When thinking about the association rule, answer the following questions this week.? What is the association rule in da
When thinking about the association rule, answer the following questions this week.
- What is the association rule in data mining?
- Why is the association rule especially important in big data analysis?
- How does the association rule allow for more advanced data interpretation?
Read:
- ch. 5 in textbook: Association Analysis: Basic Concepts and Algorithms
- Abdel-Basset, M. (2018). Neutrosophic Association Rule Mining Algorithm for Big Data Analysis. Symmetry (Basel), 10(4), 106–.
Watch:
also read attached ppt and watch the video attached. (Mandatory)
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�
Yes: 3 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
S�
X1�
X2�
X3�
Y�
Black box�
w1�
w2�
w3�
t�
Output node�
�
Input nodes�
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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
No
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 =
Single
Status =
Divorced
Status =
Married
Income
> 80K
…
Yes: 3
No: 4
{ }
Yes: 0
No: 3
Refund=
No
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)
(b) Specific-to-general
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