Rule Based Classifier

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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
Rule-based Classifier
Edited by : Arooba Saeed
(SP20-RSE-006)
Comsens lab, Department of Computer Science
Under the Supervision: Dr. Nadeem Javaid
Professor, Department of Computer Science
COMSATS University Islamabad, Islamabad Pakistan
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Rule-based Classifier
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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 pre-condition
RHS: rule consequent
Rules : R=(R1R2 …  Rk)
Examples of classification rules:
(Blood Type=Warm) (Lay Eggs=Yes) Birds
(Taxable Income < 50K)  (Refund=Yes) Evade=No
https://slideplayer.com/slide/3333694/

Example of Rule-based Classifier
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
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
https://slideplayer.com/slide/3333694/
Figure.1: Vertebrates Dataset

Application of Rule-Based Classifier
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
A rule r covers a record x if the attributes of the record satisfy the condition of the rule. Rule r is
also said to be triggered or fired whenever it covers a given record.
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
https://slideplayer.com/slide/3333694/

Rule Coverage and Accuracy
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
1Yes Single 125K No
2No Married 100K No
3No Single 70K No
4Yes Married 120K No
5No Divorced 95K Yes
6No Married 60K No
7Yes Divorced 220K No
8No Single 85K Yes
9No Married 75K No
10 No Single 90K Yes
https://slideplayer.com/slide/3333694/
Figure. 2: Taxable Income Dataset

How does Rule-based Classifier Work?
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
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 ?
https://slideplayer.com/slide/3333694/

Characteristics of Rule-Based Classifier
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
Mutually exclusive rules
Classifier contains mutually exclusive rules if no two rules are triggered by the same
record.
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
https://slideplayer.com/slide/3333694/

From Decision Trees To Rules
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
Rules are mutually exclusive and exhaustive.
Rule set contains as much information as the tree.
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
https://slideplayer.com/slide/3333694/

Rules Can Be Simplified
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
https://slideplayer.com/slide/3333694/
Figure. 2: Taxable Income Dataset

Effect of Rule Simplification
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
https://slideplayer.com/slide/3333694/

Ordered Rule Set
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
https://slideplayer.com/slide/3333694/

Rule Ordering Schemes
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
Rule-based ordering
Individual rules are ranked based on their quality
Class-based ordering
Rules that belong to the same class appear together
Rule-based Ordering
(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
Class-based Ordering
(Refund=Yes) ==> No
(Refund=No, Marital Status={Single,Divorced},
Taxable Income<80K) ==> No
(Refund=No, Marital Status={Married}) ==> No
(Refund=No, Marital Status={Single,Divorced},
Taxable Income>80K) ==> Yes
https://slideplayer.com/slide/3333694/

Building Classification Rules
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
https://slideplayer.com/slide/3333694/

Direct Method: Sequential Covering
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
(i) Original Data (ii) Step 1
https://slideplayer.com/slide/3333694/ Figure. 3: Example

Example of Sequential Covering
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
(iii) Step 2 (iv) Step 3
https://slideplayer.com/slide/3333694/
Figure. 4: Example

Aspects of Sequential Covering
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
There are many aspects of sequential covering:
Rule Growing
Instance Elimination
Rule Evaluation
Stopping Criterion
Rule Pruning
Rule Growing:
In rule growing, there are two common strategies:
(a) General-to-specific (b) Specific-to-general
https://slideplayer.com/slide/3333694/ Figure. 5: General to Specific

Rule Growing (Examples)
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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)) ] (1)
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
https://slideplayer.com/slide/3333694/

Instance Elimination
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
https://slideplayer.com/slide/3333694/
Figure. 6: Instances Elimination

Rule Evaluation
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
Metrics:
Accuracy (2)
Laplace (3)
M-estimate (4)
n : Number of instances covered by rule
nc : Number of instances covered by rule
k : Number of classes
p : Prior probability
https://slideplayer.com/slide/3333694/

Stopping Criterion and Rule Pruning
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
https://slideplayer.com/slide/3333694/

Direct Method: RIPPER (1/3)
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
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
https://slideplayer.com/slide/3333694/

Direct Method: RIPPER (2/3)
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
Measure for pruning:
 v = (p-n)/(p+n) (5)
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
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
https://slideplayer.com/slide/3333694/

Direct Method: RIPPER (3/3)
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
https://slideplayer.com/slide/3333694/

Indirect Methods
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
Extract rules from an unpruned decision tree
https://slideplayer.com/slide/3333694/

Direct Method: RIPPER
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
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
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) (5)
g is a parameter that takes into account the presence of redundant attributes in a rule set
(default value = 0.5)
https://slideplayer.com/slide/3333694/

Advantages
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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
As highly expressive as decision trees
Easy to interpret
Easy to generate
Can classify new instances rapidly
Performance comparable to decision trees
https://slideplayer.com/slide/3333694/

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Department of Computer Science, COMSATS University Islamabad, Islamabad-Pakistan
Thank You !!!