Type:	Package
Version:	0.1.0
Title:	Projection Pursuit Classification Tree Extensions
Maintainer:	Natalia da Silva <natalia.dasilva@fcea.edu.uy>
Description:	Implements extensions to the projection pursuit tree algorithm for supervised classification, see Lee, Y. (2013), <doi:10.1214/13-EJS810> and Lee, E-K. (2018) <doi:10.18637/jss.v083.i08>. The algorithm is changed in two ways: improving prediction boundaries by modifying the choice of split points-through class subsetting; and increasing flexibility by allowing multiple splits per group.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL:	https://github.com/natydasilva/PPtreeExt
LazyData:	yes
Depends:	R (≥ 4.3.0)
Imports:	Rcpp (≥ 1.1.0), ggplot2, shiny, MASS, gridExtra, MixSim, PPtreeViz
Suggests:	knitr, randomForest, rpart, GGally, RColorBrewer, roxygen2 (≥ 7.3.0), rmarkdown, rsample
Encoding:	UTF-8
LinkingTo:	Rcpp,RcppArmadillo
RoxygenNote:	7.3.3
NeedsCompilation:	yes
Packaged:	2026-02-03 16:44:46 UTC; nataliadasilva
Author:	Natalia da Silva [aut, cre], Dianne Cook [aut], Eun-Kyung Lee [aut]
Repository:	CRAN
Date/Publication:	2026-02-06 14:20:18 UTC

PP optimization using LDA index

Description

Projection Pursuit Optimization Using LDA Index

Usage

LDAopt_Ext(origclass, origdata, q = 1, weight = TRUE, ...)

Arguments

Details

Finds the q-dimensional optimal projection using the Linear Discriminant Analysis (LDA) projection pursuit index. This implementation follows the method described in PPtree.

The LDA projection pursuit index measures class separation by maximizing the ratio of between-class variance to within-class variance in the projected space. This function:

1. Calls LDAopt to find the optimal q-dimensional projection directions

2. Evaluates the LDA index for the optimal projection using LDAindex2

3. Returns both the projection matrix and its associated index value

When weight = TRUE, the index calculation accounts for class proportions, giving appropriate weight to each class in the optimization.

Value

An object of class "PPoptim", which is a list containing:

References

Lee, EK., Cook, D., Klinke, S., and Lumley, T. (2005) Projection Pursuit for Exploratory Supervised Classification, Journal of Computational and Graphical Statistics, 14(4):831-846.

See Also

PDAopt_Ext, findproj_Ext

NCI60 data set

Description

cDNA microarrays were used to examine the variation in gene expression among the 60 cell lines. The cell lines are derived from tumors with different sites of origin. This data set contain 61 observations and 30 feature variables from 8 different tissue types.

Type

has 8 different tissue types, 9 cases of breast, 5 cases of central nervous system (CNS), 7 cases pf colon, 8 cases of leukemia, 8 cases of melanoma, 9 cases of non-small-cell lung carcinoma (NSCLC), 6 cases of ovarian and 9 cases of renal.

Gene1 to Gen 30

gene expression information

Usage

data(NCI60)

Format

A data frame with 61 rows and 31 variables

Source

Dudoit, S., Fridlyand, J. and Speed, T. P. (2002). Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data. Journal of the American statistical Association 97 77-87.

PP optimization using PDA index

Description

Projection Pursuit Optimization Using PDA Index

Usage

PDAopt_Ext(origclass, origdata, q = 1, weight = TRUE, lambda = 0.1, ...)

Arguments

Details

Finds the q-dimensional optimal projection using the Penalized Discriminant Analysis (PDA) projection pursuit index. This implementation follows the method described in PPtree and is particularly useful for high-dimensional data (large p, small n).

The Penalized Discriminant Analysis (PDA) projection pursuit index extends LDA by incorporating a penalty term, making it particularly suitable for:

• High-dimensional data where the number of variables exceeds the number of observations (p > n)

• Data with multicollinearity among predictor variables

• Cases where standard LDA fails due to singular covariance matrices

The function performs the following steps:

1. Calls PDAopt to find the optimal q-dimensional projection directions with regularization

2. Evaluates the PDA index for the optimal projection using PDAindex2

3. Returns both the projection matrix and its associated index value

The lambda parameter controls the trade-off between maximizing class separation and regularization. When weight = TRUE, the index calculation accounts for class proportions in the optimization.

Value

An object of class "PPoptim", which is a list containing:

References

Lee, EK, Cook, D. (2010) A Projection Pursuit Index for Large p Small n Data, Statistics and Computing, 20:381-392.

See Also

LDAopt_Ext, findproj_Ext

Projection Pursuit Classification Tree with Random Variable Selection

Description

Constructs a projection pursuit classification tree using various projection pursuit indices. Optionally performs random variable selection at each split which can be used to include in a random forests methodology. When size.p = 1, this reduces to a PPtree algorithm.

Usage

PPtreeExt_split(
  formula,
  data,
  PPmethod = "LDA",
  size.p = 1,
  lambda = 0.1,
  entro = FALSE,
  entroindiv = FALSE,
  ...
)

Arguments

Details

This function extends the standard PPtree algorithm by incorporating random variable selection at each split, and define the split based on subsetting groups. The algorithm:

1. At each node, randomly samples size.p * 100% of the predictor variables

2. Finds the optimal projection using the selected variables and specified index (LDA or PDA)

3. Determines a cutpoint based on entropy splitting if entropy parameters are set

4. Recursively splits the data until stopping criteria are met

The entro parameter enables entropy-based stopping rules that halt splitting when nodes become sufficiently pure or small. The entroindiv parameter computes entropy at the individual observation level in the projected space, which can provide more refined splitting decisions.

When size.p = 1, all variables are used at each split and the function behaves as a standard PPtree. Values of size.p < 1 introduce randomness that can improve model robustness, especially for high-dimensional data or when building ensemble models.

Value

An object of class "PPtreeclass", which is a list containing:

References

Lee, YD, Cook, D., Park JW, and Lee, EK (2013) PPtree: Projection pursuit classification tree, Electronic Journal of Statistics, 7:1369-1386.

See Also

TreeExt.construct, findproj_Ext, LDAopt_Ext, PDAopt_Ext

Examples

data(penguins)
penguins <- na.omit(penguins[, -c(2,7, 8)])
require(rsample)
penguins_spl <- rsample::initial_split(penguins, strata=species)
penguins_train <- training(penguins_spl)
penguins_test <- testing(penguins_spl)
penguins_ppt2 <- PPtreeExt_split(species~bill_len + bill_dep +
flipper_len + body_mass, data = penguins_train, PPmethod = "LDA", tot=nrow
(penguins_train), tol =  0.5 , entro=TRUE)

Projection pursuit classification tree

Description

Projection Pursuit Classification Tree with Extensions

Usage

PPtreeExtclass(formula, data, PPmethod = "LDA", weight = TRUE,
                   lambda = 0.1,srule, tot = nrow(data), tol = 0.5,...)

Arguments

Details

Constructs a projection pursuit classification tree using various projection pursuit indices (LDA or PDA) at each split. This extended version includes customizable stopping rules based on entropy and node size criteria.

This function builds a binary classification tree where each split is determined by finding an optimal projection of the data onto a one-dimensional space using either LDA or PDA indices. The algorithm works as follows:

Tree Construction Process

1. At each node, find the optimal 1D projection that best separates classes

2. Project the data onto this direction and find an optimal cutpoint

3. Split observations based on the cutpoint into left and right child nodes

4. Recursively repeat until stopping criteria are met

Stopping Rules

When srule = TRUE, a node stops splitting if any of the following conditions hold:

• The node is pure (contains only one class)

• The node contains fewer than 5% of the total observations (n/tot <= 0.05)

• The node entropy is below the tolerance threshold (entropy < tol)

When srule = FALSE, splitting only stops for pure or empty nodes, potentially creating deeper, more complex trees.

Projection Methods

• LDA: Suitable for most classification problems with moderate dimensionality

• PDA: Recommended for high-dimensional data (p > n) or data with multicollinearity

The tol parameter controls tree complexity: smaller values allow more splits (deeper trees with potentially better training accuracy but higher risk of overfitting), while larger values create simpler trees (better generalization but potentially underfitting).

Value

An object of class c("PPtreeExtclass", "PPtreeclass"), which is a list containing:

Note

This function does not support interaction terms in the formula. Use only additive terms (e.g., y ~ x1 + x2) and not multiplicative terms (e.g., y ~ x1 * x2).

References

Lee, YD, Cook, D., Park JW, and Lee, EK (2013) PPtree: Projection Pursuit Classification Tree, Electronic Journal of Statistics, 7:1369-1386.

See Also

TreeExt.construct, PPtreeExt_split, findproj_Ext, predict.PPtreeExtclass

Examples

set.seed(234)
data(penguins)
penguins <- na.omit(penguins[, -c(2,7, 8)])
require(rsample)
penguins_spl <- rsample::initial_split(penguins, strata=species)
penguins_train <- training(penguins_spl)
penguins_test <- testing(penguins_spl)
penguins_ppt <- PPtreeExtclass(species~bill_len + bill_dep +
flipper_len + body_mass, data = penguins_train, PPmethod = "LDA", tot=nrow
(penguins_train), tol =  0.2 , srule = TRUE)

Projection pursuit classification tree extensions

Description

Construct the projection pursuit classification tree extensions

Usage

TreeExt.construct(origclass, origdata, Tree.Struct, id, rep, rep1, rep2,
projbest.node, splitCutoff.node, PPmethod, 
lambda = NULL, q = 1, weight = TRUE, srule=TRUE, tot=NULL, tol = .5,...)

Arguments

Details

Find tree structure using various projection pursuit indices of classification in each split.

This function recursively constructs a binary classification tree using projection pursuit. At each node, it finds the optimal projection direction that best separates classes, determines a cutpoint, and creates child nodes until stopping criteria are met (pure nodes, small node size, or low entropy).

Value

A list containing the complete tree structure and node information:

Australian crabs

Description

Measurements on rock crabs of the genus Leptograpsus. The data set contains 200 observations from two species of crab (blue and orange), there are 50 specimens of each sex of each species, collected on site at Fremantle, Western Australia.

Type

is the class variable and has 4 classes with the combinations of specie and sex (BlueMale, BlueFemale, OrangeMale and OrangeFemale)

.

FL

the size of the frontal lobe length, in mm

RW

rear width, in mm

CL

length of midline of the carapace, in mm

CW

maximum width of carapace, in mm

BD

depth of the body; for females, measured after displacement of the abdomen, in mm

Usage

data(crab)

Format

A data frame with 200 rows and 6 variables

Source

Campbell, N. A. & Mahon, R. J. (1974), A Multivariate Study of Variation in Two Species of Rock Crab of genus Leptograpsus, Australian Journal of Zoology 22(3), 417 - 425.

Shiny app to compare PPtree, PPtreeExt and rpart boundaries in 2D with different simulation scenarios

Description

Shiny app to compare PPtree, PPtreeExt and rpart boundaries in 2D with different simulation scenarios

Usage

explorapp(ui, server)

Arguments

Value

No return value, called for side effects. Shinyapp is launched.

Examples

if(interactive()){
explorapp(ui,server)
}

Find Optimal Projection for Class Separation

Description

Finds an optimal 1D projection of multivariate data that best separates classes using Linear Discriminant Analysis (LDA) or Penalized Discriminant Analysis (PDA), then determines a cutpoint for classification based on entropy splitting.

Usage

findproj_Ext(
  origclass,
  origdata,
  PPmethod = "LDA",
  q = 1,
  weight = TRUE,
  lambda = 0.1
)

Arguments

Details

This function performs projection pursuit to find a one-dimensional projection that optimally separates classes in multivariate data. The process involves:

1. Finding the optimal projection direction using either LDA or PDA

2. Projecting all observations onto this direction

3. Determining an optimal cutpoint using entropy-based splitting

4. Creating binary classification indicators based on the cutpoint

The cutpoint is calculated to minimize the weighted entropy of the resulting split. In edge cases where the cutpoint equals the maximum projected value, the function uses the second-largest value to ensure a valid split.

Value

A list with the following components:

Note

The vectors IOindexL and IOindexR are complementary (mutually exclusive and exhaustive), meaning every observation is assigned to exactly one group.

References

Lee, YD, Cook, D., Park JW, and Lee, EK (2013) PPtree: Projection Pursuit Classification Tree, Electronic Journal of Statistics, 7:1369-1386.

Fish catch data set

Description

There are 159 fishes of 7 species are caught and measured. Altogether there are 7 variables. All the fishes are caught from the same lake(Laengelmavesi) near Tampere in Finland.

Type

has 7 fish classes, with 35 cases of Bream, 11 cases of Parkki, 56 cases of Perch 17 cases of Pike, 20 cases of Roach, 14 cases of Smelt and 6 cases of Whitewish.

weight

Weight of the fish (in grams)

length1

Length from the nose to the beginning of the tail (in cm)

length2

Length from the nose to the notch of the tail (in cm)

length3

Length from the nose to the end of the tail (in cm)

height

Maximal height as % of Length3

width

Maximal width as % of Length3

Usage

data(fishcatch)

Format

A data frame with 159 rows and 7 variables

Source

[http://www.amstat.org/publications/jse/jse_data_archive.htm](fishcatch)

Glass data set

Description

Contains measurements 214 observations of 6 types of glass; defined in terms of their oxide content.

Type

has 6 types of glasses

X1

refractive index

X2

Sodium (unit measurement: weight percent in corresponding oxide).

X3

Magnesium

X4

Aluminum

X5

Silicon

X6

Potassium

X7

Calcium

X8

Barium

X9

Iron

Usage

data(glass)

Format

A data frame with 214 rows and 10 variables

The image data set

Description

contains 2310 observations of instances from 7 outdoor images

Type

has 7 types of outdoor images, brickface, cement, foliage, grass, path, sky, and window.

X1

the column of the center pixel of the region

X2

the row of the center pixel of the region.

X3

the number of pixels in a region = 9.

X4

the results of a line extraction algorithm that counts how many lines of length 5 (any orientation) with low contrast, less than or equal to 5, go through the region.

X5

measure the contrast of horizontally adjacent pixels in the region. There are 6, the mean and standard deviation are given. This attribute is used as a vertical edge detector.

X6

X5 sd

X7

measures the contrast of vertically adjacent pixels. Used for horizontal line detection.

X8

sd X7

X9

the average over the region of (R + G + B)/3

X10

the average over the region of the R value.

X11

the average over the region of the B value.

X12

the average over the region of the G value.

X13

measure the excess red: (2R - (G + B))

X14

measure the excess blue: (2B - (G + R))

X15

measure the excess green: (2G - (R + B))

X16

3-d nonlinear transformation of RGB. (Algorithm can be found in Foley and VanDam, Fundamentals of Interactive Computer Graphics)

X17

mean of X16

X18

hue mean

Usage

data(image)

Format

A data frame contains 2310 observations and 19 variables

Leukemia data set

Description

Leukemia data set

Usage

data(leukemia)

Format

This dataset comes from a study of gene expression in two types of acute leukemias, acute lymphoblastic leukemia (ALL) and acute myeloid leukemia (AML). Gene expression levels were measured using Affymetrix high density oligonucleotide arrays containing 6817 human genes. A data set containing 72 observations from 3 leukemia types classes.

Type

has 3 classes with 38 cases of B-cell ALL, 25 cases of AML and 9 cases of T-cell ALL.

Gene1, Gen2, ..., Gen40

gene expression levels.

A data frame with 72 rows and 41 variables

Source

Dudoit, S., Fridlyand, J. and Speed, T. P. (2002). Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data. Journal of the American statistical Association 97 77-87.

Lymphoma data set

Description

Gene expression in the three most prevalent adult lymphoid malignancies: B-cell chronic lymphocytic leukemia (B-CLL), follicular lymphoma (FL), and diffuse large B-cell lym- phoma (DLBCL). Gene expression levels were measured using a specialized cDNA microarray, the Lymphochip, containing genes that are preferentially expressed in lymphoid cells or that are of known immunologic or oncologic importance. This data set contain 80 observations from 3 lymphoma types.

Type

Class variable has 3 classes with 29 cases of B-cell ALL (B-CLL), 42 cases of diffuse large B-cell lymphoma (DLBCL) and 9 cases of follicular lymphoma (FL)

.

Gene1 to Gen 50

gene expression

Usage

data(lymphoma)

Format

A data frame with 80 rows and 51 variables

Source

Dudoit, S., Fridlyand, J. and Speed, T. P. (2002). Comparison of Discrimination Methods for the Classification of Tumors Using Gene Ex- pression Data. Journal of the American statistical Association 97 77-87.

The olive data set

Description

contains 572 observations and 10 variables

Region

Three super-classes of Italy: North, South and the island of Sardinia

area

Nine collection areas: three from North, four from South and 2 from Sardinia

palmitic

fatty acids percent x 100

palmitoleic

fatty acids percent x 100

stearic

fatty acids percent x 100

oleic

fatty acids percent x 100

linoleic

fatty acids percent x 100

linolenic

fatty acids percent x 100

arachidic

fatty acids percent x 100

eicosenoic

fatty acids percent x 100

Usage

data(olive)

Format

A data frame contains 573 observations and 10 variables

Parkinson data set

Description

A data set containing 195 observations from 2 parkinson types.

Type

Class variable has 2 classes, there are 48 cases of healthy people and 147 cases with Parkinson. The feature variables are biomedical voice measures

.

X1

Average vocal fundamental frequency

X2

Maximum vocal fundamental frequency

X3

Minimum vocal fundamental frequency

X4

MDVP:Jitter(%) measures of variation in fundamental frequency

X5

MDVP:Jitter(Abs) measures of variation in fundamental frequency

X6

MDVP:RAP measures of variation in fundamental frequency

X7

MDVP:PPQ measures of variation in fundamental frequency

X8

Jitter:DDP measures of variation in fundamental frequency

X9

MDVP:Shimmer measures of variation in amplitude

X10

MDVP:Shimmer(dB) measures of variation in amplitude

X11

Shimmer:APQ3 measures of variation in amplitude

X12

Shimmer:APQ5 measures of variation in amplitude

X13

MDVP:APQ measures of variation in amplitude

X14

Shimmer:DDA measures of variation in amplitude

X15

NHR measures of ratio of noise to tonal components in the voice

X16

HNR measures of ratio of noise to tonal components in the voice

X17

RPDE nonlinear dynamical complexity measures

X18

D2 nonlinear dynamical complexity measures

X19

DFA - Signal fractal scaling exponent

X20

spread1 Nonlinear measures of fundamental frequency variation

X21

spread2 Nonlinear measures of fundamental frequency variation

X22

PPE Nonlinear measures of fundamental frequency variation

Usage

data(parkinson)

Format

A data frame with 195 rows and 23 variables

Source

[https://archive.ics.uci.edu/ml/datasets/Parkinsons](Parkinson)

Plot Projection Pursuit Classification Tree

Description

Visualizes a Projection Pursuit (PP) classification tree using grid graphics. The function creates a hierarchical tree diagram showing the structure of splits and terminal nodes with class assignments. Supports automatic scaling for large trees.

Usage

## S3 method for class 'PPtreeExtclass'
plot(
  x,
  font.size = 17,
  width.size = 1,
  main = "Projection Pursuit Classification Tree",
  sub = NULL,
  auto.scale = TRUE,
  min.width = NULL,
  min.height = NULL,
  ...
)

Arguments

Details

The plot displays:

• Internal nodes: Shown as ellipses with the projection used for splitting (e.g., "proj1 * X")

• Terminal nodes: Shown as gray rectangles with the assigned class label

• Edges: Labeled with split rules ("< cutN" for left child, ">= cutN" for right child)

• Node IDs: Small boxes at the top of each node

Auto-scaling behavior: When auto.scale = TRUE and the tree has more than 20 terminal nodes or depth greater than 15:

• Font size is reduced: max(10, 17 - floor((n_terminal - 20) / 5))

• Width size is reduced: max(0.7, 1 - (n_terminal - 20) * 0.01)

• Width is set to: max(n_terminal, n_classes)

• Height is set to: tree depth

Manual scaling: When auto.scale = FALSE, you can control dimensions with min.width and min.height.

Value

Invisibly returns a list with:

Note

This function requires the grid package. It will create a new graphics page using grid.newpage().

For very large trees (>50 terminal nodes), consider:

• Exporting to a large PNG or PDF file

• Manually reducing font.size further

• Pruning the tree before plotting

Examples

library(grid)
# Example with penguins dataset
data(penguins)
penguins <- na.omit(penguins[, -c(2,7)])
penguins_ppt <- PPtreeExtclass(species~bill_len + bill_dep +flipper_len +
 body_mass,  data = penguins, PPmethod = "PDA", srule = FALSE )

plot(penguins_ppt,
     main = "Penguins Classification with PPtreeExt",
      font.size = 8,        
width.size = 0.7)

Predict Method for Projection Pursuit Classification Tree Extensions

Description

Predicts class labels for new observations using a fitted projection pursuit classification tree and optionally calculates prediction error when true class labels are provided.

Usage

## S3 method for class 'PPtreeExtclass'
predict(object, newdata, true.class = NULL, ...)

Arguments

Value

A list with two components:

Examples

data(penguins)
penguins <- na.omit(penguins[, -c(2,7, 8)])
require(rsample)
penguins_spl <- rsample::initial_split(penguins, strata=species)
penguins_train <- training(penguins_spl)
penguins_test <- testing(penguins_spl)
penguins_ppt <- PPtreeExtclass(species~bill_len + bill_dep +
flipper_len + body_mass, data = penguins_train, PPmethod = "LDA", tot =nrow
(penguins_train), tol=0.5)
predict(object = penguins_ppt, newdata = penguins_test[,-1], true.class = penguins_test$species)

Print Method for PPtreeExtclass Objects

Description

Prints a summary of a fitted projection pursuit classification tree, including the tree structure, optionally the projection coefficients and cutoff values, and the training error rate.

Usage

## S3 method for class 'PPtreeExtclass'
print(x, coef.print = FALSE, cutoff.print = FALSE, verbose = TRUE, ...)

Arguments

Details

The function traverses the tree structure stored in x$Tree.Struct and creates a hierarchical text representation. When coef.print = TRUE, the projection coefficients (linear combinations of features) used at each split are displayed. When cutoff.print = TRUE, the threshold values used to determine left/right splits are shown.

The training error rate is computed by applying the fitted tree to the original training data.

Value

The object x, invisibly

See Also

PPtreeExtclass, PPtreeExt_split, predict.PPtreeExtclass

Wine data set

Description

A data set containing 178 observations from 3 wine grown cultivares in Italy.

Type

Class variable has 3 classes that are 3 different wine grown cultivares in Italy.

X1 to X13

Check vbles

Usage

data(wine)

Format

A data frame with 178 rows and 14 variables