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# CENG 499 Homework 3 Decision Trees and Support Vector Machines Solved

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## 1 Introduction

In this assignment, you will have a chance to get hands-on experience with decision trees and support vector machines (SVMs). Like in the previous homework,
you will write a report called report.pdf, the structure of which is up to you.
The related material can be found in hw3 material.zip.

## 2 Decision Trees

In this section, you are using the seeds dataset. Each instance has 7 numerical
features, and it can belong one of 3 categories. However, we have removed the
first two features so there are 5 numerical features.
import numpy as np
train_set = np . load (’ hw3_material /dt/ train_set . npy ’)
train_labels = np . load (’ hw3_material /dt/ train_labels . npy ’)
test_set = np . load (’ hw3_material /dt/ test_set . npy ’)
test_labels = np . load (’ hw3_material /dt/ test_labels . npy ’)

## You should do:

• Implement the empty functions in dt.py.
• Using the training set and ID3 algorithm, grow two trees with the following
attribute selection strategies respectively: Information Gain and Average
Gini Index. For each tree, report its test accuracy and visualization.
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• You will implement binary split for the decision trees. In other words,
at each node, the data is going to be split into 2 parts if a split is going to happen. Check numerical attributes section of the lecture slide
DecTrees.pdf.
• You are not allowed to use libraries implementing decision trees and related functions such as entropy and gini index.
• Apply prepruning on the previous trees by using chi-squared test of independence (refer to your statistics books or this link). For each tree, report
its test accuracy and visualization.

You are going to stop growing the tree
when you cannot reject the null hypothesis which states that there is no
association between the two variables (in our case, the attribute selected
by the heuristic function, i.e., information gain and average gain index,
and the class variable). In this homework, you will use 90% confidence.
The critical values can be obtained from a chi-squared table.
• You do not have to directly put the (four) tree diagrams in your report.
You can refer to them in the report. At each node, the number of examples
that belong to each class in the training set that has survived until that
node should be written. You may use any drawing library and tool for
this purpose such as graphviz.

## 3 Support Vector Machines

This section consists of four tasks, and you will use scikit-learn’s SVM implementation to complete them

In this section, you are given a 2D linearly separable dataset.
import numpy as np
train_set = np . load (’ hw3_material / svm / task1 / train_set . npy ’)
train_lbs = np . load (’ hw3_material / svm / task1 / train_labels . npy ’)
• Using linear kernel, train 5 SVMs with the following C values respectively:
0.01, 0.1, 1, 10, 100.
• Visualize the decision boundary of each classifier and comment on the
effects of C values. You can use the code snippet in the recitation notebook
for that purpose.

In this section, you are given a 2D non-linearly separable dataset.
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import numpy as np
train_set = np . load (’ hw3_material / svm / task2 / train_set . npy ’)
train_lbs = np . load (’ hw3_material / svm / task2 / train_labels . npy ’)
• Fixing C as 1, train 4 SVMs with following kernels respectively: linear,
rbf, polynomial, and sigmoid.
• Visualize the decision boundary of each classifier and comment on the
effects of kernels.

In this section, you are given 32 x 32 grayscale images generated synthetically,
where each image can belong to one of two classes.
import numpy as np
train_set = np . load (’ hw3_material / svm / task3 / train_set . npy ’)
train_lbs = np . load (’ hw3_material / svm / task3 / train_labels . npy ’)
test_set = np . load (’ hw3_material / svm / task3 / test_set . npy ’)
test_labels = np . load (’ hw3_material / svm / task3 / test_labels .npy ’)
• Perform a grid search on hyperparameters of SVM (required hyperparameters are kernel, C, and gamma). For each hyperparameter configuration,
report the validation accuracy in the form of tables. And, for the best
hyperparameter configuration, use the whole training set to train an SVM
and report its test accuracy. Try at least 15 different hyperparameter configurations. Remember that you do reserve some part of your training set
as validation set and not use the test set in hyperparameter optimization
process.

In this section, you will use an imbalanced version of the Task3’s dataset.
import numpy as np
train_set = np . load (’ hw3_material / svm / task4 / train_set . npy ’)
train_lbs = np . load (’ hw3_material / svm / task4 / train_labels . npy ’)
test_set = np . load (’ hw3_material / svm / task4 / test_set . npy ’)
test_labels = np . load (’ hw3_material / svm / task4 / test_labels .npy ’)
• Using rbf kernel and C=1, train an SVM classifier. Report its test accuracy and the confusion matrix (using the test set). Comment on whether
accuracy is a good performance metric or not.
• Oversample the minority class of the training set. You can do that by
simply copying the examples of the minority class so that the number of
examples in both classes become somewhat close. Then, repeat the same
procedure in the first item.
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• Undersample the majority class of the training set. You can do that by
simply deleting some of the examples in the majority class so that the
number of examples in both classes become somewhat close. Then, repeat
the same procedure in the first item.
• Set class weight parameter of sklearn.svm.SVC to ”balanced” which adjust
the class weights inversely proportional to the class frequencies. Then,
repeat the same procedure in the first item.

## 4 Specifications

• The code must be in Python.
• You are also provided with simple testers. Note that passing a tester does
not guarantee that your code works perfectly.
• Falsifying results, changing the composition of training and test data are
strictly forbidden, and you will receive 0 if this is the case. Your programs
will be examined to see if you have actually reached the results and if they
are working correctly.
• Using any piece of code that is not your own is strictly forbidden and
constitutes as cheating. This includes friends, previous homeworks, or
the internet. The violators will be punished according to the department
regulations.

• Follow the course page on ODTUClass for any updates and clarifications.
of e-mailing.
• You have a total of 3 late days for all homeworks. The late submission
penalty will be calculated using 5d
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, that is, 1 day late submission will
cost you 5 points, 2 days will cost you 20 points, and 3 days will cost you
45 points. No late submission is accepted after reaching a total of 3 late
days.

## 5 Submission

Submission will be done via ODTUClass. You will submit a zip file called
hw3.zip that contains all your source code, report.pdf, and decision tree
diagrams. Also, please provide a README file describing how to run your
code and perform the experiments.

## 6 Resources

Homework3’s recitation notebook can be accessed through the link.
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