Unit3_Classification_Decision Tree ID4, C4.5, CART.pdf

Sigmoid function,Classification Algorithm in Machine Learning: Decision Trees ,
Ensemble Techniques: Bagging and boosting, Adaboost and gradient boost, Random
Forest,Naïve Bayes Classifier, Support Vector Machines. Performance Evaluation:
Confusion Matrix, Accuracy, Precision, Recall, AUC-ROC Curves, F-Measure

1. Course - Machine Learning
Course code-IT 312
Unit-III
Topic- Decision Tree
Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423603
(An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Department of Information Technology
(NBA Accredited)
Dr.R.D.Chintamani
Asst. Prof.
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Unit-III- Decision Tree Classification Algorithm
•Syllabus
•Decision Trees ID4, C4.5, CART
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Unit-III- Decision Tree Classification Algorithm
•Decision Tree is a Supervised learning technique that can be used for both classification
and Regression problems, but mostly it is preferred for solving Classification problems. It
is a tree-structured classifier, where internal nodes represent the features of a dataset,
branches represent the decision rules and each leaf node represents the outcome.
•In a Decision tree, there are two nodes, which are the Decision Node and Leaf Node.
Decision nodes are used to make any decision and have multiple branches, whereas Leaf
nodes are the output of those decisions and do not contain any further branches.
•The decisions or the test are performed on the basis of features of the given dataset.
•It is a graphical representation for getting all the possible solutions to a problem/decision
based on given conditions.
•It is called a decision tree because, similar to a tree, it starts with the root node, which
expands on further branches and constructs a tree-like structure.
•In order to build a tree, we use the CART algorithm, which stands for Classification and
Regression Tree algorithm.
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Unit-III- Decision Tree Classification Algorithm
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General structure of a decision tree:

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Unit-III- Decision Tree Classification Algorithm
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Job offer

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Unit-III- Decision Tree Classification Algorithm
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Job offer

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Unit-III- Decision Tree -Attribute Selection Measures
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While implementing a Decision tree, the main issue arises that how to select the
best attribute for the root node and for sub-nodes. So, to solve such problems there
is a technique which is called as Attribute selection measure or ASM.  By this
measurement, we can easily select the best attribute for the nodes of the tree.
There are two popular techniques for ASM, which are:
•Information Gain
•Gini Index

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Unit-III- Decision Tree -Attribute Selection Measures
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•Information Gain:
Information gain is the measurement of changes in entropy after the
segmentation of a dataset based on an attribute.
It calculates how much information a feature provides us about a class.
According to the value of information gain, we split the node and build the
decision tree.
A decision tree algorithm always tries to maximize the value of information gain,
and a node/attribute having the highest information gain is split first. It can be
calculated using the below formula:
•Information Gain= Entropy(S)- [(Weighted Avg)
*Entropy(each feature)

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Unit-III- Decision Tree -Attribute Selection Measures
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•Entropy: Entropy is a metric to measure the impurity in a
given attribute. It specifies randomness in data.
• Entropy can be calculated as:
•Entropy(s)= -P(yes)log2 P(yes)- P(no) log2 P(no)
•Where,
•S= Total number of samples
•P(yes)= probability of yes
•P(no)= probability of no

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Unit-III- Decision Tree -Attribute Selection Measures
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Consider a piece of data collected over the course of 14 days
where the features are Outlook, Temperature, Humidity, Wind and
the outcome variable is whether Golf was played on the day. Now,
our job is to build a predictive model which takes in above 4
parameters and predicts whether Golf will be played on the day.
We’ll build a decision tree to do that using ID3 algorithm.  

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Unit-III- ID3 Algorithm
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ID3 Algorithm will perform following tasks recursively
1.Create root node for the tree
2.If all examples are positive, return leaf node ‘positive’
3.Else if all examples are negative, return leaf node ‘negative’
4.Calculate the entropy of current state H(S)
5.For each attribute, calculate the entropy with respect to the attribute ‘x’
denoted by H(S, x)
6.Select the attribute which has maximum value of IG(S, x)
7.Remove the attribute that offers highest IG from the set of attributes
8.Repeat until we run out of all attributes, or the decision tree has all leaf
nodes.

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Unit-III- Decision Tree -Attribute Selection Measures
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Day Outlook TemperatureHumidity Wind Play Golf
D1 Sunny Hot High Weak No
D2 Sunny Hot High Strong No
D3 Overcast Hot High Weak Yes
D4 Rain Mild High Weak Yes
D5 Rain Cool Normal Weak Yes
D6 Rain Cool Normal Strong No
D7 Overcast Cool Normal Strong Yes
D8 Sunny Mild High Weak No
D9 Sunny Cool Normal Weak Yes
D10 Rain Mild Normal Weak Yes
D11 Sunny Mild Normal Strong Yes
D12 Overcast Mild High Strong Yes
D13 Overcast Hot Normal Weak Yes
D14 Rain Mild High Strong No

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Unit-III- ID3 Algorithm
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Remember that the Entropy is 0 if all members belong to the same class, and 1 when half of them
belong to one class and other half belong to other class that is perfect randomness. Here it’s 0.94
which means the distribution is fairly random. Now, the next step is to choose the attribute that
gives us highest possible Information Gain which we’ll choose as the root node. Let’s start with
‘Wind’

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Unit-III- ID3 Algorithm
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where ‘x’ are the possible values for an attribute. Here, attribute ‘Wind’ takes two
possible values in the sample data, hence x = {Weak, Strong} We’ll have to calculate:

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Unit-III- ID3 Algorithm
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Amongst all the 14 examples we have 8 places where the wind is weak
and 6 where the wind is Strong.
Wind = Weak Wind = StrongTotal
8 6 14

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Unit-III- ID3 Algorithm
Now, out of the 8 Weak examples, 6 of them were ‘Yes’ for Play
Golf and 2 of them were ‘No’ for ‘Play Golf’. So, we have,
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Similarly, out of 6 Strong examples, we have 3 examples where the outcome was ‘Yes’
for Play Golf and 3 where we had ‘No’ for Play Golf.

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Unit-III- ID3 Algorithm
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Unit-III- ID3 Algorithm
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Which tells us the Information Gain by considering ‘Wind’ as the feature and give us
information gain of 0.048. Now we must similarly calculate the Information Gain for all the
features.

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Unit-III- ID3 Algorithm
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We can clearly see that IG(S, Outlook) has the highest information gain of 0.246, hence
we chose Outlook attribute as the root node. At this point, the decision tree looks like.

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Unit-III- ID3 Algorithm
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Here we observe that whenever the outlook is Overcast, Play Golf is always ‘Yes’, it’s no
coincidence by any chance, the simple tree resulted because of the highest information
gain is given by the attribute Outlook. Now how do we proceed from this point? We can
simply apply recursion, you might want to look at the algorithm steps described earlier.
Now that we’ve used Outlook, we’ve got three of them remaining Humidity, Temperature,
and Wind. And, we had three possible values of Outlook: Sunny, Overcast, Rain. Where
the Overcast node already ended up having leaf node ‘Yes’, so we’re left with two
subtrees to compute: Sunny and Rain.

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Unit-III- ID3 Algorithm
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Table where the value of Outlook is Sunny looks like:
Temperature HumidityWindPlay Golf
HotHighWeak No
HotHighStrong No
MildHighWeak No
CoolNormal Weak Yes
MildNormal Strong Yes

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Unit-III- ID3 Algorithm
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As we can see the highest Information Gain is given by Humidity. Proceeding in the
same way with Decision Trees modified will give us Wind as the one with highest
information gain. The final Decision Tree looks something like this.

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Unit-III- ID3 Algorithm
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Unit-III- ID3 Algorithm
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Types of Decision Tree algorithms
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•Iterative Dichotomiser 3 (ID3):
uses Information Gain to decide which attribute is to be
used classify the current subset of the data.
•C4.5: This algorithm is the successor of the ID3 algorithm. This algorithm uses either
Information gain or Gain ratio to decide upon the classifying attribute. It is a direct
improvement from the ID3 algorithm as it can handle both continuous and missing
attribute values.
•Classification and Regression Tree(CART):  It is a dynamic learning
algorithm which can produce a regression tree as well as a classification
tree depending upon the dependent variable.