Package index • fda.usc

Functional Data Analysis and Utilities for Statistical Computings

Routines for exploratory and descriptive analysis of functional data such as depth measurements, atypical curves detection, regression models, supervised classification, unsupervised classification and functional analysis of variance.

fda.usc-package fda.usc: Functional Data Analysis and Utilities for Statistical Computing (fda.usc)

fdata Creation

fdata(): Converts raw data or other functional data classes into fdata class.

Utilites for fdata class

fdata2fd(): Converts fdata class object into fd class object

fdata.bootstrap(): Bootstrap samples of a functional statistic

fdata.cen(): Functional data centred (subtract the mean of each discretization point)

fdata.deriv(): Computes the derivative of functional data object.

fdata S3 Methods

Math(<fdata>) Ops(<fdata>) Summary(<fdata>) split(<fdata>) order.fdata() is.fdata(): fdata S3 Group Generic Functions

Functional PCA and PLS

fdata2pc(): Principal components for functional data

fdata2pls(): Partial least squares components for functional data.

summary(<fdata.comp>): Correlation for functional data by Principal Component Analysis

Functional Descriptives

func.mean() func.var() func.trim.FM() func.trim.mode() func.trim.RP() func.trim.RT() func.trim.RPD() func.med.FM() func.med.mode() func.med.RP() func.med.RT() func.med.RPD() func.trimvar.FM() func.trimvar.mode() func.trimvar.RP() func.trimvar.RPD() func.trimvar.RT() func.mean.formula(): Descriptive measures for functional data.

Var.y(): Sampling Variance estimates

Create Functional Basis

create.fdata.basis() create.pc.basis() create.pls.basis() create.raw.fdata(): Create Basis Set for Functional Data of fdata class

fdata2basis() summary(<basis.fdata>): Compute fucntional coefficients from functional data represented in a base of functions

Functional Depth

depth.mode() depth.RP() depth.RPD() depth.RT() depth.KFSD() depth.FSD() depth.FM(): Computation of depth measures for functional data

Multivariate Depth

mdepth.LD() mdepth.HS() mdepth.RP() mdepth.MhD() mdepth.KFSD() mdepth.FSD() mdepth.FM() mdepth.TD() mdepth.SD(): Provides the depth measure for multivariate data

Multivariate Functional Depth

depth.modep() depth.RPp() depth.FMp(): Provides the depth measure for a list of p–functional data objects

Functional Smoothing

optim.basis(): Select the number of basis using GCV method.

optim.np(): Smoothing of functional data using nonparametric kernel estimation

S.basis(): Smoothing matrix with roughness penalties by basis representation.

S.LLR() S.LPR() S.LCR() S.KNN() S.NW(): Smoothing matrix by nonparametric methods

Distance Metrics (Functional Proximities)

metric.dist(): Distance Matrix Computation

metric.DTW() metric.WDTW() metric.TWED(): DTW: Dynamic time warping

metric.hausdorff(): Compute the Hausdorff distances between two curves.

metric.kl(): Kullback–Leibler distance

metric.ldata(): Distance Matrix Computation for ldata and mfdata class object

metric.lp(): Approximates Lp-metric distances for functional data.

semimetric.basis(): Proximities between functional data

semimetric.deriv() semimetric.fourier() semimetric.hshift() semimetric.mplsr() semimetric.pca(): Proximities between functional data (semi-metrics)

Functional Plotting

plot(<fdata>) lines(<fdata>) title.fdata() plot(<mdepth>) plot(<depth>) plot(<bifd>) plot(<lfdata>): Plot functional data: fdata class object

fdata NA Handling

na.omit(<fdata>) na.fail(<fdata>): A wrapper for the na.omit and na.fail function for fdata object

Data sets

aemet: aemet data

MCO: Mithochondiral calcium overload (MCO) data set

phoneme: phoneme data

poblenou: poblenou data

tecator: tecator data

Functional Outliers

outliers.depth.pond() outliers.depth.trim() outliers.lrt() outliers.thres.lrt(): outliers for functional dataset

Functional ANOVA

fanova.hetero(): ANOVA for heteroscedastic data

fanova.onefactor(): One–way anova model for functional data

fanova.RPm() summary(<fanova.RPm>): Functional ANOVA with Random Project.

Distance Correlation

dcor.xy() dcor.dist() bcdcor.dist() dcor.test(): Distance Correlation Statistic and t-Test

Functional Regression: scalar response and functional covariate

fregre.basis.cv(): Cross-validation Functional Regression with scalar response using basis representation.

fregre.basis(): Functional Regression with scalar response using basis representation.

fregre.bootstrap(): Bootstrap regression

fregre.np.cv(): Cross-validation functional regression with scalar response using kernel estimation.

fregre.np(): Functional regression with scalar response using non-parametric kernel estimation

fregre.pc.cv(): Functional penalized PC regression with scalar response using selection of number of PC components

fregre.pc(): Functional Regression with scalar response using Principal Components Analysis

fregre.pls.cv(): Functional penalized PLS regression with scalar response using selection of number of PLS components

fregre.pls(): Functional Penalized PLS regression with scalar response

Functional Regression: scalar response and functional covariates

fregre.gkam(): Fitting Functional Generalized Kernel Additive Models.

fregre.glm(): Fitting Functional Generalized Linear Models

fregre.gls(): Fit Functional Linear Model Using Generalized Least Squares

fregre.gsam(): Fitting Functional Generalized Spectral Additive Models

fregre.igls(): Fit of Functional Generalized Least Squares Model Iteratively

fregre.lm(): Fitting Functional Linear Models

fregre.plm(): Semi-functional partially linear model with scalar response.

Functional Regression: Variable Selection

fregre.glm.vs(): Variable Selection using Functional Linear Models

fregre.gsam.vs(): Variable Selection using Functional Additive Models

LMDC.select() LMDC.regre(): Impact points selection of functional predictor and regression using local maxima distance correlation (LMDC)

Functional Response Regression

fregre.basis.fr(): Functional Regression with functional response using basis representation.

False Discovery Rate

FDR() pvalue.FDR(): False Discorvery Rate (FDR)

DFV Test

dfv.statistic() dfv.test(): Delsol, Ferraty and Vieu test for no functional-scalar interaction

Functional Distribution Tests

XYRP.test() MMD.test() MMDA.test() fEqDistrib.test(): Tests for checking the equality of distributions between two functional populations.

Functional Mean and Covariance Tests

fmean.test.fdata() cov.test.fdata(): Tests for checking the equality of means and/or covariance between two populations under gaussianity.

Functional F-test, PCvM Statistic and Random Projections

Ftest.statistic() flm.Ftest(): F-test for the Functional Linear Model with scalar response

flm.test(): Goodness-of-fit test for the Functional Linear Model with scalar response

Adot() PCvM.statistic(): PCvM statistic for the Functional Linear Model with scalar response

rp.flm.statistic(): Statistics for testing the functional linear model using random projections

rp.flm.test(): Goodness-of fit test for the functional linear model using random projections

Functional Classification

classif.DD(): DD-Classifier Based on DD-plot

classif.depth(): Classifier from Functional Data

classif.gkam(): Classification Fitting Functional Generalized Kernel Additive Models

classif.glm(): Classification Fitting Functional Generalized Linear Models

classif.gsam(): Classification Fitting Functional Generalized Additive Models

classif.gsam.vs(): Variable Selection in Functional Data Classification

classif.kfold(): Functional Classification usign k-fold CV

classif.nnet() classif.rpart() classif.svm() classif.ksvm() classif.randomForest() classif.lda() classif.qda() classif.naiveBayes() classif.cv.glmnet() classif.gbm(): Functional classification using ML algotithms

classif.np() classif.knn() classif.kernel(): Kernel Classifier from Functional Data

Functional Prediction

predict(<classif.DD>): Predicts from a fitted classif.DD object.

predict(<classif>): Predicts from a fitted classif object.

predict(<fregre.fd>): Predict method for functional linear model (fregre.fd class)

predict(<fregre.fr>): Predict method for functional response model

predict(<fregre.gls>) predict(<fregre.igls>): Predictions from a functional gls object

predict(<fregre.gkam>) predict(<fregre.glm>) predict(<fregre.gsam>) predict(<fregre.lm>) predict(<fregre.plm>): Predict method for functional linear model

Classification and Regression Summary

summary(<classif>) print(<classif>): Summarizes information from kernel classification methods.

summary(<fregre.fd>): Summarizes information from fregre.fd objects.

summary(<fregre.gkam>): Summarizes information from fregre.gkam objects.

Functional Influence Measures

influence(<fregre.fd>): Functional influence measures

influence_quan(): Quantile for influence measures

Functional K-Means

kmeans.center.ini() kmeans.fd(): K-Means Clustering for functional data

Functional Inner Products and Norm

inprod.fdata(): Inner products of Functional Data Objects o class (fdata)

int.simpson() int.simpson2(): Simpson integration

norm.fdata() norm.fd(): Approximates Lp-norm for functional data.

Functional Data Generation and Random Directions

rcombfdata() gridfdata(): Utils for generate functional data

r.ou(): Ornstein-Uhlenbeck process

rdir.pc(): Data-driven sampling of random directions guided by sample of functional data

rproc2fdata(): Simulate several random processes.

rwild(): Wild bootstrap residuals

ldata and mfdata Class

mfdata() names(<mfdata>) subset(<mfdata>): mfdata class definition and utilities

ldata() names(<ldata>) is.ldata() `[`(<ldata>) subset(<ldata>) plot(<ldata>): ldata class definition and utilities

Performance measures

cat2meas() tab2meas() pred.MSE() pred.RMSE() pred.MAE() pred2meas(): Performance measures for regression and classification models

weights4class(): Weighting tools

fda.usc Internals

trace.matrix() argvals.equi() `+`(<fdata>) `-`(<fdata>) `*`(<fdata>) `/`(<fdata>) `[`(<fdata>) `!=`(<fdata>) `==`(<fdata>) `^`(<fdata>) dim(<fdata>) ncol.fdata() nrow.fdata() length(<fdata>) NROW.fdata() NCOL.fdata() rownames.fdata() colnames.fdata() c(<fdata>) argvals() rangeval() `[`(<fdist>) is.na(<fdata>) anyNA(<fdata>) count.na.fdata() unlist_fdata(): fda.usc internal functions

subset(<fdata>): Subsetting

fda.usc Options

ops.fda.usc(): ops.fda.usc Options Settings

Conditional Distribution, Mode and Quantile Functions

cond.F(): Conditional Distribution Function

cond.mode(): Conditional mode

cond.quantile(): Conditional quantile

Utilities

Other utilities and internal functions.

CV.S(): The cross-validation (CV) score

GCV.S(): The generalized correlated cross-validation (GCCV) score

GCCV.S(): The generalized correlated cross-validation (GCCV) score.

dev.S(): The deviance score

dis.cos.cor(): Proximities between functional data

h.default(): Calculation of the smoothing parameter (h) for a functional data

Kernel.asymmetric(): Asymmetric Smoothing Kernel

Kernel.integrate(): Integrate Smoothing Kernels.

Kernel(): Symmetric Smoothing Kernels.

P.penalty(): Penalty matrix for higher order differences