Treee {LDATree}

Classification trees with Linear Discriminant Analysis terminal nodes

Description

Fit an LDATree model.

Usage

Treee(
  formula,
  data,
  missingMethod = c("meanFlag", "newLevel"),
  splitMethod = "LDscores",
  pruneMethod = "none",
  numberOfPruning = 10,
  maxTreeLevel = 4,
  minNodeSize = NULL,
  verbose = FALSE
)

Arguments

formula

an object of class formula, which has the form class ~ x1 + x2 + ...

data

a data frame that contains both predictors and the response. Missing values are allowed in predictors but not in the response.

missingMethod

Missing value solutions for numerical variables and factor variables. 'mean', 'median', 'meanFlag', 'medianFlag' are available for numerical variables. 'mode', 'modeFlag', 'newLevel' are available for factor variables. The word 'Flag' in the methods indicates whether a missing flag is added or not. The 'newLevel' method means that all missing values are replaced with a new level rather than imputing them to another existing value.

splitMethod

the splitting rule in LDATree growing process. For now, 'LDscores' is the only available option.

pruneMethod

the model selection method in the LDATree growing process, which controls the size of the tree. By default, it's set to 'none', which applies a direct stopping rule. Alternatively, 'CV' uses the alpha-pruning process from CART. Although 'CV' is often more accurate, it can be slower, especially with large datasets.

numberOfPruning

controls the number of cross-validation in the pruning. It is 10 by default.

maxTreeLevel

controls the largest tree size possible for either a direct-stopping tree or a CV-pruned tree. Adding one extra level (depth) introduces an additional layer of nodes at the bottom of the current tree. e.g., when the maximum level is 1 (or 2), the maximum tree size is 3 (or 7).

minNodeSize

controls the minimum node size. Think carefully before changing this value. Setting a large number might result in early stopping and reduced accuracy. By default, it's set to one plus the number of classes in the response variable.

verbose

a logical. If TRUE, the function provides additional diagnostic messages or detailed output about its progress or internal workings. Default is FALSE, where the function runs silently without additional output.

Details

Unlike other classification trees, LDATree integrates LDA throughout the entire tree-growing process. Here is a breakdown of its distinctive features:

• The tree searches for the best binary split based on sample quantiles of the first linear discriminant score.

• An LDA/GSVD model is fitted for each terminal node (For more details, refer to ldaGSVD()).

• Missing values can be imputed using the mean, median, or mode, with optional missing flags available.

• By default, the tree employs a direct-stopping rule. However, cross-validation using the alpha-pruning from CART is also provided.

Value

An object of class Treee containing the following components:

• formula: the formula passed to the Treee()

• treee: a list of all the tree nodes, and each node is an object of class TreeeNode.

• missingMethod: the missingMethod passed to the Treee()

  An object of class TreeeNode containing the following components:

• currentIndex: the node index of the current node

• currentLevel: the level of the current node in the tree

• idxRow, idxCol: the row and column indices showing which portion of data is used in the current node

• currentLoss: the training error (number of misclassified sample) of the current node

• accuracy: the training accuracy of the current node

• proportions: shows the observed frequency for each class

• parent: the node index of its parent

• children: the node indices of its direct children (not including its children's children)

• misReference: a data frame, serves as the reference for missing value imputation

• splitCut: the cut point of the split

• nodeModel: one of 'mode' or 'LDA'. It shows the type of predictive model fitted in the current node

• nodePredict: the fitted predictive model in the current node. It is an object of class ldaGSVD if LDA is fitted. If nodeModel = 'mode', then it is a vector of length one, showing the plurality class.

• offsprings: (available only if pruneMethod = 'CV') showing all terminal descendant nodes of the current node

• offspringLoss: (available only if pruneMethod = 'CV') sum of the currentLoss of the offsprings of the current node

• alpha: (available only if pruneMethod = 'CV') the alpha in alpha-pruning from CART

Examples

fit <- Treee(Species~., data = iris)
# Use cross-validation to prune the tree
fitCV <- Treee(Species~., data = iris, pruneMethod = "CV")
# prediction
predict(fit,iris)
# plot the overall tree
plot(fit)
# plot a certain node
plot(fit, iris, node = 1)