In dajmcdon/ubc-stat406-labs: Tutorials and labs for UBC Stat 406 in the 2020-2021 online year

library(learnr)
library(gradethis)
leaf <- UBCstat406labs::leaf
library(tree)
library(maptree)
my_tree = tree(lobes ~. -Species-Specimen_Number, data = leaf)
tree_cv = cv.tree(my_tree, K=5)
pruned_tree = prune.tree(my_tree, k=tree_cv$k[which.min(tree_cv$dev)])

tutorial_options(exercise.timelimit = 25, exercise.checker = gradethis::grade_learnr)

knitr::opts_chunk$set(message=FALSE, warning=FALSE, fig.align='center',fig.width=10,
               fig.height=6)

The Data

This activity uses the leaf dataset which is already loaded into the module. This dataset contains information about 340 leaves over the following 16 attributes:

Species - A number from 1 to 36 indicating which species the leaf represents

Specimen Number - Numbered sequentially within species

Eccentricity - Eccentricity of the ellipse with identical second moments to the image. This value ranges from 0 to 1.

Aspect Ratio - Values close to 0 indicate an elongated shape.

Elongation - The minimum is achieved for a circular region.

Solidity - It measures how well the image fits a convex shape.

Stochastic Convexity - This variable extends the usual notion of convexity in topological sense, using sampling to perform the calculation.

Isoperimetric Factor - The maximum value of 1 is reached for a circular region. Curvy intertwined con- tours yield low values.

Maximal Indentation Depth - How deep indentations are

Lobedness - This feature characterizes how lobed a leaf is.

Average Intensity - Average intensity is defined as the mean of the intensity image

Average Contrast - Average contrast is the the standard deviation of the intensity im- age

Smoothness - For a region of constant intensity, this takes the value 0 and approaches 1 as regions exhibit larger disparities in intensity values.

Third moment - a measure of the intensity histogram’s skewness

Uniformity - uniformity’s maximum value is reached when all intensity levels are equal.

Entropy - A measure of intensity randomness.

Visualizing the Data

Begin by producing a pairs plot of all continuous predictors. Color the points by lobes. Be patient as it may take some time to run.

library(GGally)
ggpairs(data=leaf, aes(color=lobes), columns = 3:16)

Tree Classifier

Train a tree classifier based on this data for predicting complexity. Use all predictors (not Species or Specimen_number obvs). Prune your tree using cross validation to choose the depth and plot the tree.

library(tree)
library(maptree)
my_tree = tree(lobes ~. -Species-Specimen_Number, data = leaf)
tree_cv = cv.tree(my_tree, K=5)
pruned_tree = prune.tree(my_tree, k=tree_cv$k[which.min(tree_cv$dev)])
draw.tree(pruned_tree)

Produce a confusion matrix and find the tree's in-sample error rate.

library(tree)
library(maptree)
my_tree = tree(lobes ~. -Species-Specimen_Number, data = leaf)
tree_cv = cv.tree(my_tree, K=5)
pruned_tree = prune.tree(my_tree, k=tree_cv$k[which.min(tree_cv$dev)])
draw.tree(pruned_tree)

tree_conf <- table(predict(pruned_tree, type='class'), leaf$lobes)
1 - sum(diag(tree_conf))/sum(tree_conf)

Random Forest

Train a random forest using 400 trees. Produce a variable importance plot, a confusion matrix, and find the in-sample error rate.

library(randomForest)
my_forest = randomForest(lobes ~. -Species-Specimen_Number, data = leaf, ntree=400)
varImpPlot(my_forest)
(forest_conf <- table(predict(my_forest), leaf$lobes))
1 - sum(diag(forest_conf))/sum(forest_conf)

dajmcdon/ubc-stat406-labs documentation built on Aug. 18, 2020, 1:23 p.m.