HW 2 UG - Jupally (1)
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HW 2 UG
2. Consider the training examples shown in the given table for a binary classification problem.
Customer ID
Gender
Car Type
Shirt Size
Class
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
M
M
M
M
M
M
F
F
F
F
M
M
M
M
F
F
F
F
F
F
Family
Sports
Sports
Sports
Sports
Sports
Sports
Sports
Sports
Luxury
Family
Family
Family
Luxury
Luxury
Luxury
Luxury
Luxury
Luxury
Luxury
Small
Medium
Medium
Large
Extra Large
Extra Large
Small
Small
Medium
Large
Large
Extra Large
Medium
Extra Large
Small
Small
Medium
Medium
Medium
Large
C0
C0
C0
C0
C0
C0
C0
C0
C0
C0
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
(c) Compute the Gini index for the Gender
attribute.
(d) Compute the Gini index for the Car Type
attribute using multiway split.
(e) Compute the Gini index for the Shirt Size
attribute using multiway split.
(f) Which attribute is better, Gender
, Car Type
, or Shirt Size
?
Solution
:
R Program
:
# Create a data frame based on the provided table
data <- data.frame(
Customer_ID = 1:20,
Gender = c('M', 'M', 'M', 'M', 'M', 'M', 'F', 'F', 'F', 'F', 'M', 'M', 'M', 'M', 'F', 'F', 'F', 'F', 'F', 'F'),
Car_Type = c('Family', 'Sports', 'Sports', 'Sports', 'Sports', 'Sports', 'Sports', 'Sports', 'Sports', 'Luxury', 'Family', 'Family', 'Family', 'Luxury', 'Luxury', 'Luxury', 'Luxury', 'Luxury', 'Luxury', 'Luxury'),
Shirt_Size = c('Small', 'Medium', 'Medium', 'Large', 'Extra Large', 'Extra Large', 'Small', 'Small', 'Medium', 'Large', 'Large', 'Extra Large', 'Medium', 'Extra Large', 'Small', 'Small', 'Medium', 'Medium', 'Medium', 'Large'),
Class = c('C0', 'C0', 'C0', 'C0', 'C0', 'C0', 'C0', 'C0', 'C0', 'C0', 'C1', 'C1', 'C1', 'C1', 'C1', 'C1', 'C1', 'C1', 'C1', 'C1')
)
# Define a function to compute Gini index for a given set
compute_gini <- function(subset) {
# Compute Gini index for a subset
total <- nrow(subset)
count <- table(subset$Class)
gini <- 1 - sum((count / total)^2)
return(gini)
}
# Compute the Gini index for a given attribute using multiway split
gini_index_for_attribute <- function(data, col_name) {
total <- nrow(data)
unique_values <- unique(data[[col_name]])
weighted_gini <- 0
for (value in unique_values) {
# Filter data for each unique value of the attribute
subset <- data[data[[col_name]] == value, ]
weight <- nrow(subset) / total
# Add up the weighted Gini index for each value of the attribute
weighted_gini <- weighted_gini + weight * compute_gini(subset)
}
return(weighted_gini)
}
# Calculate Gini index for each attribute
gini_gender <- gini_index_for_attribute(data, "Gender")
gini_car_type <- gini_index_for_attribute(data, "Car_Type")
gini_shirt_size <- gini_index_for_attribute(data, "Shirt_Size")
# Print out the results
cat("Gini for Gender:", gini_gender, "\n")
cat("Gini for Car Type:", gini_car_type, "\n")
cat("Gini for Shirt Size:", gini_shirt_size, "\n")
# Determine the best attribute based on the lowest Gini index
attributes <- c("Gender", "Car_Type", "Shirt_Size")
ginis <- c(gini_gender, gini_car_type, gini_shirt_size)
best_attribute <- attributes[which.min(ginis)]
cat("Best attribute is:", best_attribute, "\n")
Output
:
Gini for Gender: 0.48
Gini for Car Type: 0.1625 Gini for Shirt Size: 0.4914286
Best attribute is: Car_Type
Your preview ends here
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Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education