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Directional (version 5.4)

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. .

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Install

install.packages('Directional')

Monthly Downloads

656

Version

5.4

License

GPL-2

Maintainer

Michail Tsagris

Last Published

May 15th, 2022

Functions in Directional (5.4)

Summary statistics for circular data

Summary statistics for circular data
Column-wise uniformity Watson test for circular data

Column-wise uniformity tests for circular data
Circular correlations between one and many circular variables

Circular correlations between two circular variables
Circular-linear correlation

Circular-linear correlation
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
Directional-package

This is an R package that provides methods for the statistical analysis of directional data, including massive (very large scale) directional data.
Rotation axis and angle of rotation given a rotation matrix

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

Circular correlations between two circular variables
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
Density of some circular distributions

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

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

Cross validation for estimating the classification rate
Rotation matrix on SO(3) from three Euler angles

Construct a rotation matrix on SO(3) from the Euler angles.
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
Density of some (hyper-)spherical distributions

Density of some (hyper-)spherical distributions
MLE of the ESAG distribution

MLE of the ESAG distribution
Cross validation with ESAG discrminant analysis

Cross validation for estimating the classification rate of a discrminant analysis for directional data assuming an ESAG distribution
Spherical and hyperspherical median

Fast calculation of the spherical and hyperspherical median
Conversion of cosines to azimuth and plunge

Conversion of cosines to azimuth and plunge
k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance
Euclidean transformation

Euclidean transformation
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
k-NN regression

k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
The k-nearest neighbours using the cosinus distance

The k-nearest neighbours using the cosinus distance
Density of the spherical Kent and ESAG distributions

Density of the spherical Kent and ESAG distributions
Tuning of the k-NN regression

Tuning of the k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Prediction in discriminant analysis based on ESAG distribution

Prediction of a new observation using discriminant analysis based on ESAGdistribution
Inverse of the Euclidean transformation

Inverse of the Euclidean transformation
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
Mixtures of Von Mises-Fisher distributions

Mixtures of Von Mises-Fisher distributions
Read a file as a Filebacked Big Matrix

Read a file as a Filebacked Big Matrix
Prediction with some naive Bayes classifiers for circular data

Prediction with some naive Bayes classifiers for circular data
von Mises kernel density estimation

Kernel density estimation of circular data with a von Mises kernel
MLE of some circular distributions with multiple samples

MLE of some circular distributions with multiple samples
Naive Bayes classifiers for circular data

Naive Bayes classifiers for directional data
Simulation of random values from the ESAG distribution

Simulation of random values from the ESAG distribution
MLE of the Wood bimodal distribution on the sphere

MLe of the Wood bimodal distribution on the sphere
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
Spherical regression using the projected normal or the von Mises-Fisher distribution

Spherical regression using the projected normal or the von Mises-Fisher distribution
Hypothesis test for IAG distribution over the ESAG distribution

Hypothesis test for IAG distribution over the ESAG distribution
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.
MLE of the Purkayashta distribution

MLE of the Purkayashta distribution
Generate random folds for cross-validation

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

Inverse of Lambert's equal area projection
Probability density function of the von Mises-Fisher distribution

Probability density function of the von Mises-Fisher distribution
Goodness of fit test for grouped data

Goodness of fit test for grouped data
Simulation of random values from a mixture of von Mises-Fisher distributions

Simulation of random values from a mixture of von Mises-Fisher distributions
Spherical-spherical correlation

Spherical-spherical correlation
Simulation from a Matrix Fisher distribution on SO(3)

Simulation from a Matrix Fisher distribution on SO(3)
Permutation based 2-sample mean test for (hyper-)spherical data

Permutation based 2-sample mean test for (hyper-)spherical data
Simulation of random values from some circular distributions

Simulation of random values from some circular distributions
Logarithm of the Kent distribution normalizing constant

Logarithm of the Kent distribution normalizing constant
Transform unit vectors to angular data

Transform unit vectors to angular data
Converting an unsigned unit quaternion to rotation matrix on SO(3)

Converting an unsigned unit quaternion to rotation matrix on SO(3)
Angular central Gaussian random values simulation

Angular central Gaussian random values simulation
Many simple circular or angular regressions

Many simple circular or angular regressions
MLE of (hyper-)spherical distributions

MLE of (hyper-)spherical distributions
MLE of the Kent distribution

MLe of the Kent 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
MLE of the Matrix Fisher distribution on SO(3)

MLE of the Matrix Fisher distribution on SO(3)
Habeck's rotation matrix generation

Generation of three-dimensional random rotations using Habeck's algorithm.
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
Test for a given mean direction

Test for a given mean direction
Simulation from a Bingham distribution using any symmetric matrix A

Simulation from a Bingham distribution using any symmetric matrix A
Euler angles from a rotation matrix on SO(3)

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

MLE of some circular distributions
Random sample of matrices in SO(p)

Random sample of matrices in SO(p)
Rayleigh's test of uniformity

Rayleigh's test of uniformity
Haversine distance matrix

Harvesine distance matrix
Rotation matrix from a rotation axis and angle of rotation

Rotation matrix from a rotation axis and angle of rotation
Circular or angular regression

Circular or angular regression
Simulation of random values from rotationally symmetric distributions

Simulation of random values from rotationally symmetric distributions
Uniformity test for circular data

Uniformity tests for circular data.
Interactive 3D plot of spherical data

Interactive 3D plot of spherical data
von Mises-Fisher kernel density estimation for (hyper-)spherical data

Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel
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
Normalised spatial median for directional data

Normalised spatial median for directional data
Lambert's equal area projection

Lambert's equal area projection
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
Converting a rotation matrix on SO(3) to an unsigned unit quaternion

Converting a rotation matrix on SO(3) to an unsigned unit quaternion
Maps of the world and the continents

maps of the world and the continents
Summary statistics for grouped circular data

Summary statistics for grouped circular data
Rotation matrix to rotate a spherical vector along the direction of another

Rotation matrix to rotate a spherical vector along the direction of another
Tuning of the bandwidth parameter in the von Mises kernel

Tuning of the bandwidth parameter in the von Mises kernel for circular data
Generation of unit vector(s) with a given angle

Generation of unit vector(s) with a given angle
Contour plot of the Kent distribution for some data

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

Contour plot of the Kent distribution without any data
Spherical-spherical regression

Spherical-Spherical regression
Test for equality of concentration parameters for spherical data

Test for equality of concentration parameters for spherical data
Simulation of random values from a spherical Fisher-Bingham distribution

Simulation of random values from a spherical Fisher-Bingham distribution
Contour plots of the von Mises-Fisher distribution

Contour plots of the von Mises-Fisher distribution on the sphere
Simulation of random values from a spherical Kent distribution

Simulation of random values from a spherical Kent distribution
Check visually whether matrix Fisher samples is correctly generated or not

Check visually whether matrix Fisher samples is correctly generated or not.
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