fda.usc reference card

Index

1. Functional Data Representation

2. Functional Regresion Models

3. Functional Supervised Classification

4. Functional Non-Supervised Classification

5. Functional Analysis of Variance

Functional Data Representation

fdata class objects

1. Basic operations:

• Group Math: abs, sqrt, floor, ceiling, trunc, round, signif, exp, log, cos, sin, tan.
  
• Group Summary: all, any, sum, prod, min, max, range.
• Other operations: [], is.fdata, c, dim, ncol, nrow.

2. Some utilities

• The new class fdata only uses the evaluations at the discretization points and converts object of class: fd, fds, fts, sfts, vector, matrix, data.frame to an object of class fdata.
• The fdata2fd converts fdata object to fd object (using the basis representation).
• Derivatives: fdata.deriv
• Plot: plot.fdata

Resume by smoothing: min.basis, min.np

• Create smooth fixed basis: create.fdata.basis
• Create smooth Data-driven basis: create.pc.basis, create.pls.basis
  

• Create Smooth Matrix: S.NW, S.KNN, S.basis

• Validation Criteria: Cross Validation: CV.S and Generalzed Cross Validation: GCV.S

Computing distances

1. Distance between functional elements:

• Measures the proximity between curves approximating Lp-metric: metric.lp
• based on the Principal Components semimetric.pca
• based on the Partial Least Squares: semimetric.mplsr
  
• based on B-spline representation: semimetric.deriv
• measure the horizontal shift effect: semimetric.hshift
• based on ther Fourier representation: semimetric.fourier
• based on fixed basis representation: semimetric.basis
• Kullback-Leibler distance: metrip.kl
• Hausdorff distances between two curves: metric.hausdorff

2. Norm: norm.fdata
3. Inner product: inprod.fdata

Depth measures

1. Depth for univariate or multivariate data

• Mahalanobis Depth (Mean) mdepth.MhD
• Halfspace Depth, also known as Tukey Depth (Median) mdepth.HS
• Simplicial Depth mdepth.SD
• Likelihood Depth (Mode) mdepth.LD

2. Depth for univariate functional data

• Fraiman-Muniz Depth depth.FM
• Random Projections depth.RP
• Modal depth depth.mode

3. Depth for multivariate functional data

• Fraiman-Muniz Depth depth.FMp
• Random Projections depth.RPp
• Modal depth depth.modep

Outlier Detection

1. Detecting outliers one based on trimming: outliers.depth.trim

2. Detecting outliers one based on weighting: outliers.depth.pond

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Functional Regression Model

1. Linear (parametric approach):

• FRM with basis representation with a functional covariate: fregre.basis
• Functional PC with a functional covariate: fregre.pc
• Functional PLS with a functional covariate: fregre.pls
• Functional LM with more than one functional and non–functional covariate: fregre.lm

2. Non-Linear (nonparametric approach)

• Nonparametric (NP) functional regression via kernel smoothing with a functional covariate: fregre.np
• Semi-partial linear model (PLM) with a functional and nonfunctional covariate: fregre.plm

3. Generalized approach

• Generalized Functional Linear Model (GFLM): fregre.glm
• Generalized Functional Spectral Additive Model (GFSAM): fregre.gsam
• Generalized Functional Kernel Additive Model (GFKAM): fregre.gkam

4. Other procedures

• Penalized versions and parameter selection: fregre.pc.cv, fregre.basis, fregre.np.cv
• F-test for the FLM with scalar response: flm.Ftest, F-test
• Goodness-of-fit test for the FLM with scalar response: flm.test
• Measures of influence in FLM with scalar response: influence.fdata
• Beta parameter estimation by wild or smoothed bootstrap procedure: fregre.bootstrap
• FLM with a functional response: fregre.basis.fr

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Functional Supervised Classification: Discrimination

1. k-Nearest Neighbor Classifier: classif.knn
2. Kernel Classifier: classif.kernel
3. Logistic Classifier (linear model): classif.glm
4. Logistic Classifier (additive model): classif.gsam and classif.gkam
5. Distance Classifier: classif.dist
6. Maximum Depth Classifier: classif.depth
7. DD Classifier: classif.DD

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Functional Non-Supervised Classification: Clustering

• Functional k–means: kmeans.fd

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Functional Analysis of variance: FANOVA

1. One-way anova model for functional data: anova.onefactor
2. Functional ANOVA with Random Project: anova.RPm
3. ANOVA for heteroscedastic data: anova.hetero

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Documentation

RPubs documents

1. fda.usc vignette: Installation and Descriptive Statistics

2. fda.usc vignette:Functional Regression

3. fda.usc vignette: Functional Classification and ANOVA

4. fda.usc reference card Rcard

Links:

1. fda.usc R package

2. JSS paper

3. fda.usc R Manual

4. Manuel Oviedo's website

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