# Chapter 7 Nonparametric Classification

Full book chapter still delayed! Keeping up with writing every week is getting tough. Below are the notes and code from the video.

# load packages
library(tibble)
library(ggplot2)
library(rpart)
library(rpart.plot)
library(caret)
## Loading required package: lattice
library(palmerpenguins)
library(mlbench)
# set seed
set.seed(42)

# generate data
sim_data = as_tibble(mlbench.2dnormals(n = 1000, cl = 3, sd = 1.3))

# tst-trn split data
trn_idx = sample(nrow(sim_data), size = 0.8 * nrow(sim_data))
trn = sim_data[trn_idx, ]
tst = sim_data[-trn_idx, ]

# est-val split data
est_idx = sample(nrow(trn), size = 0.8 * nrow(trn))
est = trn[est_idx, ]
val = trn[-est_idx, ]

# check data
trn
## # A tibble: 800 x 3
##       x.1    x.2 classes
##     <dbl>  <dbl> <fct>
##  1 -0.929  2.32  1
##  2 -3.25   2.27  2
##  3 -0.767  1.06  2
##  4  3.42   3.10  1
##  5  2.37   0.786 3
##  6  3.90   1.54  1
##  7 -0.373 -1.89  2
##  8 -1.10  -1.58  2
##  9  0.609  1.29  1
## 10  2.31   1.49  1
## # … with 790 more rows
# visualize data

p1 = ggplot(data = trn, aes(x = x.1)) +
geom_density(aes(fill = classes), alpha = 0.5) +
scale_fill_manual(values=c("grey", 2, 3))

p2 = ggplot(data = trn, aes(x = x.2)) +
geom_density(aes(fill = classes), alpha = 0.5) +
scale_fill_manual(values=c("grey", 2, 3))

p3 = ggplot(data = trn, aes(x = x.1)) +
geom_histogram(aes(fill = classes), alpha = 0.7, position = "identity") +
scale_fill_manual(values=c("grey", 2, 3))

p4 = ggplot(data = trn, aes(x = x.2)) +
geom_histogram(aes(fill = classes), alpha = 0.7, position = "identity") +
scale_fill_manual(values=c("grey", 2, 3))

gridExtra::grid.arrange(p1, p2, p3, p4)
## stat_bin() using bins = 30. Pick better value with binwidth.
## stat_bin() using bins = 30. Pick better value with binwidth.

plot(x.2 ~ x.1, data = trn, col = classes, pch = 20, cex = 1.5)
grid()

# fit knn model
mod_knn = knn3(classes ~ ., data = trn, k = 10)

# make "predictions" with knn model
new_obs = data.frame(x.1 = 2, x.2 = -2)
predict(mod_knn, new_obs, type = "prob")
##      1 2 3
## [1,] 0 0 1
predict(mod_knn, new_obs, type = "class")
## [1] 3
## Levels: 1 2 3
# fit tree model
mod_tree = rpart(classes ~ ., data = trn, minsplit = 5)

# make "predictions" with knn model
new_obs = data.frame(x.1 = 3, x.2 = 3)
predict(mod_tree, new_obs, type = "prob")
##           1        2         3
## 1 0.7508772 0.122807 0.1263158
predict(mod_tree, new_obs, type = "class")
## 1
## 1
## Levels: 1 2 3
# visualize tree results
par(mfrow = c(1, 2))
plot(x.2 ~ x.1, data = trn, col = classes, pch = 20, cex = 1.5)
grid()
rpart.plot(mod_tree, type = 2, box.palette = list("Grays", "Reds", "Greens"))

# helper function to calculate misclassification
calc_misclass = function(actual, predicted) {
mean(actual != predicted)
}

# calculate test metric
mod_knn = knn3(classes ~ ., data = trn, k = 10)
calc_misclass(
actual = tst$classes, predicted = predict(mod_knn, tst, type = "class") ) ## [1] 0.215 mean(tst$classes != predict(mod_knn, tst, type = "class"))
## [1] 0.225

## 7.1 Example: KNN on Simulated Data

# tune knn model ###############################################################

# set seed
set.seed(42)

# k values to consider
k_val = seq(1, 101, by = 2)

# function to fit knn to est for various k
fit_knn_to_est = function(k) {
knn3(classes ~ ., data = est, k = k)
}

# fit models
knn_mods = lapply(k_val, fit_knn_to_est)

# make predictions
knn_preds = lapply(knn_mods, predict, val, type = "class")

# calculate validation misclass
knn_misclass = sapply(knn_preds, calc_misclass, actual = val\$classes)

# plot results
plot(k_val, knn_misclass, pch = 20, type = "b")
grid()

k_val[which.min(knn_misclass)]
## [1] 55
• TODO: expand possible k value
• TODO: re-fit to training data, report test misclass

## 7.2 Example: Decision Tree on Penguin Data

# trees and penguins ###########################################################
# check data
penguins
## # A tibble: 344 x 8
##    species island    bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
##    <fct>   <fct>              <dbl>         <dbl>             <int>       <int>
##  1 Adelie  Torgersen           39.1          18.7               181        3750
##  2 Adelie  Torgersen           39.5          17.4               186        3800
##  3 Adelie  Torgersen           40.3          18                 195        3250
##  4 Adelie  Torgersen           NA            NA                  NA          NA
##  5 Adelie  Torgersen           36.7          19.3               193        3450
##  6 Adelie  Torgersen           39.3          20.6               190        3650
##  7 Adelie  Torgersen           38.9          17.8               181        3625
##  8 Adelie  Torgersen           39.2          19.6               195        4675
##  9 Adelie  Torgersen           34.1          18.1               193        3475
## 10 Adelie  Torgersen           42            20.2               190        4250
## # … with 334 more rows, and 2 more variables: sex <fct>, year <int>
# visualize data
par(mfrow = c(1, 2))
plot(body_mass_g ~ flipper_length_mm, data = penguins,
col = species, pch = 20, cex = 1.5)
grid()
plot(bill_length_mm ~ flipper_length_mm, data = penguins,
col = species, pch = 20, cex = 1.5)
grid()

# fit tree and visualize
peng_mod = rpart(species ~ . - year, data = penguins)
rpart.plot(peng_mod, type = 2, box.palette = list("Grays", "Reds", "Greens"))

# fit bigger tree and visualize
peng_mod_big = rpart(species ~ . - year, data = penguins, minsplit = 2, cp = 0)
rpart.plot(peng_mod_big, type = 2, box.palette = list("Grays", "Reds", "Greens"))

• TODO: tune