area projection
Generate random folds for cross-validation

Generate random folds for cross-validation
Spherical and hyperspherical median

Fast calculation of the spherical and hyperspherical median
MLE of the Purkayashta distribution

MLE of the Purkayashta distribution
Probability density function of the von Mises-Fisher distribution

Probability density function of the von Mises-Fisher distribution
Normalised spatial median for directional data

Normalised spatial median for directional data
Bootstrap 2-sample mean test for circular data

Bootstrap 2-sample mean test for circular data
Maps of the world and the continents

maps of the world and the continents
Simulation of random values from a spherical Fisher-Bingham distribution

Simulation of random values from a spherical Fisher-Bingham distribution
Permutation based 2-sample mean test for circular data

Permutation based 2-sample mean test for circular data
Mixtures of Von Mises-Fisher distributions

Mixtures of Von Mises-Fisher distributions
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)
k-NN regression

k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Rayleigh's test of uniformity

Rayleigh's test of uniformity
Tuning of the k-NN regression

Tuning of the k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Test for a given mean direction

Test for a given mean direction
Simulation of random values from a spherical Kent distribution

Simulation of random values from a spherical Kent distribution
Simulation from a Bingham distribution using any symmetric matrix A

Simulation from a Bingham distribution using any symmetric matrix A
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.
Random sample of matrices in SO(p)

Random sample of matrices in SO(p)
Simulation of random values from some circular distributions

Simulation of random values from some circular distributions
Converting an unsigned unit quaternion to rotation matrix on SO(3)

Converting an unsigned unit quaternion to rotation matrix on SO(3)
MLE of some circular distributions with multiple samples

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

Read a file as a Filebacked Big Matrix
Simulation of random values from a mixture of von Mises-Fisher distributions

Simulation of random values from a mixture of von Mises-Fisher distributions
Angular central Gaussian random values simulation

Angular central Gaussian random values simulation
Rotation matrix from a rotation axis and angle of rotation

Rotation matrix from a rotation axis and angle of rotation
Spherical-spherical correlation

Spherical-spherical correlation
Converting a rotation matrix on SO(3) to an unsigned unit quaternion

Converting a rotation matrix on SO(3) to an unsigned unit quaternion
Rotation matrix to rotate a spherical vector along the direction of another

Rotation matrix to rotate a spherical vector along the direction of another
Spherical-spherical regression

Spherical-Spherical regression
Simulation of random values from rotationally symmetric distributions

Simulation of random values from rotationally symmetric distributions
Simulation of random values from the ESAG distribution

Simulation of random values from the ESAG distribution
von Mises kernel density estimation

Kernel density estimation of circular data with a von Mises kernel
Generation of unit vector(s) with a given angle

Generation of unit vector(s) with a given angle
Prediction with some naive Bayes classifiers for circular data

Prediction with some naive Bayes classifiers for circular data
Test for equality of concentration parameters for spherical data

Test for equality of concentration parameters for spherical data
MLE of some circular distributions

MLE of some circular distributions
Euler angles from a rotation matrix on SO(3)

Compute the Euler angles from a rotation matrix on SO(3).
Check visually whether matrix Fisher samples is correctly generated or not

Check visually whether matrix Fisher samples is correctly generated or not.
Many simple circular or angular regressions

Many simple circular or angular regressions
Naive Bayes classifiers for circular data

Naive Bayes classifiers for directional data
von Mises-Fisher kernel density estimation for (hyper-)spherical data

Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel
MLE of the Wood bimodal distribution on the sphere

MLe of the Wood bimodal distribution on the sphere
Contour plots of the von Mises-Fisher distribution

Contour plots of the von Mises-Fisher distribution on the sphere
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
MLE of (hyper-)spherical distributions

MLE of (hyper-)spherical distributions
Circular or angular regression

Circular or angular 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
Forward Backward Early Dropping selection for circular data using the SPML regression

Forward Backward Early Dropping selection for circular data using the SPML regression
Cross validation in von Mises-Fisher discrminant analysis

Cross validation for estimating the classification rate of a discrminant analysis for directional data assuming a von Mises-Fisher distribution
Prediction in discriminant analysis based on von Mises-Fisher distribution

Prediction of a new observation using discriminant analysis based on von Mises-Fisher distribution
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
Tuning of the bandwidth parameter in the von Mises kernel

Tuning of the bandwidth parameter in the von Mises kernel for circular data