8.4 Perseguição da Projeção

The term “projection pursuit” was first used by (J. H. Friedman and Tukey 1974) to name a technique for the exploratory analysis of reasonably large and reasonably multivariate data sets; projection pursuit reveals structure in the original data by offering selected low-dimensional orthogonal projections of it for inspection. (Jones and Sibson 1987)

(Kotz and Nadarajah 2004)

bustandthat indicesbasedonL2-divergencesarealsothemostrobustintheirclas

“(Nason 2001) found the Student’s indices are general ymore robust and that indices based on L2-divergences are also the most rob”

(Nason 2006)

A biblioteca NORMT3 de Guy P. Nason, dentre outras funcionalidades, avalia as densidades de t de Student esféricas, bem como da soma de distribuições gaussianas e t de Student.

(Ossani and Cirillo 2021)

An Package for projection pursuit (PP) with 17 methods and Grand Tour (Asimov 1985) with 3 methods. Being that projection pursuit searches for low-dimensional linear projections in highdimensional data structures, while grand tour is a technique used to explore multivariate statistical data through animation.

citation('Pursuit')

## To cite package 'Pursuit' in publications use:
## 
##   Ossani P, Cirillo M (2024). _Pursuit: Projection Pursuit_. R package version 1.0.5,
##   <https://CRAN.R-project.org/package=Pursuit>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {Pursuit: Projection Pursuit},
##     author = {Paulo Cesar Ossani and Marcelo Angelo Cirillo},
##     year = {2024},
##     note = {R package version 1.0.5},
##     url = {https://CRAN.R-project.org/package=Pursuit},
##   }

library(Pursuit)
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

(Lee 2018)

citation('PPtreeViz')

## To cite PPtreeViz in publications use:
## 
##   Lee E (2018). "PPtreeViz: An R Package for Visualizing Projection Pursuit Classification
##   Trees." _Journal of Statistical Software_, *83*(8), 1-30. doi:10.18637/jss.v083.i08
##   <https://doi.org/10.18637/jss.v083.i08>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     title = {{PPtreeViz}: An {R} Package for Visualizing Projection Pursuit Classification Trees},
##     author = {Eun-Kyung Lee},
##     journal = {Journal of Statistical Software},
##     year = {2018},
##     volume = {83},
##     number = {8},
##     pages = {1--30},
##     doi = {10.18637/jss.v083.i08},
##   }

Exercício 8.4 Veja a documentação de
a. Pursuit.
b. PPtreeViz.

References

Asimov, Daniel. 1985. “The Grand Tour: A Tool for Viewing Multidimensional Data.” SIAM Journal on Scientific and Statistical Computing 6 (1): 128–43. https://doi.org/10.1137/0906011.

Friedman, Jerome H, and John W Tukey. 1974. “A Projection Pursuit Algorithm for Exploratory Data Analysis.” IEEE Transactions on Computers 100 (9): 881–90. https://ieeexplore.ieee.org/document/1672644/.

Jones, M Chris, and Robin Sibson. 1987. “What Is Projection Pursuit?” Journal of the Royal Statistical Society: Series A (General) 150 (1): 1–18. https://doi.org/10.2307/2981662.

Kotz, Samuel, and Saralees Nadarajah. 2004. Multivariate t-Distributions and Their Applications. Cambridge University Press. https://doi.org/10.1017/CBO9780511550683.

Lee, Eun-Kyung. 2018. “PPtreeViz: An R Package for Visualizing Projection Pursuit Classification Trees.” Journal of Statistical Software 83 (8): 1–30. https://doi.org/10.18637/jss.v083.i08.

Nason, Guy P. 2001. “Robust Projection Indices.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (3): 551–67. https://www.jstor.org/stable/2680588.

———. 2006. “On the Sum of t and Gaussian Random Variables.” Statistics & Probability Letters 76 (12): 1280–86. https://doi.org/10.1016/j.spl.2006.01.006.

Ossani, Paulo Cesar, and Marcelo Angelo Cirillo. 2021. Projection Pursuit. https://CRAN.R-project.org/package=Pursuit.