Package: Directional 6.9

Michail Tsagris

Directional: A Collection of Functions for Directional Data Analysis

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. <doi:10.1007/s11222-017-9756-4>. 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. <doi:10.1080/23737484.2019.1684854>. 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. <doi:10.1007/s11222-019-09872-2>. 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. <doi:10.1080/03610918.2022.2045499>. e) 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. <doi:10.1214/23-EJS2210>. f) Tsagris M. and Alzeley O. (2024). "Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling". <doi:10.48550/arXiv.2302.02468>. g) Tsagris M. and Papastamoulis P. (2024). "Directional data analysis using the spherical Cauchy and the Poisson kernel-based distribution". <doi:10.48550/arXiv.2409.03292>.

Authors:Michail Tsagris [aut, cre], Giorgos Athineou [aut], Christos Adam [aut], Zehao Yu [aut], Anamul Sajib [ctb], Eli Amson [ctb], Micah J. Waldstein [ctb], Panagiotis Papastamoulis [ctb]

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# Install 'Directional' in R:

install.packages('Directional', repos = c('https://cran.r-universe.dev', 'https://cloud.r-project.org'))

This package does not link to any Github/Gitlab/R-forge repository. No issue tracker or development information is available.

4.93 score 3 stars 3 packages 127 scripts 1.0k downloads 4 mentions 234 exports 93 dependencies

Last updated 25 days agofrom:b4adf5b2ec. Checks:OK: 2. Indexed: yes.

Target	Result	Date
Doc / Vignettes	OK	Oct 30 2024
R-4.5-linux	OK	Oct 30 2024

Exports:acg.mle africa Arotation asia bic.mixpkbd bic.mixspcauchy bic.mixvmf cardio.mle cipc.mle cipc.reg circ.cor1 circ.cor2 circ.cors1 circ.cors2 circ.dcor circ.summary circbeta.mle circexp.mle circlin.cor circpurka.reg colspml.mle colvm.mle colwatsons conc.test cosap cosnn dcardio dcipc dcircbeta dcircexp dcircpurka desag dESAGd dgcpc dggvm dirda dirda.cv dirknn dirknn.tune dkent dmixpkbd dmixspcauchy dmixvmf dmmvm dpkbd dpurka dsespc dspcauchy dspml dvm dvmf dwood dwrapcauchy embed.aov embed.boot embed.circaov embed.perm embedcirc.boot embedcirc.perm esag.contour esag.mle esag.reg ESAGd.mle etoa euclid euclid.inv eul2rot europe f.rbing fb.saddle fishkent gcpc.mle gcpc.reg ggvm.mle group.gof group.vm habeck.rot haversine.dist hcf.aov hcf.boot hcf.circaov hcf.perm hcfboot hcfcirc.boot hcfcirc.perm hcfcircboot hclr.aov hclr.boot hclr.circaov hclr.perm hclrcirc.boot hclrcirc.perm het.aov het.boot het.circaov het.perm hetboot hetcirc.boot hetcirc.perm hetcircboot iag.mle iag.reg iagd iagesag kent.contour kent.logcon kent.mle knn.reg knnreg.tune kuiper lambert lambert.inv lr.aov lr.boot lr.circaov lr.perm lrcirc.boot lrcirc.perm makefolds matrixfisher.mle meandir.test mediandir mediandir_2 mixpkbd.mle mixspcauchy.mle mixvmf.contour mixvmf.mle mmvm.mle multispml.mle multivm.mle multivmf.mle north.america nsmedian oceania pc.test pcardio pcipc pcircbeta pcircexp pcircpurka pgcpc pk2 pkbd.contour pkbd.mle pkbd.mle2 pkbd.reg pkbd.reg2 pkbd2test pmmvm pspml ptest purka.contour purka.mle pvm pwrapcauchy quat2rot racg rayleigh rbingham rcipc rcircbeta rcircexp rcircpurka read.fbm resag rESAGd rfb rgcpc riag rkent rmatrixfisher rmixpkbd rmixspcauchy rmixvmf rot.matrix rot2eul rot2quat rotation rpkbd rsespc rsop rspcauchy rspml rvmf rvonmises rwrapcauchy sespc.mle sespc.reg sipc.mle sipc.reg south.america sp2 spcauchy.contour spcauchy.mle spcauchy.mle2 spcauchy.reg spcauchy2test spher.cor spher.dcor spher.esag.contour spher.kent.contour spher.mixvmf.contour spher.pkbd.contour spher.purka.contour spher.reg spher.sespc.contour spher.spcauchy.contour spher.vmf.contour spherconc.test sphereplot spml.fbed spml.mle spml.nb spml.reg spml.regs spmlnb.pred tang.conc vec visual.check vm.kde vm.nb vmf.contour vmf.kde vmf.kerncontour vmf.mle vmf.reg vmfkde.tune vmfreg vmkde.tune vmnb.pred watson wood.mle worldmap wrapcauchy.mle

Dependencies:askpass base64enc bigassertr bigparallelr bigstatsr bit bslib cachem class classInt cli codetools colorspace cowplot curl DBI digest doParallel e1071 evaluate fansi farver fastmap ff flock fontawesome foreach fs ggplot2 glue gtable highr htmltools htmlwidgets httr isoband iterators jquerylib jsonlite KernSmooth knitr labeling lattice lifecycle magrittr MASS Matrix memoise mgcv mime munsell nlme openssl parallelly pillar pkgconfig proxy ps R6 rappdirs RColorBrewer Rcpp RcppArmadillo RcppEigen RcppGSL RcppParallel RcppZiggurat Rfast Rfast2 rgl RhpcBLASctl rlang rmarkdown rmio Rnanoflann rnaturalearth RSpectra s2 sass scales sf sys terra tibble tinytex units utf8 vctrs viridisLite withr wk xfun yaml

Help page	Topics
This is an R package that provides methods for the statistical analysis of directional data, including massive (very large scale) directional data.	Directional-package
(Hyper-)spherical regression using the rotational symmetric distributions	pkbd.reg pkbd.reg2 spcauchy.reg vmfreg
A test for testing the equality of the concentration parameter among g samples, where g >= 2 for ciruclar data	tang.conc
Angular central Gaussian random values simulation	racg
Analysis of variance for (hyper-)spherical data	embed.aov hcf.aov hclr.aov het.aov lr.aov
Analysis of variance for circular data	embed.circaov hcf.circaov hclr.circaov het.circaov lr.circaov
BIC to choose the number of components in a model based clustering using mixtures of rotationally symmetric distributions	bic.mixpkbd bic.mixspcauchy bic.mixvmf
Bootstrap 2-sample mean test for (hyper-)spherical data	embed.boot hcf.boot hclr.boot het.boot lr.boot
Bootstrap 2-sample mean test for circular data	embedcirc.boot hcfcirc.boot hclrcirc.boot hetcirc.boot lrcirc.boot
Bootstrap ANOVA for (hyper-)spherical data	hcfboot hetboot
Bootstrap ANOVA for circular data	hcfcircboot hetcircboot
Check visually whether matrix Fisher samples is correctly generated or not.	visual.check
Circular correlations between two circular variables	circ.cors1 circ.cors2
Circular correlations between two circular variables	circ.cor1 circ.cor2
Circular distance correlation between two circular variables	circ.dcor
Circular or angular regression	cipc.reg circpurka.reg gcpc.reg spml.reg
Circular-linear correlation	circlin.cor
Column-wise MLE of the angular Gaussian and the von Mises Fisher distributions	colspml.mle colvm.mle
Column-wise uniformity tests for circular data	colwatsons
Contour plot (on the plane) of the ESAG and Kent and ESAG distributions without any data	esag.contour kent.contour
Contour plot (on the sphere) of a mixture of von Mises-Fisher distributions	spher.mixvmf.contour
Contour plot (on the sphere) of some spherical rotationally symmetric distributions	spher.pkbd.contour spher.purka.contour spher.spcauchy.contour spher.vmf.contour
Contour plot (on the sphere) of the ESAG and Kent distributions	spher.esag.contour spher.kent.contour
Contour plot (on the sphere) of the SESPC distribution	spher.sespc.contour
Contour plot of a mixture of von Mises-Fisher distributions model for spherical data only.	mixvmf.contour
Contour plot of spherical data using a von Mises-Fisher kernel density estimate	vmf.kerncontour
Contour plots of some rotationally symmetric distributions	pkbd.contour purka.contour spcauchy.contour vmf.contour
Conversion of cosines to azimuth and plunge	cosap
Converting a rotation matrix on SO(3) to an unsigned unit quaternion	rot2quat
Converting an unsigned unit quaternion to rotation matrix on SO(3)	quat2rot
Cross validation for estimating the classification rate	dirda.cv
Cumulative distribution function of circular distributions	pcardio pcipc pcircbeta pcircexp pcircpurka pgcpc pmmvm pspml pvm pwrapcauchy
Density of a mixture of rotationally symmetric distributions	dmixpkbd dmixspcauchy dmixvmf
Density of some (hyper-)spherical distributions	dpkbd dpurka dspcauchy dvmf iagd
Density of some circular distributions	dcardio dcipc dcircbeta dcircexp dcircpurka dgcpc dggvm dmmvm dspml dvm dwrapcauchy
Density of the SESPC distribution	dsespc
Density of the spherical ESAG and Kent distributions	desag dESAGd dkent
Density of the Wood bimodal distribution on the sphere	dwood
Euclidean transformation	euclid
Compute the Euler angles from a rotation matrix on SO(3).	rot2eul
Forward Backward Early Dropping selection for circular data using the SPML regression	spml.fbed
Generate random folds for cross-validation	makefolds
Generation of unit vector(s) with a given angle	vec
Goodness of fit test for grouped data	group.gof
Generation of three-dimensional random rotations using Habeck's algorithm.	habeck.rot
Harvesine distance matrix	haversine.dist
Hypothesis test for IAG distribution over the ESAG distribution	iagesag
Hypothesis test for SIPC distribution over the SESPC distribution	pc.test
Hypothesis test for von Mises-Fisher distribution over Kent distribution	fishkent
Interactive 3D plot of spherical data	sphereplot
Inverse of Lambert's equal area projection	lambert.inv
Inverse of the Euclidean transformation	euclid.inv
k-NN algorithm using the arc cosinus distance	dirknn
k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables	knn.reg
Lambert's equal area projection	lambert
Logarithm of the Kent distribution normalizing constant	kent.logcon
Many simple circular or angular regressions	spml.regs
maps of the world and the continents	africa asia europe north.america oceania south.america worldmap
Mixtures of rotationally symmetric distributions	mixpkbd.mle mixspcauchy.mle mixvmf.mle
MLE of (hyper-)spherical rotationally symmetric distributions	acg.mle iag.mle multivmf.mle pkbd.mle pkbd.mle2 sipc.mle spcauchy.mle spcauchy.mle2 vmf.mle
MLE of some circular distributions	cardio.mle cipc.mle circbeta.mle circexp.mle gcpc.mle ggvm.mle mmvm.mle spml.mle wrapcauchy.mle
MLE of some circular distributions with multiple samples	multispml.mle multivm.mle
MLE of the ESAG distribution	esag.mle ESAGd.mle
MLe of the Kent distribution	kent.mle
MLE of the Matrix Fisher distribution on SO(3)	matrixfisher.mle
MLE of the Purkayashta distribution	purka.mle
MLE of the SESPC distribution	sespc.mle
MLE of the Wood bimodal distribution on the sphere	wood.mle
Naive Bayes classifiers for directional data	spml.nb vm.nb
Normalised spatial median for directional data	nsmedian
Permutation based 2-sample mean test for (hyper-)spherical data	embed.perm hcf.perm hclr.perm het.perm lr.perm
Permutation based 2-sample mean test for circular data	embedcirc.perm hcfcirc.perm hclrcirc.perm hetcirc.perm lrcirc.perm
Prediction of a new observation using discriminant analysis based on some distributions	dirda
Prediction with some naive Bayes classifiers for circular data	spmlnb.pred vmnb.pred
Projections based test of uniformity	ptest
Random sample of matrices in SO(p)	rsop
Rayleigh's test of uniformity	rayleigh
Read a file as a Filebacked Big Matrix	read.fbm
Rotation axis and angle of rotation given a rotation matrix	Arotation
Rotation matrix from a rotation axis and angle of rotation	rot.matrix
Construct a rotation matrix on SO(3) from the Euler angles.	eul2rot
Rotation matrix to rotate a spherical vector along the direction of another	rotation
Saddlepoint approximations of the Fisher-Bingham distributions	fb.saddle
Simulation from a Bingham distribution using any symmetric matrix A	rbingham
Simulation from a Matrix Fisher distribution on SO(3)	rmatrixfisher
Simulating from a Bingham distribution	f.rbing
Simulation of random values from a mixture of rotationally symmetric distributions	rmixpkbd rmixspcauchy rmixvmf
Simulation of random values from a spherical Fisher-Bingham distribution	rfb
Simulation of random values from a spherical Kent distribution	rkent
Simulation of random values from rotationally symmetric distributions	riag rpkbd rspcauchy rvmf
Simulation of random values from some circular distributions	rcipc rcircbeta rcircexp rcircpurka rgcpc rspml rvonmises rwrapcauchy
Simulation of random values from the ESAG distribution	resag rESAGd
Simulation of random values from the SESPC distribution	rsespc
Spherical and hyper-spherical distance correlation	spher.dcor
Fast calculation of the spherical and hyperspherical median	mediandir mediandir_2
Spherical regression using rotationally symmetric distributions	iag.reg sipc.reg vmf.reg
Spherical regression using the ESAG distribution	esag.reg
Spherical regression using the SESPC distribution	sespc.reg
Spherical-spherical correlation	spher.cor
Spherical-Spherical regression	spher.reg
Summary statistics for circular data	circ.summary
Summary statistics for grouped circular data	group.vm
Test for a given mean direction	meandir.test
Test for equality of concentration parameters for spherical data	spherconc.test
A test for testing the equality of the concentration parameter among g samples, where g >= 2 for ciruclar data	conc.test
The k-nearest neighbours using the cosinus distance	cosnn
Transform unit vectors to angular data	etoa
Tuning of the bandwidth parameter in the von Mises kernel for circular data	vmkde.tune
Tuning of the bandwidth parameter in the von Mises-Fisher kernel for (hyper-)spherical data	vmfkde.tune
k-NN algorithm using the arc cosinus distance. Tuning the k neigbours	dirknn.tune
Tuning of the k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables	knnreg.tune
Two sample location test for (hyper-)spherical data	pk2 pkbd2test sp2 spcauchy2test
Uniformity tests for circular data.	kuiper watson
Kernel density estimation of circular data with a von Mises kernel	vm.kde
Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel	vmf.kde

Package: Directional 6.9

Directional: A Collection of Functions for Directional Data Analysis

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