Download Classification: Definition Given a collection of records (training set

Classification: Definition
Illustrating Classification Task
Given a collection of records (training
set)
Find a model for class attribute as a
function of the values of other attributes.
Goal: previously unseen records should
be assigned a class as accurately as
possible.
Tid
Attrib1
1
Yes
Large
125K
No
2
No
Medium
Attrib2
100K
Attrib3
No
Class
3
No
Small
70K
No
4
Yes
Medium
120K
No
5
No
Large
95K
Yes
6
No
Medium
60K
No
7
Yes
Large
220K
No
8
No
Small
85K
Yes
9
No
Medium
75K
No
10
No
Small
90K
Yes
Learn
Model
10
– A test set is used to determine the
accuracy.
Tid
Attrib1
11
No
Small
Attrib2
55K
Attrib3
?
12
Yes
Medium
80K
?
13
Yes
Large
110K
?
14
No
Small
95K
?
15
No
Large
67K
?
Apply
Model
Class
10
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
1
Examples of Classification Task
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
2
Classification Techniques
Decision Tree based Methods
Rule-based Methods
Memory based reasoning
Neural Networks
Naïve Bayes and Bayesian Belief Networks
Support Vector Machines
Predicting tumor cells as benign or malignant
Classifying credit card transactions
as legitimate or fraudulent
Classifying secondary structures of protein
as alpha-helix, beta-sheet, or random
coil
Categorizing news stories as finance,
weather, entertainment, sports, etc
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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Example of a Decision Tree
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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
No
7
Yes
Divorced 220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes
60K
© Tan,Steinbach, Kumar
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Yes
No
NO
MarSt
Single, Divorced
TaxInc
NO
4/18/2004
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Another Example of Decision Tree
Splitting Attributes
< 80K
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Married
NO
> 80K
YES
10
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
No
7
Yes
Divorced 220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes
60K
Married
MarSt
NO
Single,
Divorced
Refund
No
Yes
NO
TaxInc
< 80K
> 80K
NO
YES
There could be more than one tree that
fits the same data!
10
Model: Decision Tree
Training Data
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
5
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
6
Decision Tree Classification Task
Tid
Attrib1
1
Yes
Large
Attrib2
125K
Attrib3
No
2
No
Medium
100K
No
3
No
Small
70K
No
4
Yes
Medium
120K
No
5
No
Large
95K
Yes
6
No
Medium
60K
No
7
Yes
Large
220K
No
8
No
Small
85K
Yes
9
No
Medium
75K
No
10
No
Small
90K
Yes
Apply Model to Test Data
Test Data
Class
Start from the root of tree.
Refund
Yes
Learn
Model
Attrib1
11
No
Small
Attrib2
55K
Attrib3
?
Class
12
Yes
Medium
80K
?
13
Yes
Large
110K
?
14
No
Small
95K
?
15
No
Large
67K
?
No
80K
Married
?
10
MarSt
Single, Divorced
Tid
Taxable
Income Cheat
No
NO
10
Apply
Model
Refund Marital
Status
Decision
Tree
TaxInc
< 80K
Married
NO
> 80K
NO
YES
10
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
7
Apply Model to Test Data
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
Apply Model to Test Data
Test Data
Refund
Yes
Test Data
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
Refund
10
No
NO
Yes
TaxInc
< 80K
NO
TaxInc
NO
< 80K
4/18/2004
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Apply Model to Test Data
Married
NO
YES
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
Refund
Test Data
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
Refund
10
No
NO
Yes
TaxInc
< 80K
NO
© Tan,Steinbach, Kumar
Married
Introduction to Data Mining
TaxInc
< 80K
NO
4/18/2004
11
No
80K
Married
?
MarSt
NO
YES
Taxable
Income Cheat
10
Single, Divorced
> 80K
Refund Marital
Status
No
NO
MarSt
Single, Divorced
10
Apply Model to Test Data
Test Data
Yes
?
> 80K
NO
Introduction to Data Mining
80K
Married
10
Single, Divorced
YES
© Tan,Steinbach, Kumar
Taxable
Income Cheat
No
MarSt
Married
> 80K
Refund Marital
Status
No
NO
MarSt
Single, Divorced
8
© Tan,Steinbach, Kumar
Married
NO
> 80K
YES
Introduction to Data Mining
4/18/2004
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Apply Model to Test Data
Decision Tree Classification Task
Test Data
Refund
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
Tid
Attrib1
1
Yes
Large
125K
No
2
No
Medium
Attrib2
100K
Attrib3
No
Class
3
No
Small
70K
No
4
Yes
Medium
120K
No
5
No
Large
95K
Yes
6
No
Medium
60K
No
7
Yes
Large
220K
No
8
No
Small
85K
Yes
9
No
Medium
75K
No
10
No
Small
90K
Yes
10
Yes
No
NO
MarSt
Assign Cheat to “No”
Married
Single, Divorced
TaxInc
10
NO
< 80K
> 80K
NO
Learn
Model
YES
Tid
Attrib1
11
No
Small
Attrib2
55K
Attrib3
?
Class
12
Yes
Medium
80K
?
13
Yes
Large
110K
?
14
No
Small
95K
?
15
No
Large
67K
?
Apply
Model
Decision
Tree
10
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
13
Decision Tree Induction
Introduction to Data Mining
Refund
Yes
No
Don’t
Cheat
Don’t
Cheat
Refund
Refund
Yes
Yes
No
Dt = set of training
records of node t
General Procedure:
– If Dt only records of
same class yt t leaf
node labeled as yt
– Else: use an attribute
test to split the data.
Recursively apply the
procedure to each
subset.
No
15
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
No
7
Yes
Divorced 220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes
60K
10
Don’t
Cheat
Marital
Status
Single,
Divorced
Cheat
Married
Don’t
Cheat
Single,
Divorced
© Tan,Steinbach, Kumar
Marital
Status
>= 80K
Don’t
Cheat
Cheat
Introduction to Data Mining
14
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
No
7
Yes
Divorced 220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes
60K
10
Dt
?
Introduction to Data Mining
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Tree Induction
Greedy strategy.
– Split the records based on an attribute test
that optimizes a local criterion.
Issues
– Determine how to split the records
How
Don’t
Cheat
< 80K
© Tan,Steinbach, Kumar
How
Married
Taxable
Income
Don’t
Cheat
4/18/2004
4/18/2004
Hunt’s Algorithm
Don’t
Cheat
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General Structure of Hunt’s Algorithm
Many Algorithms:
– Hunt’s Algorithm (one of the earliest)
– CART
– ID3, C4.5
– SLIQ,SPRINT
© Tan,Steinbach, Kumar
© Tan,Steinbach, Kumar
to specify the attribute test condition?
to determine the best split?
– Determine when to stop splitting
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© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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Tree Induction
How to Specify Test Condition?
Greedy strategy.
– Split the records based on an attribute test
that optimizes certain criterion.
Issues
– Determine how to split the records
Depends on attribute types
– Nominal
(No order; e.g., Country)
– Ordinal
(Discrete, order; e.g., S,M,L,XL)
– Continuous (Ordered, cont.; e.g., temperature)
Depends on number of ways to split
– 2-way split
– Multi-way split
How
to specify the attribute test condition?
How to determine the best split?
– Determine when to stop splitting
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
19
Splitting Based on Nominal Attributes
© Tan,Steinbach, Kumar
CarType
Luxury
Binary split: Divides values into two subsets.
Need to find optimal partitioning.
{Sports,
Luxury}
CarType
{Family}
OR
{Family,
Luxury}
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Static – discretize once at the beginning
Dynamic – ranges can be found by equal interval
bucketing, equal frequency bucketing
(percentiles), or clustering.
– Binary Decision: (A < v) or (A ≥ v)
CarType
{Sports}
© Tan,Steinbach, Kumar
20
Different ways of handling
– Discretization to form an ordinal categorical
attribute
Sports
4/18/2004
Splitting Based on Continuous Attributes
Multi-way split: Use as many partitions as distinct
values.
Family
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21
Splitting Based on Continuous Attributes
consider all possible splits and finds the best cut
can be more compute intensive
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Introduction to Data Mining
4/18/2004
22
Tree Induction
Greedy strategy.
– Split the records based on an attribute test
that optimizes certain criterion.
Issues
– Determine how to split the records
How
How
to specify the attribute test condition?
to determine the best split?
– Determine when to stop splitting
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
23
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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How to determine the Best Split
How to determine the Best Split
Greedy approach:
– Nodes with homogeneous class distribution
are preferred
Need a measure of node impurity:
Before Splitting: 10 records of class 0,
10 records of class 1
Which test condition is the best?
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
25
Measures of Node Impurity
Gini Index
Entropy
Non-homogeneous,
Homogeneous,
High degree of impurity
Low degree of impurity
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
How to Find the Best Split
Before Splitting:
C0
C1
N00
N01
M0
A?
B?
Yes
No
Node N1
26
Misclassification error
Node N2
N10
N11
C0
C1
Yes
N20
N21
C0
C1
Node N4
N30
N31
C0
C1
M2
M1
No
Node N3
M3
M12
N40
N41
C0
C1
M4
M34
Gain = M0 – M12 vs M0 – M34
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
27
Measure of Impurity: GINI
© Tan,Steinbach, Kumar
Introduction to Data Mining
GINI (t ) = 1 − ∑ [ p ( j | t )]2
j
GINI (t ) = 1 − ∑ [ p ( j | t )]2
j
(NOTE: p( j | t) is the relative frequency of class j at node t).
– Maximum (1 - 1/nc) when records are equally
distributed among all classes, implying least
interesting information
– Minimum (0.0) when all records belong to one class,
implying most interesting information
0
6
Gini=0.000
© Tan,Steinbach, Kumar
C1
C2
1
5
Gini=0.278
28
Examples for computing GINI
Gini Index for a given node t :
C1
C2
4/18/2004
C1
C2
2
4
Gini=0.444
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C1
C2
3
3
C1
C2
0
6
P(C1) = 0/6 = 0
C1
C2
1
5
P(C1) = 1/6
C1
C2
2
4
P(C1) = 2/6
Gini=0.500
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© Tan,Steinbach, Kumar
P(C2) = 6/6 = 1
Gini = 1 – P(C1)2 – P(C2)2 = 1 – 0 – 1 = 0
P(C2) = 5/6
Gini = 1 – (1/6)2 – (5/6)2 = 0.278
P(C2) = 4/6
Gini = 1 – (2/6)2 – (4/6)2 = 0.444
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Splitting Based on GINI
Binary Attributes: Computing GINI Index
Used in CART, SLIQ, SPRINT.
When a node p is split into k partitions (children), the
quality of split is computed as,
k
GINI split = ∑
i =1
Splits into two partitions
Effect of Weighing partitions:
– Larger and Purer Partitions are sought for.
Parent
ni
GINI (i)
n
B?
Yes
No
C1
6
C2
6
Gini = 0.500
where,
Gini(N1)
= 1 – (5/6)2 – (2/6)2
= 0.194
ni = number of records at child i,
n = number of records at node p.
Node N1
C1
C2
Gini(N2)
= 1 – (1/6)2 – (4/6)2
= 0.528
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Introduction to Data Mining
4/18/2004
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Tree Induction
Greedy strategy.
– Split the records based on an attribute test
that optimizes certain criterion.
Issues
– Determine how to split the records
How
N1
5
2
N2
1
4
Gini=0.333
Gini(Children)
= 7/12 * 0.194 +
5/12 * 0.528
= 0.333
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Stopping Criteria for Tree Induction
How
© Tan,Steinbach, Kumar
Node N2
to specify the attribute test condition?
to determine the best split?
Stop expanding a node when all the records
belong to the same class
Stop expanding a node when all the records have
similar attribute values
Early termination (to be discussed later)
– Determine when to stop splitting
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
33
Decision Tree Based Classification
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Practical Issues of Classification
Advantages:
– Inexpensive to construct
– Extremely fast at classifying unknown records
– Easy to interpret for small-sized trees
– Accuracy is comparable to other classification
techniques for many simple data sets
© Tan,Steinbach, Kumar
© Tan,Steinbach, Kumar
35
Underfitting and Overfitting
Missing Values
Costs of Classification
© Tan,Steinbach, Kumar
Introduction to Data Mining
Underfitting and Overfitting
Underfitting
Overfitting due to Noise
Overfitting
Decision boundary is distorted by noise point
Underfitting: when model is too simple, both training and test errors are large
© Tan,Steinbach, Kumar
Introduction to Data Mining
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Overfitting due to Insufficient Examples
Lack of data points in the lower half of the diagram makes it difficult
to predict correctly the class labels of that region
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Notes on Overfitting
Overfitting results in decision trees that are more
complex than necessary
Training error no longer provides a good estimate
of how well the tree will perform on previously
unseen records
Need new ways for estimating errors
- Insufficient number of training records in the region causes the
decision tree to predict the test examples using other training
records that are irrelevant to the classification task
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Introduction to Data Mining
4/18/2004
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How to Address Overfitting
Stop if number of instances is less than some userspecified threshold
Stop if class distribution of instances are independent
of the available features (e.g., using χ 2 test)
Stop if expanding the current node does not improve
impurity
measures (e.g., Gini or information gain).
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How to Address Overfitting…
Pre-Pruning (Early Stopping Rule)
– Stop the algorithm before it becomes a fullygrown tree
© Tan,Steinbach, Kumar
© Tan,Steinbach, Kumar
4/18/2004
41
Post-pruning
– Grow decision tree to its entirety
– Trim the nodes of the decision tree in a
bottom-up fashion
– If generalization error improves after trimming,
replace sub-tree by a leaf node.
– Class label of leaf node is determined from
majority class of instances in the sub-tree
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Model Evaluation
Metrics for Performance Evaluation
Metrics for Performance Evaluation
– How to evaluate the performance of a
model?
Methods for Performance Evaluation
– How to obtain reliable estimates?
Focus on the predictive capability of a model
– Rather than how fast it takes to classify or
build models, scalability, etc.
Confusion Matrix:
PREDICTED CLASS
Class=Yes
Methods for Model Comparison
– How to compare the relative performance
among competing models?
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
Class=Yes
ACTUAL
CLASS Class=No
43
Metrics for Performance Evaluation…
Class=Yes
ACTUAL
CLASS Class=No
b
(FN)
c
(FP)
d
(TN)
Most widely-used metric:
Accuracy =
© Tan,Steinbach, Kumar
Introduction to Data Mining
Precision (p) =
Recall (r) =
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a
a+c
a
a+b
F - measure (F) =
2rp
2a
=
r + p 2a + b + c
Precision is biased towards C(Yes|Yes) & C(Yes|No)
Recall is biased towards C(Yes|Yes) & C(No|Yes)
F-measure is biased towards all except C(No|No)
© Tan,Steinbach, Kumar
c
d
Introduction to Data Mining
a: TP (true positive)
b: FN (false negative)
c: FP (false positive)
d: TN (true negative)
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Consider a 2-class problem
– Number of Class 0 examples = 9990
– Number of Class 1 examples = 10
If model predicts everything to be class 0,
accuracy is 9990/10000 = 99.9 %
– Accuracy is misleading because model does
not detect any class 1 example
a+d
TP + TN
=
a + b + c + d TP + TN + FP + FN
Cost-Sensitive Measures
b
Class=No
a
(TP)
a
Limitation of Accuracy
PREDICTED CLASS
Class=Yes
© Tan,Steinbach, Kumar
Class=No
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© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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