Package 'LDATree'

Plot a Treee Object

Description

This function visualizes either the entire decision tree or a specific node within the tree. The tree is displayed as an interactive network of nodes and edges, while individual nodes are scatter/density plots using ggplot2.

Usage

## S3 method for class 'Treee'
plot(x, datX, response, node = -1, ...)

Arguments

x	A fitted model object of class Treee, typically the result of the Treee() function.
datX	A data frame of predictor variables. Required for plotting individual nodes.
response	A vector of response values. Required for plotting individual nodes.
node	An integer specifying the node to plot. If node = -1, the entire tree is plotted. Default is -1.
...	Additional arguments passed to the plotting functions.

Value

A visNetwork interactive plot of the decision tree if node = -1, or a ggplot2 object if a specific node is plotted.

Overall Tree Structure

A full tree diagram is displayed using visNetwork when node is not specified (the default is -1). The color represents the most common (plurality) class within each node, and the size of each terminal node reflects its relative sample size. Below each node, the fraction of correctly predicted training samples and the total sample size for that node are shown, along with the node index. Clicking on a node opens an information panel with additional details.

Individual Node Plot

To plot a specific node, you must provide the node index along with the original training predictors (datX) and responses (response). A scatter plot is generated if more than one discriminant score is available, otherwise, a density plot is created. Samples are projected onto their linear discriminant score(s).

Examples

fit <- Treee(datX = iris[, -5], response = iris[, 5], verbose = FALSE)
plot(fit) # plot the overall tree
plot(fit, datX = iris, response = iris[, 5], node = 1) # plot a specific node

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Predictions From a Fitted Treee Object

Description

Generate predictions on new data using a fitted Treee model.

Usage

## S3 method for class 'Treee'
predict(object, newdata, type = c("response", "prob", "all"), ...)

Arguments

object	A fitted model object of class Treee, typically the result of the Treee() function.
newdata	A data frame containing the predictor variables. Missing values are allowed and will be handled according to the fitted tree's method for handling missing data.
type	A character string specifying the type of prediction to return. Options are: 'response': returns the predicted class for each observation (default). 'prob': returns a data frame of posterior probabilities for each class. 'all': returns a data frame containing predicted classes, posterior probabilities, and the predicted node indices.
...	Additional arguments passed to or from other methods.

Value

Depending on the value of type, the function returns:

• If type = 'response': A character vector of predicted class labels.

• If type = 'prob': A data frame of posterior probabilities, where each class has its own column.

• If type = 'all': A data frame containing predicted class labels, posterior probabilities, and the predicted node indices.

Note: For factor predictors, if a level not present in the training data is found in newdata, it will be treated as missing and handled according to the missingMethod specified in the fitted tree.

Examples

fit <- Treee(datX = iris[, -5], response = iris[, 5], verbose = FALSE)
head(predict(fit, iris)) # Predicted classes
head(predict(fit, iris[, -5], type = "prob")) # Posterior probabilities
head(predict(fit, iris[, -5], type = "all")) # Full details

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Classification Trees with Uncorrelated Linear Discriminant Analysis Terminal Nodes

Description

This function fits a classification tree where each node has a Uncorrelated Linear Discriminant Analysis (ULDA) model. It can also handle missing values and perform downsampling. The resulting tree can be pruned either through pre-pruning or post-pruning methods.

Usage

Treee(
  datX,
  response,
  ldaType = c("forward", "all"),
  nodeModel = c("ULDA", "mode"),
  pruneMethod = c("pre", "post"),
  numberOfPruning = 10L,
  maxTreeLevel = 20L,
  minNodeSize = NULL,
  pThreshold = NULL,
  prior = NULL,
  misClassCost = NULL,
  missingMethod = c("medianFlag", "newLevel"),
  kSample = -1,
  verbose = TRUE
)

Arguments

datX	A data frame of predictor variables.
response	A vector of response values corresponding to datX.
ldaType	A character string specifying the type of LDA to use. Options are "forward" for forward ULDA or "all" for full ULDA. Default is "forward".
nodeModel	A character string specifying the type of model used in each node. Options are "ULDA" for Uncorrelated LDA, or "mode" for predicting based on the most frequent class. Default is "ULDA".
pruneMethod	A character string specifying the pruning method. "pre" performs pre-pruning based on p-value thresholds, and "post" performs cross-validation-based post-pruning. Default is "pre".
numberOfPruning	An integer specifying the number of folds for cross-validation during post-pruning. Default is 10.
maxTreeLevel	An integer controlling the maximum depth of the tree. Increasing this value allows for deeper trees with more nodes. Default is 20.
minNodeSize	An integer controlling the minimum number of samples required in a node. Setting a higher value may lead to earlier stopping and smaller trees. If not specified, it defaults to one plus the number of response classes.
pThreshold	A numeric value used as a threshold for pre-pruning based on p-values. Lower values result in more conservative trees. If not specified, defaults to 0.01 for pre-pruning and 0.6 for post-pruning.
prior	A numeric vector of prior probabilities for each class. If NULL, the prior is automatically calculated from the data.
misClassCost	A square matrix $C$, where each element $C_{ij}$ represents the cost of classifying an observation into class $i$ given that it truly belongs to class $j$. If NULL, a default matrix with equal misclassification costs for all class pairs is used. Default is NULL.
missingMethod	A character string specifying how missing values should be handled. Options include 'mean', 'median', 'meanFlag', 'medianFlag' for numerical variables, and 'mode', 'modeFlag', 'newLevel' for factor variables. 'Flag' options indicate whether a missing flag is added, while 'newLevel' replaces missing values with a new factor level.
kSample	An integer specifying the number of samples to use for downsampling during tree construction. Set to -1 to disable downsampling.
verbose	A logical value. If TRUE, progress messages and detailed output are printed during tree construction and pruning. Default is FALSE.

Value

An object of class Treee containing the fitted tree, which is a list of nodes, each an object of class TreeeNode. Each TreeeNode contains:

• currentIndex: The node index in the tree.

• currentLevel: The depth of the current node in the tree.

• idxRow, idxCol: Row and column indices indicating which part of the original data was used for this node.

• currentLoss: The training error for this node.

• accuracy: The training accuracy for this node.

• stopInfo: Information on why the node stopped growing.

• proportions: The observed frequency of each class in this node.

• prior: The (adjusted) class prior probabilities used for ULDA or mode prediction.

• misClassCost: The misclassification cost matrix used in this node.

• parent: The index of the parent node.

• children: A vector of indices of this node’s direct children.

• splitFun: The splitting function used for this node.

• nodeModel: Indicates the model fitted at the node ('ULDA' or 'mode').

• nodePredict: The fitted model at the node, either a ULDA object or the plurality class.

• alpha: The p-value from a two-sample t-test used to evaluate the strength of the split.

• childrenTerminal: A vector of indices representing the terminal nodes that are descendants of this node.

• childrenTerminalLoss: The total training error accumulated from all nodes listed in childrenTerminal.

References

Wang, S. (2024). FoLDTree: A ULDA-Based Decision Tree Framework for Efficient Oblique Splits and Feature Selection. arXiv preprint arXiv:2410.23147. Available at https://arxiv.org/abs/2410.23147.

Wang, S. (2024). A New Forward Discriminant Analysis Framework Based On Pillai's Trace and ULDA. arXiv preprint arXiv:2409.03136. Available at https://arxiv.org/abs/2409.03136.

Examples

fit <- Treee(datX = iris[, -5], response = iris[, 5], verbose = FALSE)
# Use cross-validation to prune the tree
fitCV <- Treee(datX = iris[, -5], response = iris[, 5], pruneMethod = "post", verbose = FALSE)
head(predict(fit, iris)) # prediction
plot(fit) # plot the overall tree
plot(fit, datX = iris[, -5], response = iris[, 5], node = 1) # plot a certain node

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