Help for package Pursuit

Type:

Package

Title:

Projection Pursuit

Version:

1.0.9

Date:

2025-04-19

Imports:

graphics, grDevices, MASS, stats

Description:

Projection pursuit (PP) with 17 methods and grand tour with 3 methods. Being that projection pursuit searches for low-dimensional linear projections in high-dimensional data structures, while grand tour is a technique used to explore multivariate statistical data through animation.

License:

GPL-3

Encoding:

UTF-8

NeedsCompilation:

yes

Author:

Paulo Cesar Ossani

[aut, cre], Marcelo Angelo Cirillo

[aut]

Maintainer:

Paulo Cesar Ossani <ossanipc@hotmail.com>

Repository:

CRAN

Packaged:

2025-04-18 18:39:27 UTC; Ossan

Date/Publication:

2025-04-18 19:10:11 UTC

Animation technique Grand Tour.

Description

Performs the exploration of the data through the technique of animation Grand Tour.

Usage

GrandTour(data, method = "Interpolation", title = NA, xlabel = NA, 
          ylabel = NA, size = 1.1, grid = TRUE, color = TRUE, linlab = NA, 
          class = NA, classcolor = NA, posleg = 2, boxleg = TRUE,  
          axesvar = TRUE, axes = TRUE, numrot = 200, choicerot = NA, 
          savptc = FALSE, width = 3236, height = 2000, res = 300)

Arguments

data

Numerical data set.

method

Method used for rotations:
"Interpolation" - Interpolation method (default),
"Torus" - Torus method,
"Pseudo" - Pseudo Grand Tour method.

title

Titles of the graphics, if not set, assumes the default text.

xlabel

Names the X axis, if not set, assumes the default text.

ylabel

Names the Y axis, if not set, assumes the default text.

size

Size of the points in the graphs.

grid

Put grid on graphs (default = TRUE).

color

Colored graphics (default = TRUE).

linlab

Vector with the labels for the observations.

class

Vector with names of data classes.

classcolor

Vector with the colors of the classes.

posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.

boxleg

Puts the frame in the caption (default = TRUE).

axesvar

Puts axes of rotation of the variables (default = TRUE).

axes

Plots the X and Y axes (default = TRUE).

numrot

Number of rotations (default = 200). If method = "Interpolation", numrot represents the angle of rotation.

choicerot

Choose specific rotation and display on the screen, or save the image if savptc = TRUE.

savptc

Saves graphics images to files (default = FALSE).

width

Graphics images width when savptc = TRUE (defaul = 3236).

height

Graphics images height when savptc = TRUE (default = 2000).

res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).

Value

Graphs with rotations.

proj.data

Projected data.

vector.opt

Vector projection.

method

method used on Grand Tour.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

ASIMOV, D. The Grand Tour: A Tool for Viewing Multidimensional data. SIAM Journal of Scientific and Statistical Computing, 6(1), 128-143, 1985.

ASIMOV, D.; BUJA, A. The grand tour via geodesic interpolation of 2-frames. in Visual data Exploration and Analysis. Symposium on Electronic Imaging Science and Technology, IS&T/SPIE. 1994.

BUJA, A. ; ASIMOV, D. Grand tour methods: An outline. Computer Science and Statistics, 17:63-67. 1986.

BUJA, A.; COOK, D.; ASIMOV, D.; HURLEY, C. Computational methods for High-Dimensional Rotations in data Visualization, in C. R. Rao, E. J. Wegman & J. L. Solka, eds, "Handbook of Statistics: data Mining and Visualization", Elsevier/North Holland, http://www.elsevier.com, pp. 391-413. 2005.

HURLEY, C.; BUJA, A. Analyzing high-dimensional data with motion graphics, SIAM Journal of Scientific and Statistical Computing, 11 (6), 1193-1211. 1990.

MARTINEZ, W. L., MARTINEZ, A. R., SOLKA, J.; Exploratory data Analysis with MATLAB, 2th. ed. New York: Chapman & Hall/CRC, 2010. 499 p.

YOUNG, F. W.; RHEINGANS P. Visualizing structure in high-dimensional multivariate data, IBM Journal of Research and Development, 35:97-107, 1991.

YOUNG, F. W.; FALDOWSKI R. A.; McFARLANE M. M. Multivariate statistical visualization, in Handbook of Statistics, Vol 9, C. R. Rao (ed.), The Netherlands: Elsevier Science Publishers, 959-998, 1993.

Examples

data(iris) # database

res <- GrandTour(iris[,1:4], method = "Torus", title = NA, xlabel = NA, ylabel = NA,
                 color = TRUE, linlab = NA, class = NA, posleg = 2, boxleg = TRUE, 
                 axesvar = TRUE, axes = FALSE, numrot = 10, choicerot = NA,
                 savptc = FALSE, width = 3236, height = 2000, res = 300)

print("Projected data:"); res$proj.data
print("Projection vectors:"); res$vector.opt
print("Grand Tour projection method:"); res$method

        
res <- GrandTour(iris[,1:4], method = "Interpolation", title = NA, xlabel = NA, ylabel = NA,
                 color = TRUE, linlab = NA, posleg = 2, boxleg = FALSE, axesvar = FALSE, 
                 axes = FALSE, numrot = 10, choicerot = NA, class = iris[,5],
                 classcolor = c("goldenrod3","gray53","red"),savptc = FALSE, 
                 width = 3236, height = 2000, res = 300)
         
print("Projected data:"); res$proj.data
print("Projection vectors:"); res$vector.opt
print("Grand Tour projection method:"); res$method

Function for better position of the labels in the graphs.

Description

Function for better position of the labels in the graphs.

Usage

LocLab(x, y = NULL, labels = seq(along = x), cex = 1,
       method = c("SANN", "GA"), allowSmallOverlap = FALSE,
       trace = FALSE, shadotext = FALSE, 
       doPlot = TRUE, ...)

Arguments

x

Coordinate x

y

Coordinate y

labels

The labels

cex

cex

method

Not used

allowSmallOverlap

Boolean

trace

Boolean

shadotext

Boolean

doPlot

Boolean

...

Other arguments passed to or from other methods

Value

See the text of the function.

Function to find the Projection Pursuit indexes (PP).

Description

Function used to find Projection Pursuit indexes (PP).

Usage

PP_Index(data, class = NA, vector.proj = NA, 
         findex = "HOLES", dimproj = 2, weight = TRUE, 
         lambda = 0.1, r = 1, ck = NA)

Arguments

data

Numeric dataset without class information.

class

Vector with names of data classes.

vector.proj

Vector projection.

findex

Projection index function to be used:
"lda" - LDA index,
"pda" - PDA index,
"lr" - Lr index,
"holes" - Holes index (default),
"cm" - Central Mass index,
"pca" - PCA index,
"friedmantukey" - Friedman Tukey index,
"entropy" - Entropy index,
"legendre" - Legendre index,
"laguerrefourier" - Laguerre Fourier index,
"hermite" - Hermite index,
"naturalhermite" - Natural Hermite index,
"kurtosismax" - Maximum kurtosis index,
"kurtosismin" - Minimum kurtosis index,
"moment" - Moment index,
"mf" - MF index,
"chi" - Chi-square index.

dimproj

Dimension of data projection (default = 2).

weight

Used in index LDA, PDA and Lr to weight the calculations for the number of elements in each class (default = TRUE).

lambda

Used in the PDA index (default = 0.1).

r

Used in the Lr index (default = 1).

ck

Internal use of the CHI index function.

Value

num.class

Number of classes.

class.names

Class names.

findex

Projection index function used.

vector.proj

Projection vectors found.

index

Projection index found in the process.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

OSSANI, P. C.; FIGUEIRA, M. R.; CIRILLO, M. A. Proposition of a new index for projection pursuit in the multiple factor analysis. Computational and Mathematical Methods, v. 1, p. 1-18, 2020.

COOK, D., BUJA, A., CABRERA, J.. Projection pursuit indexes based on orthonormal function expansions. Journal of Computational and Graphical Statistics, 2(3):225-250, 1993.

COOK, D., BUJA, A., CABRERA, J., HURLEY, C.. Grand tour and projection pursuit, Journal of Computational and Graphical Statistics, 4(3), 155-172, 1995.

COOK, D., SWAYNE, D. F.. Interactive and Dynamic Graphics for data Analysis: With R and GGobi. Springer. 2007.

ESPEZUA, S., VILLANUEVA, E., MACIEL, C.D., CARVALHO, A.. A projection pursuit framework for supervised dimension reduction of high dimensional small sample datasets. Neurocomputing, 149, 767-776, 2015.

FRIEDMAN, J. H., TUKEY, J. W. A projection pursuit algorithm for exploratory data analysis. IEEE Transaction on Computers, 23(9):881-890, 1974.

HASTIE, T., BUJA, A., TIBSHIRANI, R.: Penalized discriminant analysis. The Annals of Statistics. 23(1), 73-102 . 1995.

HUBER, P. J.. Projection pursuit. Annals of Statistics, 13(2):435-475, 1985.

JONES, M. C., SIBSON, R.. What is projection pursuit, (with discussion), Journal of the Royal Statistical Society, Series A 150, 1-36, 1987.

LEE, E. K., COOK, D.. A projection pursuit index for large p small n data. Statistics and Computing, 20(3):381-392, 2010.

LEE, E., COOK, D., KLINKE, S., LUMLEY, T.. Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics, 14(4):831-846, 2005.

MARTINEZ, W. L., MARTINEZ, A. R.; Computational Statistics Handbook with MATLAB, 2th. ed. New York: Chapman & Hall/CRC, 2007. 794 p.

MARTINEZ, W. L., MARTINEZ, A. R., SOLKA, J.; Exploratory data Analysis with MATLAB, 2th. ed. New York: Chapman & Hall/CRC, 2010. 499 p.

PENA, D., PRIETO, F.. Cluster identification using projections. Journal of the American Statistical Association, 96(456):1433-1445, 2001.

POSSE, C.. Projection pursuit exploratory data analysis, Computational Statistics and data Analysis, 29:669-687, 1995a.

POSSE, C.. Tools for two-dimensional exploratory projection pursuit, Journal of Computational and Graphical Statistics, 4:83-100, 1995b.

Examples

data(iris) # data set

data <- iris[,1:4]

# Example 1 - Without the classes in the data
ind <- PP_Index(data = data, class = NA, vector.proj = NA, 
                findex = "moment", dimproj = 2, weight = TRUE, 
                lambda = 0.1, r = 1)

print("Number of classes:"); ind$num.class
print("class Names:"); ind$class.names
print("Projection index function:"); ind$findex
print("Projection vectors:"); ind$vector.proj  
print("Projection index:"); ind$index


# Example 2 - With the classes in the data
class <- iris[,5] # data class

findex <- "pda" # index function

sphere <- TRUE # spherical data

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "SA", dimproj = 2, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 1000, half = 30)

# Comparing the result obtained
if (match(toupper(findex),c("LDA", "PDA", "LR"), nomatch = 0) > 0) {
  if (sphere) {
     data <- apply(predict(prcomp(data)), 2, scale) # spherical data
  }
} else data <- as.matrix(res$proj.data[,1:Dim])

ind <- PP_Index(data = data, class = class, vector.proj = res$vector.opt, 
                findex = findex, dimproj = 2, weight = TRUE, lambda = 0.1,
                r = 1)

print("Number of classes:"); ind$num.class
print("class Names:"); ind$class.names
print("Projection index function:"); ind$findex
print("Projection vectors:"); ind$vector.proj  
print("Projection index:"); ind$index
print("Optimized Projection index:"); res$index[length(res$index)]

Optimization function of the Projection Pursuit index (PP).

Description

Optimization function of the Projection Pursuit index (PP).

Usage

PP_Optimizer(data, class = NA, findex = "HOLES",   
             dimproj = 2, sphere = TRUE, optmethod = "GTSA",   
             weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9,  
             eps = 1e-3, maxiter = 3000, half = 30)

Arguments

data

Numeric dataset without class information.

class

Vector with names of data classes.

findex

dimproj

Dimension of the data projection (default = 2).

sphere

Spherical data (default = TRUE).

optmethod

Optimization method GTSA - Grand Tour Simulated Annealing or SA - Simulated Annealing (default = "GTSA").

weight

Used in index LDA, PDA and Lr to weight the calculations for the number of elements in each class (default = TRUE).

lambda

Used in the PDA index (default = 0.1).

r

Used in the Lr index (default = 1).

cooling

Cooling rate (default = 0.9).

eps

Approximation accuracy for cooling (default = 1e-3).

maxiter

Maximum number of iterations of the algorithm (default = 3000).

half

Number of steps without incrementing the index, then decreasing the cooling value (default = 30).

Value

num.class

Number of classes.

class.names

Class names.

proj.data

Projected data.

vector.opt

Projection vectors found.

index

Vector with the projection indices found in the process, converging to the maximum, or the minimum.

findex

Projection index function used.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

COOK, D., LEE, E. K., BUJA, A., WICKHAM, H.. Grand tours, projection pursuit guided tours and manual controls. In Chen, Chunhouh, Hardle, Wolfgang, Unwin, e Antony (Eds.), Handbook of data Visualization, Springer Handbooks of Computational Statistics, chapter III.2, p. 295-314. Springer, 2008.

LEE, E., COOK, D., KLINKE, S., LUMLEY, T.. Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics, 14(4):831-846, 2005.

Examples

data(iris) # data set

# Example 1 - Without the classes in the data
data <- iris[,1:4]

class <- NA # data class

findex <- "kurtosismax" # index function

dim <- 1 # dimension of data projection

sphere <- TRUE # spherical data

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 1000, half = 30)
 
print("Number of classes:"); res$num.class
print("class Names:"); res$class.names
print("Projection index function:"); res$findex
print("Projected data:"); res$proj.data
print("Projection vectors:"); res$vector.opt
print("Projection index:"); res$index


# Example 2 - With the classes in the data
class <- iris[,5] # classe dos dados

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 1000, half = 30)

print("Number of classes:"); res$num.class
print("class Names:"); res$class.names
print("Projection index function:"); res$findex
print("Projected data:"); res$proj.data
print("Projection vectors:"); res$vector.opt
print("Projection index:"); res$index

Graphics of the Projection Pursuit (PP).

Description

Graphics of the Projection Pursuit (PP).

Usage

Plot.PP(PP, titles = NA, xlabel = NA, ylabel = NA, posleg = 2, boxleg = TRUE,
        size = 1.1, grid = TRUE, color = TRUE, classcolor = NA, linlab = NA, 
        axesvar = TRUE, axes = TRUE, savptc = FALSE, width = 3236, height = 2000, 
        res = 300, casc = TRUE)

Arguments

PP

Data of the PP_Optimizer function.

titles

Titles of the graphics, if not set, assumes the default text.

xlabel

Names the X axis, if not set, assumes the default text.

ylabel

Names the Y axis, if not set, assumes the default text.

posleg

0 with no caption,
1 for caption in the left upper corner,
2 for caption in the right upper corner (default),
3 for caption in the right lower corner,
4 for caption in the left lower corner.

boxleg

Puts the frame in the caption (default = TRUE).

size

Size of the points in the graphs.

grid

Put grid on graphs (default = TRUE).

color

Colored graphics (default = TRUE).

classcolor

Vector with the colors of the classes.

linlab

Vector with the labels for the observations.

axesvar

Puts axes of rotation of the variables, only when dimproj > 1 (default = TRUE).

axes

Plots the X and Y axes (default = TRUE).

savptc

Saves graphics images to files (default = FALSE).

width

Graphics images width when savptc = TRUE (defaul = 3236).

height

Graphics images height when savptc = TRUE (default = 2000).

res

Nominal resolution in ppi of the graphics images when savptc = TRUE (default = 300).

casc

Cascade effect in the presentation of the graphics (default = TRUE).

Value

Graph of the evolution of the indices, and graphs whose data were reduced in two dimensions.

Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

Examples

data(iris) # dataset

# Example 1 - Without the classes in the data
data <- iris[,1:4]

findex <- "kurtosismax" # index function

dim <- 1 # dimension of data projection

sphere <- TRUE # spherical data

res <- PP_Optimizer(data = data, class = NA, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 500, half = 30)

Plot.PP(res, titles = NA, posleg = 1, boxleg = FALSE, color = TRUE,
        linlab = NA, axesvar = TRUE, axes = TRUE, savptc = FALSE, 
        width = 3236, height = 2000, res = 300, casc = FALSE)


# Example 2 - With the classes in the data
class <- iris[,5] # data class

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 500, half = 30)

tit <- c(NA,"Graph example") # titles for the graphics

Plot.PP(res, titles = tit, posleg = 1, boxleg = FALSE, color = TRUE, 
        classcolor = c("blue3","red","goldenrod3"), linlab = NA, 
        axesvar = TRUE, axes = TRUE, savptc = FALSE, width = 3236,
        height = 2000, res = 300, casc = FALSE)


# Example 3 - Without the classes in the data, but informing 
#             the classes in the plot function
res <- PP_Optimizer(data = data, class = NA, findex = "Moment",
                    optmethod = "GTSA", dimproj = 2, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 500, half = 30)

lin <- c(rep("a",50),rep("b",50),rep("c",50)) # data class

Plot.PP(res, titles = NA, posleg = 1, boxleg = FALSE, color = TRUE,
        linlab = lin, axesvar = TRUE, axes = TRUE, savptc = FALSE, 
        width = 3236, height = 2000, res = 300, casc = FALSE)


# Example 4 - With the classes in the data, but not informed in plot function
class <- iris[,5] # data class

dim <- 2 # dimension of data projection

findex <- "lda" # index function

res <- PP_Optimizer(data = data, class = class, findex = findex,
                    optmethod = "GTSA", dimproj = dim, sphere = sphere, 
                    weight = TRUE, lambda = 0.1, r = 1, cooling = 0.9, 
                    eps = 1e-3, maxiter = 500, half = 30)

tit <- c("",NA) # titles for the graphics

Plot.PP(res, titles = tit, posleg = 1, boxleg = FALSE, color = TRUE,
        linlab = NA, axesvar = TRUE, axes = TRUE, savptc = FALSE, 
        width = 3236, height = 2000, res = 300, casc = FALSE)

Projection Pursuit

Description

Details

Package:	Pursuit
Type:	Package
Version:	1.0.7
Date:	2025-04-19
License:	GPL(>= 2)
LazyLoad:	yes

Author(s)

Paulo Cesar Ossani and Marcelo Angelo Cirillo.

Maintainer: Paulo Cesar Ossani <ossanipc@hotmail.com>

References

ASIMOV, D. The Grand Tour: A Tool for Viewing Multidimensional Data. SIAM Journal of Scientific and Statistical Computing, 6(1), 128-143, 1985.

ASIMOV, D.; BUJA, A. The grand tour via geodesic interpolation of 2-frames. in Visual Data Exploration and Analysis. Symposium on Electronic Imaging Science and Technology, IS&T/SPIE. 1994.

BUJA, A.; ASIMOV, D. Grand tour methods: An outline. Computer Science and Statistics, 17:63-67. 1986.

BUJA, A.; COOK, D.; ASIMOV, D.; HURLEY, C. Computational Methods for High-Dimensional Rotations in Data Visualization, in C. R. Rao, E. J. Wegman & J. L. Solka, eds, "Handbook of Statistics: Data Mining and Visualization", Elsevier/North Holland, http://www.elsevier.com, pp. 391-413. 2005.

COOK, D., LEE, E. K., BUJA, A., WICKHAM, H.. Grand tours, projection pursuit guided tours and manual controls. In Chen, Chunhouh, Hardle, Wolfgang, Unwin, e Antony (Eds.), Handbook of Data Visualization, Springer Handbooks of Computational Statistics, chapter III.2, p. 295-314. Springer, 2008.

COOK, D., BUJA, A., CABRERA, J.. Projection pursuit indexes based on orthonormal function expansions. Journal of Computational and Graphical Statistics, 2(3):225-250, 1993.

COOK, D., BUJA, A., CABRERA, J., HURLEY, C.. Grand tour and projection pursuit, Journal of Computational and Graphical Statistics, 4(3), 155-172, 1995.

COOK, D., SWAYNE, D. F.. Interactive and Dynamic Graphics for Data Analysis: With R and GGobi. Springer. 2007.