1. Classification 1

2. Classification – most familiar & most popular data mining technique.
Classification algorithms – statistical, decision tree,
neural network, rules, etc.
True positive: predicted, and actually in it
False positive: predicted, but is not actually in it
True negative: not predicted, and not actually in it
False negative: not predicted, but is actually in it q 2

3. Classification vs. Predictionq •
predicts categorical class labels (discrete or nominal)
classifies data (constructs a model) based on the
training set and the values (class labels) in a
classifying attribute and uses it in classifying new data
Prediction q •
models continuous-valued functions, i.e., predicts
unknown or missing values
Typical applications q •
Credit approval
Target marketing
Medical diagnosis
Fraud detection 3
Han & Kamber

4. Classification—A Two-Step Process
Model construction: describing a set of predetermined classes q •
Each tuple/sample is assumed to belong to a predefined class, as
determined by the class label attribute
The set of tuples used for model construction is training set
The model is represented as classification rules, decision trees, or
mathematical formulae
Model usage: for classifying future or unknown objects q •
Estimate accuracy of the model
• The known label of test sample is compared with the classified result
from the model
• Accuracy rate is the percentage of test set samples that are correctly
classified by the model
• Test set is independent of training set, otherwise over-fitting will
occur
If the accuracy is acceptable, use the model to classify data tuples
whose class labels are not known 4
Han & Kamber

5. Process (1): Model Construction Classification
Algorithms
Training
Data
Classifier
(Model)
IF rank = ‘professor’
OR years > 6
NAME
RANK
YEARS
TENURED
Mike
Assistant Prof 3 no
Mary 7
yes
Bill
Professor 2
Jim
Associate Prof
Dave 6
Anne
THEN tenured = ‘yes’
Han & Kamber 5

6. Process (2): Using the Model in Prediction
Classifier
Testing
Data
Unseen Data
(Jeff, Professor, 4)
Tenured?
NAME
RANK
YEARS
TENURED
Tom
Assistant Prof 2 no
Merlisa
Associate Prof 7
George
Professor 5
yes
Joseph 6
Han & Kamber

7. Supervised vs. Unsupervised Learning
Supervised learning (classification) q •
Supervision: The training data (observations,
measurements, etc.) are accompanied by labels
indicating the class of the observations
New data is classified based on the training set
Unsupervised learning (clustering) q •
The class labels of training data is unknown
Given a set of measurements, observations, etc. with
the aim of establishing the existence of classes or
clusters in the data 7
Han & Kamber

8. Issues: Data Preparation
Data cleaning q •
Preprocess data in order to reduce noise and handle
missing values
Relevance analysis (feature selection) q •
Remove the irrelevant or redundant attributes
Data transformation q •
Generalize and/or normalize data 8
Han & Kamber

9. Issues: Evaluating Classification Methods
Accuracy q •
classifier accuracy: predicting class label
predictor accuracy: guessing value of predicted attributes
Speed q •
time to construct the model (training time)
time to use the model (classification/prediction time)
Robustness: handling noise and missing values
Scalability: efficiency in disk-resident databases
Interpretability q •
understanding and insight provided by the model
Other measures, e.g., goodness of rules, such as decision
tree size or compactness of classification rules q 9
Han & Kamber

10. Classification Performance
True Positive
False Positive
False Negative
True Negative 10
Dunham

11. Confusion Matrix
Predicted Class
YES NO
Actual Class TP FN FP TN 11

12. Accuracy = number of correct prediction s total number of predictions
= TP + TN
TP + TN + FP + FN
Error rate = number of wrong predictions
= FN + FP
Sensitivity = TP rate =TP / (TP + FP)
Specificity = TN rate = TN / (TN + FN) q 12

13. This follows an example of Quinlan’s ID3 (Playing Tennis)
Decision Tree Induction: Training Dataset
This
follows an
example of
Quinlan’s
ID3
(Playing
Tennis)
age
income
student
credit_rating
buys_computer
<=30
high no
fair
excellent
31…40
yes
>40
medium
low
ID3 : Iterative Dichotomizer 13
Han & Kamber

14. Output: A Decision Tree for “buys_computer” root
arc
age?
node
<=30
student?
31..40
yes
>40
credit rating?
excellent no
fair
yes no
yes no 14
Han & Kamber

15. Algorithm for Decision Tree Induction
Basic algorithm (a greedy algorithm) q •
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 q •
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 15
Han & Kamber

16. 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|
m m
i i
i = i = 1
log2 n is used because information is encoded in bits. If m=4, then the
outcomes can be measured in bits as  1 
log10 n  m 
log10 2
Entropy: a measure of uncertainty in communication systems (Shannon, 1948)
Expected information (entropy) needed to classify a tuple in
D: Info( D) = − ∑ p log ( p ) = − ∑ | ci | log | ci |
| D |
| D |
− log 2 
 = 2
log 2 n =
D: Data Partition
m: number of distinct classes 16
Han & Kamber

17. ∑ Information needed (after using A to split D into vq
partitions) to classify D:
v | D j |
j = 1 | D | ∑
InfoA ( D) =
× I ( D j ); v ∈ A
| D j |
| D |
= weightage of the jth partition
Information gained by branching on attribute A
Gain(A) = Info(D) − InfoA(D) q 17

18. Gain(credit _ rating ) = 0.048
Attribute Selection: Information Gain
Class P: buys_computer = “yes” 5 14 4 14
Class N: buys_computer = “no”
Infoage ( D) =
I (2,3) +
I (4,0) 9 14 9 14 5 14 5 14 5 14
Info( D) = I (9,5) = -
log 2 (
) -
) = 0.940 +
I (3,2) = 0.694
log 2 (
age
<=30
31…40
>40 pi 2 4 3
ni I(pi, ni) 5 14
out of 14 samples, with 2
yes’es and 3 no’s. Hence
Gain(age) = Info( D) − Infoage ( D) = 0.246
I (2,3) means “age <=30” has 5
age
income
student
credit_rating
buys_computer
<=30
high no
fair
excellent
31…40
yes
>40
medium
low
Similarly,
Gain(income) = 0.029
Gain(student ) = 0.151
Gain(credit _ rating ) = 0.048 18
Han & Kamber

19. Computing Information-Gain for Continuous-Value Attributes
Let attribute A be a continuous-valued attribute
Must determine the best split point for A q •
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: q •
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 19
Han & Kamber

20. 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
j = 1 | D | | D | q
| D j | | D j |
SplitInfo A ( D) = − ∑
× log 2 ( )
GainRatio(A) = Gain(A)/SplitInfo(A) 6 14 4 14 4 14
SplitInfo A ( D) = −
× log 2 (
) −
× log 2 (
) −
× log 2 (
) = 0.926 •
Ex. q •
gain_ratio(income) = 0.029/0.926 = 0.031
The attribute with the maximum gain ratio is selected
as the splitting attribute q 20
Han & Kamber

21. Gini index (CART, IBM IntelligentMiner)
If a data set D contains examples from n classes, gini index,
gini(D) is defined as n
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
( D gini(D2)
|D| |D| q 2
index gini(D) is defined asD) = |D1| gini(
|D2 |
) +
gini A
∆ gini( A) = gini(D) − giniA (D)
Reduction in Impurity: q
The attribute provides the smallest ginisplit(D) (or the largest q
reduction in impurity) is chosen to split the node (need to
enumerate all the possible splitting points for each attribute)Han & Kamber 21

22. Gini index (CART, IBM IntelligentMiner)
Ex. D has 9 tuples in buys_computer = “yes” and 5 in “no”
gini( D) = 1 −   −   = 0.459
 14   14 
Suppose the attribute income partitions D into 10 in D1: {low, q
 9 
 5 
medium} and 4 in D giniincome∈ {low,medium}
 10   4 
( D) = 
 Gini( D ) + 
 Gini( D )
 14 
 14 
but gini{medium,high} is 0.30 and thus the best since it is the lowest
All attributes are assumed continuous-valued
May need other tools, e.g., clustering, to get the possible split
values q 22
Can be modified for categorical attributes q
Han & Kamber

23. Naïve Bayesian Classifier: Training Dataset
age
income studentcredit_ratingbuys_compu
<=30
high no
fair
excellent no
Class:
C1:buys_computer = ‘yes’
C2:buys_computer = ‘no’
Data sample
X = (age <=30,
Income = medium,
Student = yes
Credit_rating = Fair)
31…40
>40
<=30
high
medium
low no
yes
fair
excellent
yes no
>40
medium no
excellent no 23

24. Naïve Bayesian Classifier: An Example
P(Ci): q
P(buys_computer = “yes”) = 9/14 = 0.643
P(buys_computer = “no”) = 5/14= 0.357
Compute P(X|Ci) for each class
P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222
P(income = “medium” | buys_computer = “yes”) = 4/9 = 0.444
P(student = “yes” | buys_computer = “yes) = 6/9 = 0.667
P(credit_rating = “fair” | buys_computer = “yes”) = 6/9 = 0.667
P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6
P(income = “medium” | buys_computer = “no”) = 2/5 = 0.4
P(student = “yes” | buys_computer = “no”) = 1/5 = 0.2
P(credit_rating = “fair” | buys_computer = “no”) = 2/5 = 0.4
X = (age <= 30 , income = medium, student = yes, credit_rating = fair) q
P(X|Ci) : P(X|buys_computer = “yes”) = x x x = 0.044
P(X|buys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019
P(X|Ci)*P(Ci) : P(X|buys_computer = “yes”) * P(buys_computer = “yes”) = 0.028
P(X|buys_computer = “no”) * P(buys_computer = “no”) = 0.007
Therefore, X belongs to class (“buys_computer = yes”) 24