Chapter5PPT.ppt

Data Mining

Classification: Alternative Techniques
Lecture Notes for Chapter 5

Introduction to Data Mining
by
Tan, Steinbach, Kumar

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 *

Rule-Based Classifier
Classify records by using a collection of “if…then…” rules

Rule: (Condition)  y
where
Condition is a conjunctions of attributes
y is the class label
LHS: rule antecedent or condition
RHS: rule consequent
Examples of classification rules:
(Blood Type=Warm)  (Lay Eggs=Yes)  Birds
(Taxable Income < 50K)  (Refund=Yes)  Evade=No Rule-based Classifier (Example) R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians Application of Rule-Based Classifier A rule r covers an instance x if the attributes of the instance satisfy the condition of the rule R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians The rule R1 covers a hawk => Bird
The rule R3 covers the grizzly bear => Mammal

Rule Coverage and Accuracy
Coverage of a rule:
Fraction of records that satisfy the antecedent of a rule
Accuracy of a rule:
Fraction of records that satisfy both the antecedent and consequent of a rule

(Status=Single)  No
Coverage = 40%, Accuracy = 50%

Tid

Refund

Marital

Status

Taxable

Income

Class

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

10

How does Rule-based Classifier Work?
R1: (Give Birth = no)  (Can Fly = yes)  Birds
R2: (Give Birth = no)  (Live in Water = yes)  Fishes
R3: (Give Birth = yes)  (Blood Type = warm)  Mammals
R4: (Give Birth = no)  (Can Fly = no)  Reptiles
R5: (Live in Water = sometimes)  Amphibians
A lemur triggers rule R3, so it is classified as a mammal
A turtle triggers both R4 and R5
A dogfish shark triggers none of the rules

Characteristics of Rule-Based Classifier
Mutually exclusive rules
Classifier contains mutually exclusive rules if the rules are independent of each other
Every record is covered by at most one rule

Exhaustive rules
Classifier has exhaustive coverage if it accounts for every possible combination of attribute values
Each record is covered by at least one rule

From Decision Trees To Rules
Rules are mutually exclusive and exhaustive
Rule set contains as much information as the tree

Rules Can Be Simplified
Initial Rule: (Refund=No)  (Status=Married)  No
Simplified Rule: (Status=Married)  No

Tid

Refund

Marital

Status

Taxable

Income

Cheat

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

10

Effect of Rule Simplification
Rules are no longer mutually exclusive
A record may trigger more than one rule
Solution?
Ordered rule set
Unordered rule set – use voting schemes

Rules are no longer exhaustive
A record may not trigger any rules
Solution?
Use a default class

Ordered Rule Set
Rules are rank ordered according to their priority
An ordered rule set is known as a decision list
When a test record is presented to the classifier
It is assigned to the class label of the highest ranked rule it has triggered
If none of the rules fired, it is assigned to the default class

R1: (Give Birth = no)  (Can Fly = yes)  Birds
R2: (Give Birth = no)  (Live in Water = yes)  Fishes
R3: (Give Birth = yes)  (Blood Type = warm)  Mammals
R4: (Give Birth = no)  (Can Fly = no)  Reptiles
R5: (Live in Water = sometimes)  Amphibians

Rule Ordering Schemes
Rule-based ordering
Individual rules are ranked based on their quality
Class-based ordering
Rules that belong to the same class appear together

Building Classification Rules
Direct Method:
Extract rules directly from data
e.g.: RIPPER, CN2, Holte’s 1R

Indirect Method:
Extract rules from other classification models (e.g.

decision trees, neural networks, etc).
e.g: C4.5rules

Direct Method: Sequential Covering
Start from an empty rule
Grow a rule using the Learn-One-Rule function
Remove training records covered by the rule
Repeat Step (2) and (3) until stopping criterion is met

Aspects of Sequential Covering
Rule Growing

Instance Elimination

Rule Evaluation

Stopping Criterion

Rule Pruning

Rule Growing
Two common strategies

(a) General-to-specific�

Refund= No�

Status = Single�

Status = Divorced�

Status = Married�

Income �> 80K �

…�

{ }�

Yes: 0
No: 3�

Yes: 3
No: 4�

Yes: 3
No: 4�

Yes: 2
No: 1�

Yes: 1
No: 0�

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No: 1�

Refund=No,�Status=Single,�Income=85K
(Class=Yes)�

Refund=No,�Status=Single,�Income=90K
(Class=Yes)�

Refund=No,�Status = Single�(Class = Yes)�

(b) Specific-to-general�

Rule Growing (Examples)
CN2 Algorithm:
Start from an empty conjunct: {}
Add conjuncts that minimizes the entropy measure: {A}, {A,B}, …
Determine the rule consequent by taking majority class of instances covered by the rule
RIPPER Algorithm:
Start from an empty rule: {} => class
Add conjuncts that maximizes FOIL’s information gain measure:
R0: {} => class (initial rule)
R1: {A} => class (rule after adding conjunct)
Gain(R0, R1) = t [ log (p1/(p1+n1)) – log (p0/(p0 + n0)) ]
where t: number of positive instances covered by both R0 and R1

p0: number of positive instances covered by R0
n0: number of negative instances covered by R0
p1: number of positive instances covered by R1
n1: number of negative instances covered by R1

Instance Elimination
Why do we need to eliminate instances?
Otherwise, the next rule is identical to previous rule
Why do we remove positive instances?
Ensure that the next rule is different
Why do we remove negative instances?
Prevent underestimating accuracy of rule
Compare rules R2 and R3 in the diagram

Stopping Criterion and Rule Pruning
Stopping criterion
Compute the gain
If gain is not significant, discard the new rule

Rule Pruning
Similar to post-pruning of decision trees
Reduced Error Pruning:
Remove one of the conjuncts in the rule
Compare error rate on validation set before and after pruning
If error improves, prune the conjunct

Summary of Direct Method
Grow a single rule

Remove Instances from rule

Prune the rule (if necessary)

Add rule to Current Rule Set

Repeat

Direct Method: RIPPER
For 2-class problem, choose one of the classes as positive class, and the other as negative class
Learn rules for positive class
Negative class will be default class
For multi-class problem
Order the classes according to increasing class prevalence (fraction of instances that belong to a particular class)
Learn the rule set for smallest class first, treat the rest as negative class
Repeat with next smallest class as positive class

Direct Method: RIPPER
Growing a rule:
Start from empty rule
Add conjuncts as long as they improve FOIL’s information gain
Stop when rule no longer covers negative examples
Prune the rule immediately using incremental reduced error pruning
Measure for pruning: v = (p-n)/(p+n)
p: number of positive examples covered by the rule in

the validation set
n: number of negative examples covered by the rule in

the validation set
Pruning method: delete any final sequence of conditions that maximizes v

Direct Method: RIPPER
Building a Rule Set:
Use sequential covering algorithm
Finds the best rule that covers the current set of positive examples
Eliminate both positive and negative examples covered by the rule
Each time a rule is added to the rule set, compute the new description length
stop adding new rules when the new description length is d bits longer than the smallest description length obtained so far

Direct Method: RIPPER
Optimize the rule set:
For each rule r in the rule set R
Consider 2 alternative rules:

Replacement rule (r*): grow new rule from scratch
Revised rule(r’): add conjuncts to extend the rule r
Compare the rule set for r against the rule set for r*

and r’
Choose rule set that minimizes MDL principle
Repeat rule generation and rule optimization for the remaining positive examples

Indirect Method: C4.5rules
Extract rules from an unpruned decision tree
For each rule, r: A  y,
consider an alternative rule r’: A’  y where A’ is obtained by removing one of the conjuncts in A
Compare the pessimistic error rate for r against all r’s
Prune if one of the r’s has lower pessimistic error rate
Repeat until we can no longer improve generalization error

Indirect Method: C4.5rules
Instead of ordering the rules, order subsets of rules (class ordering)
Each subset is a collection of rules with the same rule consequent (class)
Compute description length of each subset
Description length = L(error) + g L(model)
g is a parameter that takes into account the presence of redundant attributes in a rule set

(default value = 0.5)

Advantages of Rule-Based Classifiers
As highly expressive as decision trees
Easy to interpret
Easy to generate
Can classify new instances rapidly
Performance comparable to decision trees

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

Nearest Neighbor Classifiers
Basic idea:
If it walks like a duck, quacks like a duck, then it’s probably a duck

Training Records
Test Record

Compute Distance

Choose k of the “nearest” records

Nearest-Neighbor Classifiers
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)

Unknown record�

Nearest Neighbor Classification
Compute distance between two points:
Euclidean distance

Determine the class from nearest neighbor list
take the majority vote of class labels among the k-nearest neighbors
Weigh the vote according to distance
weight factor, w = 1/d2

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

Nearest neighbor Classification…
k-NN classifiers are lazy learners
It does not build models explicitly
Unlike eager learners such as decision tree induction and rule-based systems
Classifying unknown records are relatively expensive

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

Bayes Classifier
A probabilistic framework for solving classification problems
Conditional Probability:

Bayes theorem:

Bayesian Classifiers
Consider each attribute and class label as random variables

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 )

Can we estimate P(C| A1, A2,…,An ) directly from data?

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.

How to Estimate Probabilities from Data?
For continuous attributes:
Discretize the range into bins
one ordinal attribute per bin
violates independence assumption
Two-way split: (A < v) or (A > v)
choose only one of the two splits as new attribute
Probability density estimation:
Assume attribute follows a normal distribution
Use data to estimate parameters of distribution

(e.g., mean and standard deviation)
Once probability distribution is known, can use it to estimate the conditional probability P(Ai|c)

k

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)

Artificial Neural Networks (ANN)
Model is an assembly of inter-connected nodes and weighted links

Output node sums up each of its input value according to the weights of its links

Compare output node against some threshold t

Perceptron Model
or

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w1�

w2�

w3�

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Algorithm for learning ANN
Initialize the weights (w0, w1, …, wk)

Adjust the weights in such a way that the output of ANN is consistent with class labels of training examples
Objective function:

Find the weights wi’s that minimize the above objective function
e.g., backpropagation algorithm (see lecture notes)

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

Examples of Ensemble Methods
How to generate an ensemble of classifiers?
Bagging

Boosting

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

Name

Blood Type

Give Birth

Can Fly

Live in Water

Class

human

warm

yes

no

no

mammals

python

cold

no

no

no

reptiles

salmon

cold

no

no

yes

fishes

whale

warm

yes

no

yes

mammals

frog

cold

no

no

sometimes

amphibians

komodo

cold

no

no

no

reptiles

bat

warm

yes

yes

no

mammals

pigeon

warm

no

yes

no

birds

cat

warm

yes

no

no

mammals

leopard shark

cold

yes

no

yes

fishes

turtle

cold

no

no

sometimes

reptiles

penguin

warm

no

no

sometimes

birds

porcupine

warm

yes

no

no

mammals

eel

cold

no

no

yes

fishes

salamander

cold

no

no

sometimes

amphibians

gila monster

cold

no

no

no

reptiles

platypus

warm

no

no

no

mammals

owl

warm

no

yes

no

birds

dolphin

warm

yes

no

yes

mammals

eagle

warm

no

yes

no

birds

Name

Blood Type

Give Birth

Can Fly

Live in Water

Class

hawk

warm

no

yes

no

?

grizzly bear

warm

yes

no

no

?

Tid Refund Marital

Status

Taxable

Income

Class

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

10

Name

Blood Type

Give Birth

Can Fly

Live in Water

Class

lemur

warm

yes

no

no

?

turtle

cold

no

no

sometimes

?

dogfish shark

cold

yes

no

yes

?

YES

YES

NO

NO

NO

NO

NO

NO

Yes

No

{Married}

{Single,

Divorced}

< 80K > 80K

Taxable

Income

Marital

Status

Refund

Classification Rules

(Refund=Yes) ==> No

(Refund=No, Marital Status={Single,Divorced},

Taxable Income<80K) ==> No

(Refund=No, Marital Status={Single,Divorced},

Taxable Income>80K) ==> Yes

(Refund=No, Marital Status={Married}) ==> No

Tid

Refund

Marital

Status

Taxable

Income

Cheat

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

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7

Yes

Divorced

220K

No

8

No

Single

85K

Yes

9

No

Married

75K

No

10

No

Singl

e

90K

Yes

10

Name

Blood Type

Give Birth

Can Fly

Live in Water

Class

turtle

cold

no

no

sometimes

?

Status =

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Status =

Divorced

Status =

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Income

> 80K

Yes: 3

No: 4

{ }

Yes: 0

No: 3

Refund=

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Yes: 3

No: 4

Yes: 2

No: 1

Yes: 1

No: 0

Yes: 3

No: 1

(a) General-to-specific

Refund=No,

Status=Single,

Income=85K

(Class=Yes)

Refund=No,

Status=Single,

Income=90K

(Class=Yes)

Refund=No,

Status = Single

(Class = Yes)

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