Published on Jul 16,2018
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Let us consider a scenario where a new planet is discovered by a group of  astronomers. Now the question is whether it could be ‘the next earth?’ The answer to this question will revolutionize the way people live. Well, literally!

There are n number of deciding factors which need to be thoroughly researched to take an intelligent decision. These factors can be whether water is present on the planet, what is the temperature, whether the surface is prone to continuous storms, flora and fauna survives the climate or not, etc.

Let us create a decision tree to find out whether we have discovered a new habitat.

The habitable temperature falls into the range 0 to 100 Celsius.

001

Whether water is present or not?

002

Whether  flora and fauna flourishes?

003

The planet has a stormy surface?

004

Thus, we a have a decision tree with us.

Classification Rules:

Classification rules are the cases in which all the scenarios are taken into consideration and a class variable is assigned to each.

Class Variable :

Each leaf node is assigned a class-variable. A class-variable is the final output which leads to our decision.

Let us derive the classification rules from the Decision Tree created:

1. If Temperature is not between 273 to 373K, -> Survival Difficult

2. If Temperature is between 273 to 373K, and  water is not present, -> Survival Difficult

3. If Temperature is between 273 to 373K, water is present, and flora and fauna is not present -> Survival Difficult

4. If Temperature is between 273 to 373K, water is present, flora and fauna is present, and stormy surface is not present -> Survival Probable

5. If Temperature is between 273 to 373K, water is present, flora and fauna is present, and stormy surface is present -> Survival Difficult 

Decision Tree 

A decision tree has the following constituents :

Root Node : The factor of ‘temperature’ is considered as the root in this case.

Internal Node : The nodes with one incoming edge and 2 or more outgoing edges.

Leaf Node : This is the terminal node with no out-going edge.

As the decision tree is now constructed, starting from the root-node we check the test condition and assign the control to one of the outgoing edges, and so the condition is again tested and a node is assigned. The decision tree is said to be complete when all the test conditions lead to leaf node. The leaf node contains the class-labels, which vote in-favor or against the decision.

Now, you might think why did we start with the ‘temperature’ attribute at the root? If you choose any other attribute, the decision tree constructed will be different.

Correct. For a particular set of attributes, there can be numerous different trees created. We need to choose the optimal tree which is done by following an algorithmic approach. We will now see ‘the greedy approach’ to create a perfect decision tree.

The Greedy Approach

“Greedy Approach is based on the concept of heuristic Problem Solving by making optimal local choice at each node. By making these local optimal choices, we reach the approximate optimal solution globally.”

The algorithm can be summarized as :

1. At each stage (node), pick out the best feature as the test condition.

2. Now split the node into the possible outcomes (internal nodes).

3. Repeat the above steps till all the test conditions have been exhausted into leaf nodes.

When you start to implement the algorithm, the first question is: ‘How to pick the starting test condition?’

The answer to this question lies in the values of ‘Entropy’ and ‘Information Gain’. Let us see what are they and how do they impact our decision tree creation.

Entropy : Entropy in Decision Tree stands for homogeneity. If the data is completely homogenous, the entropy is 0, else if the data is divided (50-50%) entropy is 1.

Information Gain : Information Gain is the dec/inc in Entropy value when the node is split.

An attribute should have the highest information gain to be selected for splitting. Based on the computed values of Entropy and Information Gain, we choose the best attribute at any particular step.

slide-1

Let us consider the following data:

data

There can be n number of decision trees that can be formulated from these set of attributes.

Tree Creation Trial-1 :

 Here we take up the attribute ‘Student’ as the initial test condition.

tree1

Tree Creation Trial-2 :

 Similarly, why to choose ‘Student’ ? We can choose ‘Income’ as the test condition.

tree2

Creating the Perfect Decision Tree With Greedy Approach 

Let us follow the ‘Greedy Approach’ and construct the optimal decision tree.

There are two classes involved : ‘Yes’ i.e. whether the person buys a computer or ‘No’ i.e. he does not. To calculate Entropy and Information Gain, we are computing the value of Probability for each of these 2 classes.
»Positive: For ‘buys_computer=yes’ probability will come out to be  :
1 (1)
»Negative: For ‘buys_computer=no’ probability comes out to be :
2
Entropy in D : We now put calculate the Entropy by putting probability values in the formula stated above.
3
We have already classified the values of Entropy, which are:
Entropy =0  : Data is completely homogenous (pure)
Entropy =1   : Data is divided into 50- 50 % (impure)
Our value of Entropy is 0.940, which means our set is almost impure.
Let’s delve deep, to find out the suitable attribute and calculate the Information Gain.
What is information gain if we split on “Age”?
This data represents how many people falling into a specific age bracket, buy and do not buy the product.
For example, for people with Age 30 or less, 2 people buy (Yes) and 3 people do not buy (No) the product, the Info (D)  is calculated for these 3 category of people, that is represented in the last column.
4
The Info (D) for the age attribute is computed by the total of these 3 range of age values. Now, the question is what is the ‘information gain’ if we split on ‘Age’ attribute.
The difference of the total Information value ( 0.940) and the information computed for age attribute (0.694) gives the ‘information gain’.
5
This is the deciding factor for whether we should split at ‘Age’ or any other attribute. Similarly, we calculate the ‘information gain’ for the rest of the attributes:
Information Gain (Age) =0.246
Information Gain (Income) =0.029
Information Gain (Student) = 0.151
Information Gain (credit_rating) =0.048
slide2
On comparing these values of gain for all the attributes, we find out that the ‘information gain’ for ‘Age’ is the highest. Thus, splitting at ‘age’ is a good decision.
Similarly, at each split we compare the information gain to find out whether that attribute should be chosen for split or not.
Thus, the optimal tree created looks like :
tree3

The classification rules for this tree can be jotted down as:

If person’s age is less than 30 and he is not a student, he will not buy the product.

Age(<30) ^ student(no) = NO

If person’s age is less than 30 and he is a student, he will buy the product.
Age(<30) ^ student(yes) = YES

If person’s age is between 31 and 40, he is most likely to buy.

Age(31…40) = YES

If person’s age is greater than 40, and has an excellent credit rating, he will not buy.

Age(>40) ^ credit_rating(excellent) = NO

If person’s age is greater than 40, with a fair credit rating, he will probably buy.
Age(>40) ^ credit_rating(fair) = Yes

Thus, we achieve the perfect Decision Tree!!

Got a question for us? Please mention them in the comments section and we will get back to you.

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