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Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation. Lecture Notes for Chapter 3. Why Data Mining. Credit ratings/targeted marketing : Given a database of 100,000 names, which persons are the least likely to default on their credit cards?

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data mining classification basic concepts decision trees and model evaluation
Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation

Lecture Notes for Chapter 3

slide2

Why Data Mining

  • Credit ratings/targeted marketing:
    • Given a database of 100,000 names, which persons are the least likely to default on their credit cards?
    • Identify likely responders to sales promotions
  • Fraud detection
    • Which types of transactions are likely to be fraudulent, given the demographics and transactional history of a particular customer?
  • Customer relationship management:
    • Which of my customers are likely to be the most loyal, and which are most likely to leave for a competitor? :

Data Mining helps extract such information

examples of classification task
Examples of Classification Task
  • 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
applications
Applications
  • Banking: loan/credit card approval
    • predict good customers based on old customers
  • Customer relationship management:
    • identify those who are likely to leave for a competitor.
  • Targeted marketing:
    • identify likely responders to promotions
  • Fraud detection: telecommunications, financial transactions
    • from an online stream of event identify fraudulent events
  • Manufacturing and production:
    • automatically adjust knobs when process parameter changes
slide6

4.1 Preliminary

MODELING PROCESS

CLASSIFICATION

MODEL

OUTPUT

CLASS LABEL

Y

INPUT ATTRIBUTE SET

X

classification definition
Classification: Definition
  • Given a collection of records (training set )
    • Each record contains a set of attributes, one of the attributes is the class.
  • 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.
    • A test set is used to determine the accuracy of the model. Usually, the given data set is divided into training and test sets, with training set used to build the model and test set used to validate it.
purposes
* Purposes
  • Descriptive modeling
    • To have descriptive model that explains and distinguishes between objects of different classes.
  • Predictive Modeling
    • Predict class label of (new) unknown records. To automatically assigns a class label when presented with the attribute set of an unknown record.
classification
* classification
  • ดีกับ
    • Predict, describe data sets ที่เป็น binary or nominal categories
  • ไม่ค่อยดีกับ
    • Ordinal categories เพราะไม่สามารถพิจารณาลำดับได้
    • ลำดับขั้น เช่นมนุษย์ สัตว์เลือดอุ่น
4 2 approach to solving a classification problem
* 4.2 Approach to solving a classification problem
  • แต่ละเทคนิคจะใช้ Learning algorithm ที่แตกต่างกันไปเพื่อสร้างตัวแบบที่ best fit กับ relationship ระหว่าง attribute set กับ class label ที่ให้มาจาก input data
  • จุดหมายคือ สร้างให้ถูกต้องสำหรับแต่ละ record ของ train และ test sets และถูกต้องกับข้อมูลทั่วไปหรือ unseen records
slide12
* วัดความถูกต้อง
  • ให้ fijแทนจำนวน obj ที่ actual class i และ predicted class j
    • Accuracy = (#correct predictions) / (#total predictions)
    • = (f11 + f00)/(f11 + f10 + f01 + f00)
    • Error rate = (#wrong predictions) / (#total predictions)
    • = (f10 + f01)/(f11 + f10 + f01 + f00)
classification techniques
Classification Techniques
  • Decision Tree based Methods
  • Rule-based Methods
  • Memory based reasoning
  • Neural Networks
  • Naïve Bayes and Bayesian Belief Networks
  • Support Vector Machines
4 3 decision tree generation
*4.3 Decision tree generation

Decision tree:

  • Root node has no incoming edges and zero or more outgoing edges (condition att)
  • Internal node has exactly one incoming edge and two or more outgoing edges (condition att)
  • Leaf or terminal nodes have exactly one incoming edge and no outgoing edges (for class label)
example of a decision tree

categorical

categorical

continuous

class

Example of a Decision Tree

Splitting Attributes

Refund

Yes

No

NO

MarSt

Married

Single, Divorced

TaxInc

NO

< 80K

> 80K

YES

NO

Model: Decision Tree

Training Data

another example of decision tree

NO

Another Example of Decision Tree

categorical

categorical

continuous

class

Single, Divorced

MarSt

Married

NO

Refund

No

Yes

TaxInc

< 80K

> 80K

YES

NO

There could be more than one tree that fits the same data! (exponential no.) ทำได้แค่สร้างต้นไม้ที่ถูกต้องเกือบ optimal หรือแค่ ใช้เวลาไม่มากเกินไป

apply model to test data

Refund

Yes

No

NO

MarSt

Married

Single, Divorced

TaxInc

NO

< 80K

> 80K

YES

NO

Apply Model to Test Data

Test Data

Start from the root of tree.

apply model to test data1
Apply Model to Test Data

Test Data

Refund

Yes

No

NO

MarSt

Assign Cheat to “No”

Married

Single, Divorced

TaxInc

NO

< 80K

> 80K

YES

NO

4 3 2 decision tree induction
4.3.2 Decision Tree Induction
  • Many Algorithms:
    • Hunt’s Algorithm (one of the earliest)
    • CART
    • ID3, C4.5
    • SLIQ,SPRINT

Hunt’s algo เป็นวิธีแบบ recursive ที่ partition training records ให้ได้เป็น subsets ที่ pure ขึ้น

general structure of hunt s algorithm
General Structure of Hunt’s Algorithm
  • Let Dt be the set of training records that reach a node t
  • General Procedure:
    • If Dt contains records that belong the same class yt, then t is a leaf node labeled as yt
    • If Dt is an empty set, then t is a leaf node labeled by the default class, yd
    • If Dt contains records that belong to more than one class, use an attribute test to split the data into smaller subsets. Recursively apply the procedure to each subset.

Dt

?

hunt s algorithm

Refund

Refund

Yes

No

Yes

No

Don’t

Cheat

Marital

Status

Don’t

Cheat

Marital

Status

Single,

Divorced

Refund

Married

Married

Single,

Divorced

Yes

No

Don’t

Cheat

Taxable

Income

Cheat

Don’t

Cheat

Don’t

Cheat

Don’t

Cheat

< 80K

>= 80K

Don’t

Cheat

Cheat

Hunt’s Algorithm

Default = no

Don’t

Cheat

tree induction
Tree Induction
  • Greedy strategy.
    • Split the records based on an attribute test that optimizes certain criterion.
  • Issues
    • Determine how to split the records
      • How to specify the attribute test condition?
      • How to determine the best split?
    • Determine when to stop splitting
      • เมื่อทุก records ตกอยู่ที่ class ต่าง ๆ หมด?
tree induction1
Tree Induction
  • Greedy strategy.
    • Split the records based on an attribute test that optimizes certain criterion.
  • Issues
    • Determine how to split the records
      • How to specify the attribute test condition?
      • How to determine the best split?
    • Determine when to stop splitting
how to specify test condition
How to Specify Test Condition?
  • Depends on attribute types
    • Nominal
    • Ordinal
    • Continuous
  • Depends on number of ways to split
    • 2-way split (ถ้าเป็น binary ก็อย่างนี้อยู่แล้ว)
    • Multi-way split
splitting based on nominal attributes

CarType

Family

Luxury

Sports

CarType

CarType

{Sports, Luxury}

{Family, Luxury}

{Family}

{Sports}

Splitting Based on Nominal Attributes
  • Multi-way split: Use as many partitions as distinct values.
  • Binary split: Divides values into two subsets. Need to find optimal partitioning.

OR

แบบ binary split ถ้ามี k attributes จะ split ได้กี่แบบ?

2k-1 – 1 แบบ

splitting based on ordinal attributes

Size

Small

Large

Medium

Size

Size

Size

{Small, Medium}

{Small, Large}

{Medium, Large}

{Medium}

{Large}

{Small}

Splitting Based on Ordinal Attributes
  • Multi-way split: Use as many partitions as distinct values.
  • Binary split: Divides values into two subsets. Need to find optimal partitioning.
  • What about this split?

OR

splitting based on continuous attributes
Splitting Based on Continuous Attributes
  • Different ways of handling
    • Discretization to form an ordinal categorical attribute
      • 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)
      • consider all possible splits and finds the best cut
      • can be more compute intensive
splitting based on continuous attributes1
Splitting Based on Continuous Attributes

vi =< A < vi+1 , i = 1, 2, …, k

tree induction2
Tree Induction
  • Greedy strategy.
    • Split the records based on an attribute test that optimizes certain criterion.
  • Issues
    • Determine how to split the records
      • How to specify the attribute test condition?
      • How to determine the best split?
    • Determine when to stop splitting
how to determine the best split
How to determine the Best Split

Before Splitting: 10 records of class 0, 10 records of class 1

Purer!

Which test condition is the best?

how to determine the best split1
How to determine the Best Split
  • Greedy approach:
    • Nodes with homogeneous class distribution are preferred
  • Need a measure of node impurity:

Non-homogeneous,

High degree of impurity

Homogeneous,

Low degree of impurity

measures of node impurity
Measures of Node Impurity
  • Gini Index
  • Entropy
  • Misclassification error
  • ทั้งสามอย่างวัด impurity ยิ่งมากยิ่งไม่ดี เช่น (0,1) จะมี zero impurity แต่ (0.5, 0.5) จะมี highest impurity
how to find the best split

M0

M2

M3

M4

M1

M12

M34

How to Find the Best Split

Before Splitting:

A?

B?

Yes

No

Yes

No

Node N1

Node N2

Node N3

Node N4

Gain = M0 – M12 vs M0 – M34

measure of impurity gini
Measure of Impurity: GINI
  • Gini Index for a given node t :

(NOTE: p( j | t) or pi is the relative frequency of class j at node t, c เป็นจำนวน classes).

    • Maximum (1 - 1/nc) when records are equally distributed among all classes, implying least interesting information
    • Minimum (0) when all records belong to one class, implying most interesting information
examples for computing gini
Examples for computing GINI

P(C1) = 0/6 = 0 P(C2) = 6/6 = 1

Gini = 1 – P(C1)2 – P(C2)2 = 1 – 0 – 1 = 0

P(C1) = 1/6 P(C2) = 5/6

Gini = 1 – (1/6)2 – (5/6)2 = 0.278

P(C1) = 2/6 P(C2) = 4/6

Gini = 1 – (2/6)2 – (4/6)2 = 0.444

splitting based on gini
Splitting Based on GINI

การตัดสินใจว่าจะ split att ไหนก่อน จะต้องเปรียบเทียบค่า GINI ระหว่าง parent node (ก่อน split) กับ child node (หลัง split) ยิ่งผลต่างหรือที่เรียกว่า Gain ต่างกันเท่าไหร่ก็แสดงว่า att นั้นดีสุด

  • Used in CART, SLIQ, SPRINT.
  • When a node p is split into k partitions (children), the quality of split is computed as,

Gain = 1 - Ginisplit

where, ni = number of records at child i,

n = number of records at node p.

binary attributes computing gini index
Binary Attributes: Computing GINI Index
  • Splits into two partitions
  • Effect of Weighing partitions:
    • Larger and Purer Partitions are sought for.

B?

Yes

No

Node N1

Node N2

Gini(N1) = 1 – (5/6)2 – (2/6)2= 0.194

Gini(N2) = 1 – (1/6)2 – (4/6)2= 0.528

Gini(Children) = 7/12 * 0.194 + 5/12 * 0.528= 0.333

แสดงว่าควร split ที่ B

categorical attributes computing gini index
Categorical Attributes: Computing Gini Index
  • For each distinct value, gather counts for each class in the dataset
  • Use the count matrix to make decisions

Two-way split

(find best partition of values)

Multi-way split

Gini({spo,Lux})=1 – 3/52 - 2/52

= 0.48

Gini({family}) = 1 – 1/52 - 4/52

= 0.32

GINIsplit = (5/20)*.48

+(5/20)*0.32 =0.2

ดีกว่า

continuous attributes computing gini index
Continuous Attributes: Computing Gini Index
  • Use Binary Decisions based on one value
  • Several Choices for the splitting value
    • Number of possible splitting values = Number of distinct values
  • Each splitting value has a count matrix associated with it
    • Class counts in each of the partitions, A < v and A  v
  • Simple method to choose best v
    • For each v, scan the database to gather count matrix and compute its Gini index
    • Computationally Inefficient! Repetition of work.
  • วิธีนี้สำหรับ N records ต้องใช้ O(N) และคำนวณ GINI ใช้ O(N) จึงต้องใช้รวมกัน O(N2)
continuous attributes computing gini index1

Sorted Values

Split Positions

Continuous Attributes: Computing Gini Index
  • ใช้แค่ O(NlogN)
  • For efficient computation: for each attribute,
    • Sort the attribute on values
    • Linearly scan these values, each time updating the count matrix and computing Gini index
    • Choose the split position that has the least Gini index
slide47

A?

Yes

No

Node N1

Node N2

Gini

Gini(N1) = 1 – (3/3)2 – (0/3)2= 0

Gini(N2) = 1 – (4/7)2 – (3/7)2= 0.489

Gini(Children) = 3/10 * 0 + 7/10 * 0.489= 0.342

Gini improves !!

แสดงว่าควร split ที่ A

alternative splitting criteria based on info
Alternative Splitting Criteria based on INFO
  • Entropy at a given node t:

(NOTE: p( j | t) is the relative frequency of class j at node t).

    • Measures homogeneity of a node.
      • Maximum (log nc) when records are equally distributed among all classes implying least information
      • Minimum (0) when all records belong to one class, implying most information
    • Entropy based computations are similar to the GINI index computations
examples for computing entropy
Examples for computing Entropy

P(C1) = 0/6 = 0 P(C2) = 6/6 = 1

Entropy = – 0 log 0– 1 log 1 = – 0 – 0 = 0

ดีสุด

P(C1) = 1/6 P(C2) = 5/6

Entropy = – (1/6) log2 (1/6)– (5/6) log2 (1/6) = 0.65

P(C1) = 2/6 P(C2) = 4/6

Entropy = – (2/6) log2 (2/6)– (4/6) log2 (4/6) = 0.92

แย่สุด

splitting based on info
Splitting Based on INFO...
  • Information Gain:

Parent Node, p is split into k partitions;

ni is number of records in partition I

    • Measures Reduction in Entropy achieved because of the split. Choose the split that achieves most reduction (maximizes GAIN)
    • Used in ID3 and C4.5
drawback
* Drawback
  • Disadvantage: Tends to prefer splits that result in large number of partitions, each being small but pure.
  • วิธีแก้แรก คือ ใช้ binary split เท่านั้น
splitting based on info1
Splitting Based on INFO...
  • Gain Ratio:

Parent Node, p is split into k partitions

ni is the number of records in partition i

    • Adjusts Information Gain by the entropy of the partitioning (SplitINFO). Higher entropy partitioning (large number of small partitions) is penalized!
    • Used in C4.5
    • Designed to overcome the disadvantage of Information Gain
    • เมื่อ for all i, P(vi) = 1/k, split info = log2k
splitting criteria based on classification error
Splitting Criteria based on Classification Error
  • Classification error at a node t :
  • Measures misclassification error made by a node.
      • Maximum (1 - 1/nc) when records are equally distributed among all classes, implying least interesting information
      • Minimum (0) when all records belong to one class, implying most interesting information
examples for computing error
Examples for Computing Error

P(C1) = 0/6 = 0 P(C2) = 6/6 = 1

Error = 1 – max (0, 1) = 1 – 1 = 0

ดีสุด

P(C1) = 1/6 P(C2) = 5/6

Error = 1 – max (1/6, 5/6) = 1 – 5/6 = 1/6

P(C1) = 2/6 P(C2) = 4/6

Error = 1 – max (2/6, 4/6) = 1 – 4/6 = 1/3

แย่สุด

tree induction3
Tree Induction
  • Greedy strategy.
    • Split the records based on an attribute test that optimizes certain criterion.
  • Issues
    • Determine how to split the records
      • How to specify the attribute test condition?
      • How to determine the best split?
    • Determine when to stop splitting
stopping criteria for tree induction
Stopping Criteria for Tree Induction
  • 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)
argmag operator
*argmag operator
  • It returns the argument i that maximizes the expression p(i|t)
4 3 5 decision tree induction algo
*4.3.5 Decision tree induction algo
  • หลังจากสร้างแล้วจำเป็นต้องมีขั้นตอน tree-pruning ที่เป็นขั้นตอนการลดขนาดต้นไม้ เมื่อใหญ่มากเกินไปและมี overfitting เกิดขึ้น

Leaf.label – argmax p(i|t)

Find_best_split –

entropy, Gini, Chi square

4 3 6 web robot detection
* 4.3.6 Web Robot Detection
  • Web usage mining – extract useful patterns from Web access logs.
  • Web robot or Web crawler – software program that automatically locates and retrieves information from the Internet by following the hyperlinks.
interpretation
Interpretation
  • Web robot accesses are broad but shallow, human accesses are more narrow but deep.
  • Web robot retrieve the image pages.
  • Sessions due to Web robots are long and contain a large number of requested pages.
  • Web robot make repeated requests for the same document since human have cached by the browser.
4 3 7 decision tree based classification
*4.3.7 Decision Tree Based Classification
  • Advantages:
    • Nonparametric tree induction: ไม่ต้องใช้ prior assumption เกี่ยวกับ probability distributions ของ class และ condition attributes
    • หา optimal tree เป็น NP-complete จึงมักใช้ heuristic-based approach
    • Inexpensive to construct
    • Extremely fast at classifying unknown records (worst-case O(w), w เป็น max ความลึกของต้นไม้)
    • Easy to interpret for small-sized trees
    • Accuracy is comparable to other classification techniques for many simple data sets
    • It is robust to the presence of noise
    • Robust to redundant - จะไม่เลือกอันที่ซ้ำมาหรือถ้าเลือกมาก็จะแค่ใหญ่กว่าปกติ
disadvantages
Disadvantages
  • ทำได้ไม่ค่อยดีสำหรับ Boolean function บางอย่าง เพราะต้องสร้าง full decision tree นั่นคือ 2d nodes เมื่อ d เป็น จำนวนของ Boolean attributes
  • Data fragmentation problem – เมื่อท่องไปจนถึง leaf บางครั้งจะมีจำนวน obj ที่น้อยเกินไปที่จะมีนัยสำคัญทางสถิติในการตัดสินใจใด ๆ เกี่ยวกับ decision นั้น
  • Subtree อาจมีส่วนที่ซ้ำกันได้
expressiveness
Expressiveness
  • Decision tree provides expressive representation for learning discrete-valued function
    • But they do not generalize well to certain types of Boolean functions
      • Example: parity function:
        • Class = 1 if there is an even number of Boolean attributes with truth value = True
        • Class = 0 if there is an odd number of Boolean attributes with truth value = True
      • For accurate modeling, must have a complete tree
  • Not expressive enough for modeling continuous variables
    • Particularly when test condition involves only a single attribute at-a-time
data fragmentation
Data Fragmentation
  • Number of instances gets smaller as you traverse down the tree
  • Number of instances at the leaf nodes could be too small to make any statistically significant decision
search strategy
Search Strategy
  • Finding an optimal decision tree is NP-hard
  • The algorithm presented so far uses a greedy, top-down, recursive partitioning strategy to induce a reasonable solution
  • Other strategies?
    • Bottom-up
    • Bi-directional
tree replication
Tree Replication
  • Same subtree appears in multiple branches
disadvantages1
*Disadvantages
  • Impurity measure ที่เลือก และ tree pruning ที่ใช้ส่งผลต่อคุณภาพของต้นไม้ โดยการ prune มีผลมากกว่าเยอะมาก
  • Decision boundary –ขอบของสอง neighboring regionsของ classต่าง ๆ
  • Border line between two neighboring regions of different classes is known as decision boundary
  • Decision boundary is parallel to axes because test condition involves a single attribute at-a-time
oblique decision trees

x + y < 1

Class = +

Class =

Oblique Decision Trees
  • Test condition may involve multiple attributes
  • More expressive representation
  • Finding optimal test condition is computationally expensive
nonregtangular
*วิธีแก้ nonregtangular
  • 1. ใช้ oblique decision tree เช่น x + y <1 เป็นต้น แต่ก็จะคำนวณนานมาก
  • 2. ใช้ constructive induction ใช้ composition attribute ที่เชื่อมโดย logical combinations ของ att เดิม (ปัญหาคือ มี redundant)
example c4 5
Example: C4.5
  • Simple depth-first construction.
  • Uses Information Gain
  • Sorts Continuous Attributes at each node.
  • Needs entire data to fit in memory.
  • Unsuitable for Large Datasets.
    • Needs out-of-core sorting.
  • You can download the software from:http://www.cse.unsw.edu.au/~quinlan/c4.5r8.tar.gz
practical issues of classification
Practical Issues of Classification
  • Underfitting and Overfitting
  • Missing Values
  • Costs of Classification
4 4 model overfitting
* 4.4 Model overfitting
  • ประเภทของ error โดยทั่วไปสำหรับ classification คือ

1. Training error or resubstitution error or apparent error คือ จำนวนที่ classify ผิดบน training set

2. Generalization error or test error คือ expected error ของตัวแบบบน unseen records

  • ตัวแบบที่ดีต้อง fit data ได้ดีและต้อง classify unseen record ได้ดีด้วย นั่นคือ low training error และ low generalization error
  • เนื่องจาก ตัวแบบที่ fit data มากเกินไปเพื่อจะได้มี low training error จะมี generalization error ที่สูง เรียกว่า model overfitting
underfitting and overfitting example
Underfitting and Overfitting (Example)

500 circular and 500 triangular data points.

Circular points:

0.5  sqrt(x12+x22)  1

Triangular points:

sqrt(x12+x22) > 0.5 or

sqrt(x12+x22) < 1

underfitting and overfitting
Underfitting and Overfitting

Overfitting

เกิดจากการพยายาม fit noise ก็ได้

Underfitting: when model is too simple, both training and test errors are large

4 4 1 overfitting due to noise
4.4.1 Overfitting due to Noise

Decision boundary is distorted by noise point

นอกจากนี้อาจมี exceptional case ที่ class label ของ test set ตรงกันข้ามกับ record ที่เหมือนกันใน training Set ซึ่งเป็นปัญหาที่หลีกเลี่ยงไม่ได้และเป็นตัวบอก min error rate ของ ทุก classifier อยู่แล้ว

4 4 2 overfitting due to insufficient examples
4.4.2 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

- 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

4 4 3 overfitting and the multiple comparison procedure
*4.4.3 Overfitting and the Multiple Comparison Procedure
  • การเลือก split node ต่อไปเรื่อย ๆ จากการเปรียบเทียบผลจาก set of att ที่มีเมื่อมี record เยอะ ๆ อาจทำให้เกิด overfitting ขึ้นได้
  • คล้ายกับเลือกบริษัทซื้อหุ้น
notes on overfitting
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