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Introduction to LDATree

Source: vignettes/LDATree.Rmd
LDATree.Rmd

LDATree is an R modeling package for fitting classification trees with oblique splits.

  • If you are unfamiliar with classification trees, here is a tutorial about the traditional CART and its R implementation rpart.

  • More details about the LDATree can be found in Wang, S. (2024). FoLDTree: A ULDA-Based Decision Tree Framework for Efficient Oblique Splits and Feature Selection. arXiv preprint arXiv:2410.23147. Link.

Why use the LDATree package?

Compared to other similar trees, LDATree distinguishes itself in the following ways:

  • Using Uncorrelated Linear Discriminant Analysis (ULDA) from the folda package, it can efficiently find oblique splits.

  • It provides both ULDA and forward ULDA as the splitting rule and node model. Forward ULDA has intrinsic variable selection, which helps mitigate the influence of noise variables.

  • It automatically handles missing values.

  • It can output both predicted class and class probability.

  • It supports downsampling, which can be used to balance classes or accelerate the model fitting process.

  • It includes several visualization tools to provide deeper insights into the data.

Basic Usage of LDATree

We offer two main tree types in the LDATree package: LDATree and FoLDTree. For the splitting rule and node model, LDATree uses ULDA, while FoLDTree uses forward ULDA.

To build an LDATree (or FoLDTree):

library(LDATree)
set.seed(443)
diamonds <- as.data.frame(ggplot2::diamonds)[sample(53940, 2000),]
datX <- diamonds[, -2]
response <- diamonds[, 2] # we try to predict "cut"
fit <- Treee(datX = datX, response = response, verbose = FALSE) # by default, it is a pre-stopping FoLDTree
# fit <- Treee(datX = datX, response = response, verbose = FALSE, ldaType = "all", pruneMethod = "post") # if you want to fit a post-pruned LDATree.

To plot the LDATree (or FoLDTree):

# View the overall tree.
plot(fit)

# Three types of individual plots
# 1. Scatter plot on first two LD scores
plot(fit, datX = datX, response = response, node = 1)

# 2. Density plot on the first LD score
plot(fit, datX = datX, response = response, node = 7)

# 3. A message
plot(fit, datX = datX, response = response, node = 2)
#> [1] "Every observation in node 2 is predicted to be Fair"

To make predictions:

# Prediction only.
predictions <- predict(fit, datX)
head(predictions)
#> [1] "Ideal" "Ideal" "Ideal" "Ideal" "Ideal" "Ideal"
# A more informative prediction
predictions <- predict(fit, datX, type = "all")
head(predictions)
#>   response node         Fair        Good Very Good     Premium     Ideal
#> 1    Ideal    6 4.362048e-03 0.062196349 0.2601145 0.056664046 0.6166630
#> 2    Ideal    6 1.082022e-04 0.006308281 0.1290079 0.079961227 0.7846144
#> 3    Ideal    6 7.226446e-03 0.077434549 0.2036148 0.023888946 0.6878352
#> 4    Ideal    6 1.695119e-02 0.115233616 0.1551836 0.008302145 0.7043295
#> 5    Ideal    6 4.923729e-05 0.004157352 0.1498265 0.187391975 0.6585749
#> 6    Ideal    6 4.827312e-03 0.061274797 0.1978061 0.027410359 0.7086815

Additional Features

  • Missing values: The solution to the missing value problem is inherited from the folda package. Check here for more details.

  • Downsampling: Optional downsampling occurs only when fitting the ULDA model. Check here for more details.

  • misClassCost: This parameter is useful in situations where misclassifying certain classes has a more severe impact than others. Check here for more details.

References

  • Wang, S. (2024). A new forward discriminant analysis framework based on Pillai’s trace and ULDA. arXiv preprint, arXiv:2409.03136. Retrieved from https://arxiv.org/abs/2409.03136.

  • Wang, S. (2024). FoLDTree: A ULDA-based decision tree framework for efficient oblique splits and feature selection. arXiv preprint, arXiv:2410.23147. Retrieved from https://arxiv.org/abs/2410.23147.