2.
Introduction Decision trees let you construct decision models They can be used for forecasting, classification or decision At each branch the data is spit based on a particular field of data Decision trees are constructed using Divide and Conquer techniques
3.
Divide-and-Conquer: Constructing Decision Trees Steps to construct a decision tree recursively: Select an attribute to placed at root node and make one branch for each possible value Repeat the process recursively at each branch, using only those instances that reach the branch If at any time all instances at a node have the classification, stop developing that part of the tree Problem: How to decide which attribute to split on
4.
Divide-and-Conquer: Constructing Decision Trees Steps to find the attribute to split on: We consider all the possible attributes as option and branch them according to different possible values Now for each possible attribute value we calculate Information and then find the Information gain for each attribute option Select that attribute for division which gives a Maximum Information Gain Do this until each branch terminates at an attribute which gives Information = 0
5.
Divide-and-Conquer: Constructing Decision Trees Calculation of Information and Gain: For data: (P1, P2, P3……Pn) such that P1 + P2 + P3 +……. +Pn = 1 Information(P1, P2 …..Pn) = -P1logP1 -P2logP2 – P3logP3 ……… -PnlogPn Gain = Information before division – Information after division
6.
Divide-and-Conquer: Constructing Decision Trees Example: Here we have consider each attribute individually Each is divided into branches according to different possible values Below each branch the number of class is marked
7.
Divide-and-Conquer: Constructing Decision Trees Calculations: Using the formulae for Information, initially we have Number of instances with class = Yes is 9 Number of instances with class = No is 5 So we have P1 = 9/14 and P2 = 5/14 Info[9/14, 5/14] = -9/14log(9/14) -5/14log(5/14) = 0.940 bits Now for example lets consider Outlook attribute, we observe the following:
8.
Divide-and-Conquer: Constructing Decision Trees Example Contd. Gain by using Outlook for division = info([9,5]) – info([2,3],[4,0],[3,2]) = 0.940 – 0.693 = 0.247 bits Gain (outlook) = 0.247 bits Gain (temperature) = 0.029 bits Gain (humidity) = 0.152 bits Gain (windy) = 0.048 bits So since Outlook gives maximum gain, we will use it for division And we repeat the steps for Outlook = Sunny and Rainy and stop for Overcast since we have Information = 0 for it
9.
Divide-and-Conquer: Constructing Decision Trees Highly branching attributes: The problem If we follow the previously subscribed method, it will always favor an attribute with the largest number of branches In extreme cases it will favor an attribute which has different value for each instance: Identification code
10.
Divide-and-Conquer: Constructing Decision Trees Highly branching attributes: The problem Information for such an attribute is 0 info([0,1]) + info([0,1]) + info([0,1]) + …………. + info([0,1]) = 0 It will hence have the maximum gain and will be chosen for branching But such an attribute is not good for predicting class of an unknown instance nor does it tells anything about the structure of division So we use gain ratio to compensate for this
11.
Divide-and-Conquer: Constructing Decision Trees Highly branching attributes: Gain ratio Gain ratio = gain/split info To calculate split info, for each instance value we just consider the number of instances covered by each attribute value, irrespective of the class Then we calculate the split info, so for identification code with 14 different values we have: info([1,1,1,…..,1]) = -1/14 x log1/14 x 14 = 3.807 For Outlook we will have the split info: info([5,4,5]) = -1/5 x log 1/5 -1/4 x log1/4 -1/5 x log 1/5 = 1.577
Be the first to comment