Transcript Rule-Based Classifier

Classification: Alternative Techniques
Lecture Notes for Chapter 5
Introduction to Data Mining
by
Tan, Steinbach, Kumar
© Tan,Steinbach, Kumar
Introduction to Data Mining
1
Instance-Based Classifiers
Set of Stored Cases
Atr1
……...
AtrN
Class
A
• Store the training records
• Use training records to
predict the class label of
unseen cases
B
B
C
A
Unseen Case
Atr1
C
B
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
……...
AtrN
Instance Based Classifiers

Examples:
– Rote-learner
Memorizes entire training data and performs
classification only if attributes of record match one of
the training examples exactly

– Nearest neighbor
Uses k “closest” points (nearest neighbors) for
performing classification

© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Nearest Neighbor Classifiers

Basic idea:
– If it walks like a duck, quacks like a duck, then
it’s probably a duck
Compute
Distance
Training
Records
© Tan,Steinbach, Kumar
Test
Record
Choose k of the
“nearest” records
Introduction to Data Mining
‹#›
Nearest-Neighbor Classifiers
Unknown record

Requires three things
– The set of stored records
– Distance Metric to compute
distance between records
– The value of k, the number of
nearest neighbors to retrieve

To classify an unknown record:
– Compute distance to other
training records
– Identify k nearest neighbors
– Use class labels of nearest
neighbors to determine the
class label of unknown record
(e.g., by taking majority vote)
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Definition of Nearest Neighbor
X
(a) 1-nearest neighbor
X
X
(b) 2-nearest neighbor
(c) 3-nearest neighbor
K-nearest neighbors of a record x are data points
that have the k smallest distance to x
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Nearest Neighbor Classification

Compute distance between two points:
– Euclidean distance
d ( p, q ) 

 ( pi
i
q )
2
i
Determine the class from nearest neighbor list
– take the majority vote of class labels among
the k-nearest neighbors
– Weight the vote according to distance

weight factor, w = 1/d2
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Nearest Neighbor Classification…

Choosing the value of k:
– If k is too small, sensitive to noise points
– If k is too large, neighborhood may include points from
other classes
X
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Nearest Neighbor Classification…

Scaling issues
– Attributes may have to be scaled to prevent
distance measures from being dominated by
one of the attributes
– Example:
height of a person may vary from 1.5m to 1.8m
 weight of a person may vary from 90lb to 300lb
 income of a person may vary from $10K to $1M

originalVa lue  oldMin
newValue 
oldMax  oldMin
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Nearest neighbor Classification…

k-NN classifiers are lazy learners
– It does not build models explicitly
– Unlike eager learners such as decision tree
induction
– Classifying unknown records are relatively
expensive
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Example: PEBLS

PEBLS: Parallel Examplar-Based Learning
System (Cost & Salzberg)
– Works with both continuous and nominal
features
For
nominal features, distance between two
nominal values is computed using modified value
difference metric (MVDM)
– Each record is assigned a weight factor
– Number of nearest neighbor, k = 1
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Example: PEBLS
Tid Refund Marital
Status
Taxable
Income Cheat
1
Yes
Single
125K
No
d(Single,Married)
2
No
Married
100K
No
= | 2/4 – 0/4 | + | 2/4 – 4/4 | = 1
3
No
Single
70K
No
d(Single,Divorced)
4
Yes
Married
120K
No
5
No
Divorced 95K
Yes
6
No
Married
No
d(Married,Divorced)
7
Yes
Divorced 220K
No
= | 0/4 – 1/2 | + | 4/4 – 1/2 | = 1
8
No
Single
85K
Yes
d(Refund=Yes,Refund=No)
9
No
Married
75K
No
= | 0/3 – 3/7 | + | 3/3 – 4/7 | = 6/7
10
No
Single
90K
Yes
60K
Distance between nominal attribute values:
= | 2/4 – 1/2 | + | 2/4 – 1/2 | = 0
10
Class
Marital Status
Single
Married
Divorced
Yes
2
0
1
No
2
4
n
4
4
© Tan,Steinbach, Kumar
Class
Refund
Yes
No
Yes
0
3
1
No
3
4
2
n
3
7
Introduction to Data Mining
d (V1 ,V2 )  
i
‹#›
n1i n2i

n1 n2
Example: PEBLS
Tid Refund Marital
Status
Taxable
Income Cheat
X
Yes
Single
125K
No
Y
No
Married
100K
No
10
Distance between record X and record Y:
d
( X , Y )  wX wY  d ( X i , Yi )
2
i 1
where:
Number of times X is used for prediction
wX 
Number of times X predicts correctly
wX  1 if X makes accurate prediction most of the time
wX > 1 if X is not reliable for making predictions
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Bayes Classifier
A probabilistic framework for solving classification
problems
Joint
Prob.
 Posterior Probability:
P ( A, C )
P (C | A) 
P ( A)
Prior

P ( A, C )
P( A | C ) 
P (C )

Bayes theorem:
P( A | C ) P(C )
P(C | A) 
P( A)
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Prob.
Example of Bayes Theorem

Given:
– A doctor knows that meningitis causes stiff neck 50% (0.5) of
the time
– Prior probability of any patient having meningitis is 1/50,000
– Prior probability of any patient having stiff neck is 1/20

If a patient has stiff neck, what’s the probability
he/she has meningitis?
P( S | M ) P( M ) 0.5 1 / 50000
P( M | S ) 

 0.0002
P( S )
1 / 20
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Bayesian Classifiers

Given a record with attributes (A1, A2,…,An)
– Goal is to predict class C
– Specifically, we want to find the value of C that
maximizes P(C| A1, A2,…,An )
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Bayesian Classifiers

Approach:
– compute the posterior probability P(C | A1, A2, …, An) for
all values of C using the Bayes theorem
P ( A A  A | C ) P (C )
P (C | A A  A ) 
P( A A  A )
1
1
2
2
n
n
1
2
n
– Choose value of C that maximizes
P(C | A1, A2, …, An)
– Equivalent to choosing value of C that maximizes
P(A1, A2, …, An|C) P(C)
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Naïve Bayes Classifier

Assume independence among attributes Ai when class is
given:
– P(A1, A2, …, An |C) = P(A1| Cj) P(A2| Cj)… P(An| Cj)
– Can estimate P(Ai| Cj) for all Ai and Cj.
– New point is classified to Cj if P(Cj)  P(Ai| Cj) is
maximal.
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
How to Estimate
Probabilities
from
Data?
l
l
c
Tid
at
Refund
o
eg
a
c
i
r
c
at
o
eg
a
c
i
r
c
on
u
it n
s
u
o
s
s
a 
cl
Marital
Status
Taxable
Income
Evade
1
Yes
Single
125K
No
2
No
Married
100K
No
3
No
Single
70K
No
4
Yes
Married
120K
No
5
No
Divorced
95K
Yes
6
No
Married
60K
No
7
Yes
Divorced
220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes
Class: P(C) = Nc/N
– e.g., P(No) = 7/10,
P(Yes) = 3/10

For nominal attributes:
P(Ai | Ck) = |Aik|/ Nc k
– where |Aik| is number of
instances having attribute
Ai and belongs to class Ck
– Examples:
10
© Tan,Steinbach, Kumar
Introduction to Data Mining
P(Status=Married|No) = 4/7
P(Refund=Yes|Yes)=0
‹#›
How to Estimate
Probabilities
f
or
continues
s
al
al
u
c
c
o
ri
ri
u
o
o
g
tin
attributes
ss
eg
e?
t
t
n
a
l
a
a
c
Tid
Refund
co
c
Marital
Status
Taxable
Income
c
Evade
1
Yes
Single
125K
No
2
No
Married
100K
No
3
No
Single
70K
No
4
Yes
Married
120K
No
5
No
Divorced
95K
Yes
6
No
Married
60K
No
7
Yes
Divorced
220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes

Normal distribution:
1
P( A | c ) 
e
2
i
j

( Ai   ij ) 2
2  ij2
2
ij
– One for each (Ai,ci) pair

For (Income, Class=No):
– If Class=No

sample mean = 110

sample variance = 2975
10
1
P( Income  120 | No) 
e
2 (54.54)
© Tan,Steinbach, Kumar
Introduction to Data Mining

( 120110) 2
2 ( 2975)
‹#›
 0.0072
Example of Naïve Bayes Classifier
Given a Test Record:
X  (Refund  No, Married, Income  120K)
naive Bayes Classifier:
P(Refund=Yes|No) = 3/7
P(Refund=No|No) = 4/7
P(Refund=Yes|Yes) = 0
P(Refund=No|Yes) = 1
P(Marital Status=Single|No) = 2/7
P(Marital Status=Divorced|No)=1/7
P(Marital Status=Married|No) = 4/7
P(Marital Status=Single|Yes) = 2/7
P(Marital Status=Divorced|Yes)=1/7
P(Marital Status=Married|Yes) = 0
For taxable income:
If class=No:
sample mean=110
sample variance=2975
If class=Yes: sample mean=90
sample variance=25
© Tan,Steinbach, Kumar

P(X|Class=No) = P(Refund=No|Class=No)
 P(Married| Class=No)
 P(Income=120K| Class=No)
= 4/7  4/7  0.0072 = 0.0024

P(X|Class=Yes) = P(Refund=No| Class=Yes)
 P(Married| Class=Yes)
 P(Income=120K| Class=Yes)
= 1  0  (1.2  10-9)= 0
Since P(X|No)P(No) > P(X|Yes)P(Yes)
Therefore P(No|X) > P(Yes|X)
=> Class = No
Introduction to Data Mining
‹#›
Naïve Bayes Classifier
If one of the conditional probability is zero, then
the entire expression becomes zero
 Probability estimation:

N ic
Original : P( Ai | C ) 
Nc
N ic  1
Laplace : P( Ai | C ) 
Nc  c
N ic  mp
m - estimate : P( Ai | C ) 
Nc  m
© Tan,Steinbach, Kumar
Introduction to Data Mining
c: number of classes
p: prior probability
m: parameter
‹#›
Example of Naïve Bayes Classifier
Name
human
python
salmon
whale
frog
komodo
bat
pigeon
cat
leopard shark
turtle
penguin
porcupine
eel
salamander
gila monster
platypus
owl
dolphin
eagle
Give Birth
yes
Give Birth
yes
no
no
yes
no
no
yes
no
yes
yes
no
no
yes
no
no
no
no
no
yes
no
Can Fly
no
no
no
no
no
no
yes
yes
no
no
no
no
no
no
no
no
no
yes
no
yes
Can Fly
no
© Tan,Steinbach, Kumar
Live in Water Have Legs
no
no
yes
yes
sometimes
no
no
no
no
yes
sometimes
sometimes
no
yes
sometimes
no
no
no
yes
no
Class
yes
no
no
no
yes
yes
yes
yes
yes
no
yes
yes
yes
no
yes
yes
yes
yes
no
yes
mammals
non-mammals
non-mammals
mammals
non-mammals
non-mammals
mammals
non-mammals
mammals
non-mammals
non-mammals
non-mammals
mammals
non-mammals
non-mammals
non-mammals
mammals
non-mammals
mammals
non-mammals
Live in Water Have Legs
yes
no
Class
?
Introduction to Data Mining
A: attributes
M: mammals
N: non-mammals
6 6 2 2
P( A | M )      0.06
7 7 7 7
1 10 3 4
P( A | N )      0.0042
13 13 13 13
7
P( A | M ) P ( M )  0.06   0.021
20
13
P( A | N ) P( N )  0.004   0.0027
20
P(A|M)P(M) > P(A|N)P(N)
=> Mammals
‹#›
Naïve Bayes (Summary)

Robust to isolated noise points

Handle missing values by ignoring the instance
during probability estimate calculations

Robust to irrelevant attributes

Independence assumption may not hold for some
attributes
– Use other techniques such as Bayesian Belief
Networks (BBN)
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Ensemble Methods

Construct a set of classifiers from the training
data

Predict class label of previously unseen records
by aggregating predictions made by multiple
classifiers
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
General Idea
D
Step 1:
Create Multiple
Data Sets
Step 2:
Build Multiple
Classifiers
D1
D2
C1
C2
Step 3:
Combine
Classifiers
© Tan,Steinbach, Kumar
....
Original
Training data
Dt-1
Dt
Ct -1
Ct
C*
Introduction to Data Mining
‹#›
Why does it work?

Suppose there are 25 base classifiers
– Each classifier has error rate,  = 0.35
– Assume classifiers are independent
– Probability that the ensemble classifier makes
a wrong prediction:
 25  i
25i



(
1


)
 0.06

 i 
i 13 

25
If the base classifiers are independent, the ensemble
makes a wrong prediction only if more than half of them
predict incorrectly.
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Examples of Ensemble Methods

How to generate an ensemble of classifiers?
– Bagging
– Boosting
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Bagging

Sampling with replacement
Original Data
Bagging (Round 1)
Bagging (Round 2)
Bagging (Round 3)

1
7
1
1
2
8
4
8
3
10
9
5
4
8
1
10
5
2
2
5
6
5
3
5
7
10
2
9
8
10
7
6
9
5
3
3
10
9
2
7
Build classifier on each bootstrap sample
Approximately 63% of the original training data
are presented in each round
 Each sample has probability 1-(1-1/N)^N=1 – 1/e
= 0.63 of being selected

© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Bagging (example)
Error rate = 2/10
actual
Error rate = 2/10
Error rate = 2/10
Error rate = 2/10
Error rate = 2/10
Error rate = 1/10
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Bagging (example)
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Boosting

An iterative procedure to adaptively change
distribution of training data by focusing more on
previously misclassified records
– Initially, all N records are assigned equal
weights
– Unlike bagging, weights may change at the
end of boosting round
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Boosting
Records that are wrongly classified will have their
weights increased
 Records that are classified correctly will have
their weights decreased

Original Data
Boosting (Round 1)
Boosting (Round 2)
Boosting (Round 3)
1
7
5
4
2
3
4
4
3
2
9
8
4
8
4
10
5
7
2
4
6
9
5
5
7
4
1
4
8
10
7
6
9
6
4
3
10
3
2
4
• Example 4 is hard to classify
• Its weight is increased, therefore it is more
likely to be chosen again in subsequent rounds
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›
Example for boosting
5.16 = -1* 1,738+ 1 * 2,7784+ 1 * 4,1195
© Tan,Steinbach, Kumar
Introduction to Data Mining
‹#›