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Datamining & Warehousing

Unit 3 – Decision Tree

Dr.VIDHYA B
ASSISTANT PROFESSOR & HEAD
Department of Computer Technology
Sri Ramakrishna College of Arts and Science
Coimbatore - 641 006
Tamil Nadu, India
Chapter 8. Classification: Basic
Concepts
 Classification: Basic Concepts
 Decision Tree Induction
 Bayes Classification Methods
 Rule-Based Classification
 Model Evaluation and Selection
 Techniques to Improve Classification Accuracy:
Ensemble Methods
 Summary
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Decision Tree Induction: An
Example
age income student credit_rating buys_computer
<=30 high no fair no
 Training data set: Buys_computer <=30 high no excellent no
 The data set follows an example of 31…40 high no fair yes
>40 medium no fair yes
Quinlan’s ID3 (Playing Tennis) >40 low yes fair yes
 Resulting tree: >40 low yes excellent no
31…40 low yes excellent yes
age? <=30 medium no fair no
<=30 low yes fair yes
>40 medium yes fair yes
<=30 medium yes excellent yes
<=30 overcast
31..40 >40 31…40 medium no excellent yes
31…40 high yes fair yes
>40 medium no excellent no

student? yes credit rating?

no yes excellent fair

no yes no yes
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Algorithm for Decision Tree
Induction
 Basic algorithm (a greedy algorithm)
 Tree is constructed in a top-down recursive divide-and-

conquer manner
 At start, all the training examples are at the root

 Attributes are categorical (if continuous-valued, they are

discretized in advance)
 Examples are partitioned recursively based on selected

attributes
 Test attributes are selected on the basis of a heuristic or

statistical measure (e.g., information gain)

 Conditions for stopping partitioning
 All samples for a given node belong to the same class

 There are no remaining attributes for further partitioning –

majority voting is employed for classifying the leaf

 There are no samples left
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Brief Review of Entropy

m=2

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Attribute Selection Measure:
Information Gain (ID3/C4.5)
 Select the attribute with the highest information gain
 Let pi be the probability that an arbitrary tuple in D belongs to
class Ci, estimated by |Ci, D|/|D|
 Expected information (entropy) needed to classify
m a tuple in D:
Info( D)   pi log 2 ( pi )
i 1
 Information needed (after using A to split D into v partitions) to
v | D |
classify D:
Info A ( D ) 
j
Info( D j )
j 1 | D |

 Information gained by branching on attribute A

Gain(A) Info(D)  Info A(D)
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Attribute Selection: Information
Gain
 Class P: buys_computer = “yes” 5 4
Infoage ( D )  I (2,3)  I (4,0)
 Class N: buys_computer = “no” 14 14
9 9 5 5 5
Info( D) I (9,5)  log 2 ( )  log 2 ( ) 0.940  I (3,2) 0.694
14 14 14 14 14
age pi ni I(p i, n i) 5
<=30 2 3 0.971 I (2,3)means “age <=30” has 5 out of
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31…40 4 0 0 14 samples, with 2 yes’es and 3
>40 3 2 0.971 no’s. Hence
age
<=30
income student credit_rating
high no fair
buys_computer
no
Gain(age) Info( D )  Infoage ( D ) 0.246
<=30 high no excellent no
31…40 high no fair yes
>40 medium no fair yes Similarly,
>40 low yes fair yes
>40 low yes excellent no
31…40 low yes excellent yes Gain(income) 0.029
<=30 medium no fair no
<=30
>40
low
medium
yes
yes
fair
fair
yes
yes
Gain( student ) 0.151
<=30
31…40
medium
medium
yes
no
excellent
excellent
yes
yes Gain(credit _ rating ) 0.048
31…40 high yes fair yes
>40 medium no excellent no 7
for Continuous-Valued
Attributes
 Let attribute A be a continuous-valued attribute
 Must determine the best split point for A
 Sort the value A in increasing order
 Typically, the midpoint between each pair of adjacent values
is considered as a possible split point
 (ai+ai+1)/2 is the midpoint between the values of ai and ai+1
 The point with the minimum expected information
requirement for A is selected as the split-point for A
 Split:
 D1 is the set of tuples in D satisfying A ≤ split-point, and D2 is
the set of tuples in D satisfying A > split-point
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Gain Ratio for Attribute
Selection (C4.5)
 Information gain measure is biased towards attributes with a
large number of values
 C4.5 (a successor of ID3) uses gain ratio to overcome the
problem (normalization to information gain)
v | Dj | | Dj |
SplitInfo A ( D)   log 2 ( )
j 1 |D| |D|
 GainRatio(A) = Gain(A)/SplitInfo(A)
 Ex.

 gain_ratio(income) = 0.029/1.557 = 0.019

 The attribute with the maximum gain ratio is selected as the
splitting attribute
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Gini Index (CART, IBM
IntelligentMiner)
 If a data set D contains examples from n classes, gini index, gini(D)
is defined as n 2
gini( D) 1  p j
j 1
where pj is the relative frequency of class j in D
 If a data set D is split on A into two subsets D1 and D2, the gini
index gini(D) is defined as |D | |D |
gini A ( D)  1 gini( D1)  2 gini( D 2)
|D| |D|
 Reduction in Impurity:
gini( A) gini( D)  giniA ( D)
 The attribute provides the smallest ginisplit(D) (or the largest
reduction in impurity) is chosen to split the node (need to
enumerate all the possible splitting points for each attribute)
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Computation of Gini Index
 Ex. D has 9 tuples in buys_computer = “yes”
2
and
2
5 in “no”
 9  5
gini ( D) 1       0.459
 14   14 
 Suppose the attribute income partitions D into 10 in D1: {low,
 10   4
medium} and 4 in D2 giniincome{low,medium} ( D)  14 Gini( D1 )   14 Gini( D2 )
   

Gini{low,high} is 0.458; Gini{medium,high} is 0.450. Thus, split on the

{low,medium} (and {high}) since it has the lowest Gini index
 All attributes are assumed continuous-valued
 May need other tools, e.g., clustering, to get the possible split
values
 11
Comparing Attribute Selection
Measures
 The three measures, in general, return good results but
 Information gain:

biased towards multivalued attributes
 Gain ratio:

tends to prefer unbalanced splits in which one partition is
much smaller than the others
 Gini index:

biased to multivalued attributes

has difficulty when # of classes is large

tends to favor tests that result in equal-sized partitions
and purity in both partitions
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Other Attribute Selection
Measures
 CHAID: a popular decision tree algorithm, measure based on χ2 test for
independence
 C-SEP: performs better than info. gain and gini index in certain cases
 G-statistic: has a close approximation to χ2 distribution
 MDL (Minimal Description Length) principle (i.e., the simplest solution is
preferred):
 The best tree as the one that requires the fewest # of bits to both (1)
encode the tree, and (2) encode the exceptions to the tree
 Multivariate splits (partition based on multiple variable combinations)
 CART: finds multivariate splits based on a linear comb. of attrs.
 Which attribute selection measure is the best?
 Most give good results, none is significantly superior than others
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Overfitting and Tree Pruning
 Overfitting: An induced tree may overfit the training data
 Too many branches, some may reflect anomalies due to

noise or outliers
 Poor accuracy for unseen samples

 Two approaches to avoid overfitting

 Prepruning: Halt tree construction early ̵ do not split a node

if this would result in the goodness measure falling below a

threshold

Difficult to choose an appropriate threshold
 Postpruning: Remove branches from a “fully grown” tree—

get a sequence of progressively pruned trees


Use a set of data different from the training data to
decide which is the “best pruned tree” 14
Enhancements to Basic Decision Tree
Induction
 Allow for continuous-valued attributes
 Dynamically define new discrete-valued attributes that
partition the continuous attribute value into a discrete set of
intervals
 Handle missing attribute values
 Assign the most common value of the attribute
 Assign probability to each of the possible values
 Attribute construction
 Create new attributes based on existing ones that are
sparsely represented
 This reduces fragmentation, repetition, and replication
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Classification in Large Databases
 Classification—a classical problem extensively studied by
statisticians and machine learning researchers
 Scalability: Classifying data sets with millions of examples and
hundreds of attributes with reasonable speed
 Why is decision tree induction popular?

relatively faster learning speed (than other classification
methods)

convertible to simple and easy to understand classification
rules

can use SQL queries for accessing databases

comparable classification accuracy with other methods
 RainForest (VLDB’98 — Gehrke, Ramakrishnan & Ganti)

Builds an AVC-list (attribute, value, class label)
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Scalability Framework for
RainForest

 Separates the scalability aspects from the criteria that

determine the quality of the tree
 Builds an AVC-list: AVC (Attribute, Value, Class_label)
 AVC-set (of an attribute X )
 Projection of training dataset onto the attribute X and
class label where counts of individual class label are
aggregated
 AVC-group (of a node n )
 Set of AVC-sets of all predictor attributes at the node n

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Rainforest: Training Set and Its
AVC Sets

Training Examples AVC-set on Age AVC-set on income

age income studentcredit_rating
buys_computerAge Buy_Computer income Buy_Computer

<=30 high no fair no yes no

yes no
<=30 high no excellent no
high 2 2
31…40 high no fair yes <=30 2 3
31..40 4 0 medium 4 2
>40 medium no fair yes
>40 low yes fair yes >40 3 2 low 3 1
>40 low yes excellent no
31…40 low yes excellent yes
AVC-set on
<=30 medium no fair no AVC-set on Student
credit_rating
<=30 low yes fair yes
student Buy_Computer Buy_Computer
>40 medium yes fair yes
Credit
<=30 medium yes excellent yes yes no
rating yes no
31…40 medium no excellent yes yes 6 1 fair 6 2
31…40 high yes fair yes no 3 4 excellent 3 3
>40 medium no excellent no
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Optimistic Algorithm for Tree
Construction)
 Use a statistical technique called bootstrapping to create
several smaller samples (subsets), each fits in memory
 Each subset is used to create a tree, resulting in several
trees
 These trees are examined and used to construct a new
tree T’
 It turns out that T’ is very close to the tree that would
be generated using the whole data set together
 Adv: requires only two scans of DB, an incremental alg.

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Presentation of Classification
Results

February 28, 2025 Data Mining: Concepts and Techniques 20

SGI/MineSet 3.0

February 28, 2025 Data Mining: Concepts and Techniques 21

Perception-Based Classification
(PBC)

Data Mining: Concepts and Techniques 22