7class - Laurentian University | Program Detail

Transcript 7class - Laurentian University | Program Detail

Data Mining: Concepts and Techniques

(3

ed.) — Chapter 8 —

Chapter 8. Classification: Basic Concepts

        Classification: Basic Concepts Decision Tree Induction Bayes Classification Methods Rule-Based Classification Model Evaluation and Selection Techniques to Improve Classification Accuracy: Ensemble Methods Handling Different Kinds of Cases in Classification Summary

Supervised vs. Unsupervised Learning

  Supervised learning (classification)   Supervision: The training data (observations, measurements, etc.) are accompanied by labels indicating the class of the observations New data is classified based on the training set Unsupervised learning (clustering)  The class labels of training data is unknown  Given a set of measurements, observations, etc. with the aim of establishing the existence of classes or clusters in the data 4

  

Prediction Problems: Classification vs. Numeric Prediction

Classification   predicts categorical class labels (discrete or nominal) classifies data (constructs a model) based on the training set and the values ( class labels ) in a classifying attribute and uses it in classifying new data Numeric Prediction   models continuous-valued functions, i.e., predicts unknown or missing values Regression analysis used for numeric prediction Typical applications  Credit/loan approval:    Medical diagnosis: if a tumor is cancerous or benign Fraud detection: if a transaction is fraudulent Web page categorization: which category it is 5

  

Classification—A Two-Step Process

Data Classification Step 1 consists of a learning step, and Step 2 is the classification step Model construction : describing a set of predetermined classes  Each tuple/sample is assumed to belong to a predefined class, as determined by the class label attribute  The set of tuples used for model construction is training set  The model is represented as classification rules, decision trees, or mathematical formulae Model usage : for classifying future or unknown objects   Estimate accuracy  of the model The known label of test sample is compared with the classified result from the model   Accuracy rate is the percentage of test set samples that are correctly classified by the model Test set is independent of training set (otherwise overfitting) If the accuracy is acceptable, use the model to classify data tuples whose class labels are not known 6

Process (1): Model Construction

Classification Algorithms Training Data

N A M E R A N K

M ik e M ary B ill J im D ave A n n e A ssistan t P ro f A ssistan t P ro f P ro fesso r A sso c iate P ro f A ssistan t P ro f A sso c iate P ro f

Y E A R S T E N U R E D

3 7 2 7 6 3 n o yes yes yes n o n o Classifier (Model) IF rank = ‘professor’ OR years > 6 THEN tenured = ‘yes’ 7

Process (2): Using the Model in Prediction

Classifier Testing Data Unseen Data

N A M E R A N K

T o m A ssistan t P ro f M erlisa A sso ciate P ro f G eo rg e P ro fesso r Jo sep h A ssistan t P ro f

Y E A R S T E N U R E D

2 7 5 7 n o n o yes yes (Jeff, Professor, 4)

Tenured?

Chapter 8. Classification: Basic Concepts

Decision Tree Induction: Training Dataset

age <=30 high This follows an example of Quinlan’s ID3 (Playing Tennis) <=30 high 31…40 high >40 >40 >40 low 31…40 low <=30 <=30 >40 medium low medium low medium <=30 medium 31…40 medium 31…40 high >40 medium income student no no no no yes yes yes no yes yes yes no yes no credit_rating fair excellent fair fair fair excellent excellent fair fair fair excellent excellent fair excellent buys_computer no no yes yes yes no yes no yes yes yes yes yes no 10

Output: A Decision Tree for “ buys_computer”

age?

<=30

no no student?

yes yes yes

>40

credit rating?

excellent fair yes 11

Algorithm for Decision Tree Induction

  Basic algorithm (a greedy algorithm)  Tree is constructed in a top-down recursive divide-and-conquer manner     At start, all the training examples are at the root Attributes are categorical (if continuous-valued, they are discretized in advance) Tuples are partitioned recursively based on selected attributes Splitting attributes are selected on the basis of a heuristic or statistical measure (e.g., information gain ) Conditions for stopping partitioning  All samples for a given node belong to the same class   There are no remaining attributes for further partitioning – majority voting is employed for classifying the leaf There are no samples left 12

    

Attribute Selection Measure: Information Gain (ID3/C4.5)

Select the attribute with the highest information gain Let

p

i be the probability that an arbitrary tuple in D belongs to class C i , estimated by |C the set of tuples of class C i in D.

i , D |/|D| where C i,D Expected information in D: (entropy) needed to classify a tuple

Info

(

)  

i m

  1

p i

log 2 (

p i

) is Information needed (after using A to split D into v partitions) to classify D: Information gained

Info A

(

) 

j v

  1 | |

D D j

| | by branching on attribute A 

Info

(

D j

)

Gain(A)



Info(D)



Info

(D)

Attribute Selection: Information Gain

  Class P: buys_computer = “yes” Class N: buys_computer = “no”

Info

(

) 

( 9 , 5 )   9 14 log 2 9 ( 14 )  5 14 log 2 5 ( 14 )  0 .

940

Info age

(

)  5 14

( 2 , 3 )  4 14

( 4 , 0 )  5 14

( 3 , 2 )  0 .

694 age <=30 31…40 >40 p i 2 4 3 n i I(p i , n 3 0.971

0 0 2 0.971

age <=30 high <=30 high 31…40 high >40 >40 <=30 <=30 income student medium low >40 low 31…40 low medium low >40 >40 medium <=30 medium 31…40 medium 31…40 high medium no no no no yes yes yes no yes yes yes no yes no credit_rating fair excellent fair fair fair excellent excellent fair fair fair excellent excellent fair excellent i ) buys_computer no no yes yes yes no yes no yes yes yes yes yes no 5 14

( 2 , 3 ) means “age <=30” has 5 out of 14 samples, with 2 yes’es and 3 no’s. Hence

Gain

(

age

) 

Info

(

) 

Info age

(

)  0 .

246 Similarly,

Gain Gain

(

student

)

Gain

( (

income credit

_ )   0 .

029 0 .

151

rating

)  0 .

048 14

Attribute Selection: Information Gain

youth: <= 30 middle-aged: 31..40

Senior: > 40 age?

<=30 >40

no no student?

yes yes yes credit rating?

excellent fair yes 15

  

Computing Information-Gain for Continuous-Valued Attributes

Let attribute A be a continuous-valued attribute Must determine the

best split point

for A  Sort the value A in increasing order   Typically, the midpoint between each pair of adjacent values is considered as a possible

split point

 (a i +a i+1 )/2 is the midpoint between the values of a i and a i+1 The point with the

minimum expected information requirement

, for A is selected as the split-point for A Split:  D 1 D 2 is the set of tuples in D satisfying A ≤ split-point, and is the set of tuples in D satisfying A > split-point 16

Gain Ratio for Attribute Selection (C4.5)

  Information gain measure is biased towards attributes with a large number of values C4.5 (a successor of ID3) uses gain ratio to overcome the problem (normalization to information gain)  

SplitInfo A

(

)  

j v

  1 | |

D j D

| |  log 2 ( | |

D D j

| | )  Ex.

GainRatio(A) = Gain(A)/SplitInfo A (D)  gain_ratio(income) = 0.029/1.557 = 0.019

The attribute with the maximum gain ratio is selected as the splitting attribute 17

Gini index (CART, IBM IntelligentMiner)

      If a data set D contains tuples from n classes, gini index, measures the impurity of D as where p j If a data set is the relative frequency of class C j D is split on A into two subsets D 1 gini ( D ) is defined as

gini

(

gini D

)

( 

1 )   |

j n

  1

1 |

| |

gini

(

1 ) in D and and is |C i , D |/|D| D 2 , the gini index  | |

D D

2 | |

gini

(

2 ) For discrete-valued attribute, the subset that gives the minimum gini index for that attribute is selected as its splitting subset For continuous-valued attributes, each possible split-point must be considered Reduction in Impurity: 

gini

(

) 

gini

(

) 

gini A

(

) The attribute provides the smallest gini split ( D ) (or the largest reduction in impurity) is chosen to split the node ( need to enumerate all the possible splitting points for each attribute ) 18

Gini index (CART, IBM IntelligentMiner)

  Ex. D has 9 tuples in buys_computer = “yes” and 5 in “no” 2

gini

(

)  1  9 14 2 5 14  0 .

459 Suppose the attribute income partitions D into 10 tuples for D medium} and 4 in D 2

gini income

 {

low

medium

} (

)     10 14   

Gini

(

1 )     4 14    1 : {low,

Gini

(

2 )    Gini {low,high} is 0.458; Gini {medium,high} is 0.450. Therefore, split on the {low,medium} (and {high}) since it has the lowest Gini index {youth, senior} (or{middle_aged}) is the best split for age with Gini index 0.357

Student and credit_rating are both binary with Gini index values 0.367 and 0.429

Attribute age and splitting subset {youth, senior} give minimum Gini index with reduction in impurity of 0.459 – 0.357 = 0.102

Comparing Attribute Selection Measures

 The three measures, in general, return good results but  Information gain:  biased towards multivalued attributes   Gain ratio:  tends to prefer unbalanced splits in which one partition is much smaller than the others Gini index:    biased to multivalued attributes has difficulty when # of classes is large tends to favor tests that result in equal-sized partitions and purity in both partitions 20

Other Attribute Selection Measures

      CHAID: a popular decision tree algorithm, measure based on χ 2 for independence test C-SEP: performs better than info. gain and gini index in certain cases G-statistic: has a close approximation to χ 2 distribution MDL (Minimal Description Length) principle (i.e., the simplest solution is preferred):  The best tree as the one that requires the fewest # of bits to both (1) encode the tree, and (2) encode the exceptions to the tree Multivariate splits (partition based on multiple variable combinations)  CART: finds multivariate splits based on a linear comb. of attrs.

Which attribute selection measure is the best?

 Most give good results, none is significantly superior than others 21

Overfitting and Tree Pruning

  Overfitting: An induced tree may overfit the training data   Too many branches, some may reflect anomalies due to noise or outliers Poor accuracy for unseen samples Two approaches to avoid overfitting   Prepruning: Halt tree construction early ̵ do not split a node if this would result in the goodness measure falling below a threshold  Difficult to choose an appropriate threshold Postpruning: Remove branches from a “fully grown” tree—get a sequence of progressively pruned trees  Use a set of data different from the training data to decide which is the “best pruned tree” 22

Tree Pruning

 Cost complexity (CART) pruning is a postpruning approach    Cost complexity of a tree is a function of the number of leaves in the tree and the error rate of the tree  Error rate – percentage of tuples misclassified by the tree Starts from the bottom of the tree For each internal node N, it computes the cost complexity of the subtree at N and the cost complexity of the subtree at N if it were to be pruned  Compare the two values – if cost complexity is lower by pruning, then prune the subtree at N   A pruning set of class-labeled tuples is used to estimate cost complexity Pruning set is independent of the training set and test set 23

Tree Pruning

     Pessimistic pruning (C4.5) – uses error rate estimates for subtree pruning   Does not require prune set Uses training set to estimate error rates which is overly optimistic, thus strongly biased  Add penalty to error rates obtained from training set to offset bias Combination of prepruning and postpruning Decision trees can suffer from repetition Replication and replication Repetition – an attribute is repeatedly tested along a given branch of tree (age < 60? followed by age < 45?) – duplicate subtrees exist within a tree 24

Enhancements to Basic Decision Tree Induction

   Allow for continuous-valued attributes  Dynamically define new discrete-valued attributes that partition the continuous attribute value into a discrete set of intervals Handle missing attribute values  Assign the most common value of the attribute  Assign probability to each of the possible values

Attribute construction

  Create new attributes based on existing ones that are sparsely represented This reduces fragmentation, repetition, and replication 25

Classification in Large Databases

   Classification—a classical problem extensively studied by statisticians and machine learning researchers Scalability: Classifying data sets with millions of examples and hundreds of attributes with reasonable speed Why decision tree induction in data mining?

    relatively faster learning speed (than other classification methods) convertible to simple and easy to understand classification rules can use SQL queries for accessing databases comparable classification accuracy with other methods 26

Scalable Decision Tree Induction Methods

     SLIQ  (EDBT’96 — Mehta et al.) Builds an index for each attribute and only class list and the current attribute list reside in memory SPRINT  (VLDB’96 — J. Shafer et al.) Constructs an attribute list data structure PUBLIC  (VLDB’98 — Rastogi & Shim) Integrates tree splitting and tree pruning: stop growing the tree earlier RainForest  Builds an AVC-list (attribute-value, class label) BOAT (PODS’99 — Gehrke, Ganti, Ramakrishnan & Loh)  (VLDB’98 — Gehrke, Ramakrishnan & Ganti) Uses bootstrapping to create several small samples 27

Scalability Framework for RainForest

 Separates the scalability (memory size) aspects from the criteria that determine the quality of the tree  It adapts to the amount of main memory available and applies to any decision tree induction algorithm  Builds an AVC-set

(

Attribute-Value, Classlabel ) for each attribute, at each tree node, describing the training tuples at the node 

AVC-set

of an attribute A at node N gives the class label counts for each value of A for the tuples at N 

AVC-group

(of a node N )  Set of AVC-sets of all predictor attributes at the node N 28

Scalability Framework for RainForest

 The size of an AVC-set for attribute A at node N depends only on the number of distinct values of A and the number of classes in the set of tuples at N 

This size should fit in memory, even for real-world data

 29

Rainforest: Training Set and Its AVC Sets

Training Examples AVC-set on Age age <=30 income studentcredit_rating Age high <=30 high 31…40 high no no no fair excellent fair no no yes <=30 >40 >40 medium low no yes fair fair yes yes 31..40

>40 >40 31…40 low <=30 <=30 >40 >40 low medium low medium <=30 medium 31…40 medium 31…40 high medium yes yes no yes yes yes no yes no excellent excellent fair fair fair excellent excellent fair excellent no yes no yes yes yes yes yes no AVC-set on student yes no Buy_Computer yes 3 4 3 yes 6 3 no 2 0 2 Student Buy_Computer no 1 4 AVC-set on income income high medium low AVC-set on credit_rating Credit rating fair excellent Buy_Computer yes 2 4 3 no 2 2 1 Buy_Computer yes 6 3 no 2 3 30

Data Cube-Based Decision-Tree Induction

   Integration of generalization with decision-tree induction (Kamber et al.’97) Classification at primitive concept levels  E.g., precise temperature, humidity, outlook, etc.

  Low-level concepts, scattered classes, bushy classification-trees Semantic interpretation problems Cube-based multi-level classification  Relevance analysis at multi-levels  Information-gain analysis with dimension + level 31

BOAT (Bootstrapped Optimistic Algorithm for Tree Construction)

 Use a statistical technique called

bootstrapping

to create several smaller samples (subsets), each fits in memory  Each subset is used to create a tree, resulting in several trees  These trees are examined and used to construct a new tree

T’

 It turns out that

T’

is very close to the tree that would be generated using the whole data set together  Adv: requires only two scans of DB, an incremental algorithm  BOAT can take new insertions and deletions for the training data and update the decision tree 32

Presentation of Classification Results

Visualization of a Decision Tree in SGI/MineSet 3.0

Interactive Visual Mining by Perception-Based Classification (PBC

)

       Interactive approach based on multidimensional visualization techniques Resulting trees tend to be smaller than traditional decision tree methods with same accuracy PBC uses a pixel-oriented approach to view multidimensional data with its class label information The circle segments approach is adapted, which maps d dimensional data objects to a circle that is partitioned into d segments, each representing an attribute An attribute value is mapped to one colored pixel reflecting the class label of the object Data Interaction window : displays the circle segments Knowledge Interaction window : displays the decision tree 35

Interactive Visual Mining by Perception-Based Classification (PBC )

Chapter 8. Classification: Basic Concepts

Bayesian Classification: Why?

     A statistical classifier: performs

i.e., probabilistic prediction,

predicts class membership probabilities Foundation: Based on Bayes’ Theorem. Performance: A simple Bayesian classifier,

naïve Bayesian classifier

, has comparable performance with decision tree and selected neural network classifiers Incremental: Each training example can incrementally increase/decrease the probability that a hypothesis is correct — prior knowledge can be combined with observed data Standard: Even when Bayesian methods are computationally intractable, they can provide a standard of optimal decision making against which other methods can be measured 38

Bayesian Theorem: Basics

      Let X be a data sample (“

evidence

”): class label is unknown Let H be a

hypothesis

that X belongs to class C Classification is to determine P(H|X), (

probability),

the observed data sample X

posteriori

the probability that the hypothesis holds given P(H) (

prior probability

), the initial probability  E.g., X will buy computer, regardless of age, income, … P(X): probability that sample data is observed P(X|H) (likelyhood), the probability of observing the sample X, given that the hypothesis holds  E.g., Given that X will buy computer, the prob. that X is 31..40, medium income 39

Bayesian Theorem

 Given training data X

, posteriori probability of a hypothesis

,

P(H|X)

,

follows the Bayes theorem

(

|

)



(

|

)

(

)

(

)

   Informally, this can be written as posteriori = likelihood x prior/evidence Predicts X belongs to C i iff the probability P(C i |X) is the highest among all the P(C k |X) for all the

k

classes Practical difficulty: require initial knowledge of many probabilities, significant computational cost 40

Towards Naïve Bayesian Classifier

      Let D be a training set of tuples and their associated class labels, and each tuple is represented by an n-D attribute vector X = (x 1 , x 2 , …, x n ) Suppose there are

m

classes C 1 , C 2 , …, C m .

Classification is to derive the maximum posteriori , the maximal P(C i |X), i.e. tuple X belongs to the class C i only if P(C i |X) > P(C j |X) for 1  j  m, j This can be derived from Bayes’ theorem  i if and

(

C i

) 

(

C i

)

P P

(

) (

C i

) needs to be maximized

(

C i

) 

(

C i

)

(

C i

If class prior probabilities are not known, then assume classes are equally likely, i.e. P(C 1 ) = P(C 2 ) = …= P(C m ) 41

Derivation of Naïve Bayes Classifier

    A simplified assumption: attributes are conditionally independent (i.e., no dependence relation between attributes):

(

) 

k n

  1

(

x k

) 

(

1 |

) 

(

2 |

)  ...



(

x n

This greatly reduces the computation cost: Only counts the class distribution |

) If A k If A k and is categorical, P(x k |C i ) is the # of tuples of C i value x k for A k is continous-valued, P(x based on Gaussian distribution with a mean μ and standard deviation σ

(

x k

| divided by |C i, D | (# of tuples of C i

) 

(

x k

, 

C i g

, (  k

|C )  , i ) is usually computed  )  1 2  

 (

2    2 ) 2 having in D) 42

Derivation of Naïve Bayes Classifier

 Example:  Let X = (35, $40,000) where A1 = age, A2 = income   Class label = buys_computer Associated class label for X is yes (i.e. buys_computer = yes)   Let age be a continuous valued attribute Suppose from training set, customers in D who buy computer are 38  12 years of age, i.e. for age  = 38 years and  = 12  P(age = 35|buys_computer = yes) = g(x age =35,  buys_computer=yes ,  buys_computer=yes ) 43

Naïve Bayesian Classifier: Training Dataset

Class: C1:buys_computer = ‘yes’ C2:buys_computer = ‘no’ Data sample X = (age <=30, Income = medium, Student = yes Credit_rating = Fair) age <=30 high <=30 high 31…40 high >40 medium >40 low >40 low 31…40 low <=30 medium <=30 low >40 >40 medium <=30 medium 31…40 medium 31…40 high medium no no no no yes yes yes no yes yes yes no yes no fair excellent fair fair fair excellent excellent fair fair fair excellent excellent fair excellent no no yes yes yes no yes no yes yes yes yes yes no 44

Naïve Bayesian Classifier: An Example

 P(C i ): P(buys_computer = “yes”) = 9/14 = 0.643

P(buys_computer = “no”) = 5/14= 0.357

  Compute P(X|C i ) for each class P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222

P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6

P(income = “medium” | buys_computer = “yes”) = 4/9 = 0.444

P(income = “medium” | buys_computer = “no”) = 2/5 = 0.4

P(student = “yes” | buys_computer = “yes) = 6/9 = 0.667

P(student = “yes” | buys_computer = “no”) = 1/5 = 0.2

P(credit_rating = “fair” | buys_computer = “yes”) = 6/9 = 0.667

P(credit_rating = “fair” | buys_computer = “no”) = 2/5 = 0.4

X = (age <= 30 , income = medium, student = yes, credit_rating = fair) P(X|C i

) : P(X|buys_computer = “yes”) = 0.222 x 0.444 x 0.667 x 0.667 = 0.044

P(X|buys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019

P(X|C i )*P(C i

) : P(X|buys_computer = “yes”) * P(buys_computer = “yes”) = 0.028

P(X|buys_computer = “no”) * P(buys_computer = “no”) = 0.007

Therefore, X belongs to class (“buys_computer = yes”)

Avoiding the 0-Probability Problem

 Naïve Bayesian prediction requires each conditional prob. be non- zero. Otherwise, the predicted prob. will be zero

(

) 

k n

 

1 (

)   Ex. Suppose a dataset with 1000 tuples, income=low (0), income= medium (990), and income = high (10), Use Laplacian correction (or Laplacian estimator)  Adding 1 to each case  Prob(income = low) = 1/1003 = 0.001 (uncorrected value = 0) Prob(income = medium) = 991/1003 = 0.988 (uncorrected = 0.990) Prob(income = high) = 11/1003 = 0.011 (uncorrected = 0.010) The “corrected” prob. estimates are close to their “uncorrected” counterparts 46

Naïve Bayesian Classifier: Comments

   Advantages  Easy to implement  Good results obtained in most of the cases Disadvantages   Practically, dependencies exist among variables  E.g., hospitals: patients: Profile: age, family history, etc. Symptoms: fever, cough etc., Disease: lung cancer, diabetes, etc.  Dependencies among these cannot be modeled by Naïve Bayesian Classifier How to deal with these dependencies?

 Assumption: class conditional independence, therefore loss of accuracy Bayesian Belief Networks (Chapter 9) 47

Chapter 8. Classification: Basic Concepts

Using IF-THEN Rules for Classification

   Represent the knowledge in the form of IF-THEN rules R: IF age = youth AND student = yes THEN buys_computer  Rule antecedent/precondition vs. rule consequent Assessment of a rule: coverage and accuracy = yes  n covers = # of tuples covered by R  n correct = # of tuples correctly classified by R coverage(R) = n covers /|D| /* D: training data set */ accuracy(R) = n correct / n covers If more than one rule are triggered, need conflict resolution    Size ordering: assign the highest priority to the triggering rules that has the “toughest” requirement (i.e., with the most attribute tests ) Class-based ordering: classes are sorted in decreasing order of prevalence or misclassification cost per class Rule-based ordering (decision list): rules are organized into one long priority list, according to some measure of rule quality (accuracy, coverage, size) or by experts 49

Using IF-THEN Rules for Classification

 If no rule is satisfied by tuple X  Default rule set up to specify a default class based on training set    Class in majority or majority class of tuples that were not covered by any rule Default rule is evaluated at the end, if and only if, no other rule covers X Condition in the default rule is empty 50

Rule Extraction from a Decision Tree

age?

    

<=30

Rules are easier to understand than large trees One rule is created for each path to a leaf from the root Each attribute-value pair along a path forms a conjunction: the leaf holds the class prediction no no student?

yes yes

31..40

yes Rules are mutually exclusive and exhaustive Example: Rule extraction from our buys_computer decision-tree IF age = young AND student = no IF age = young AND student = yes THEN buys_computer = no THEN buys_computer = yes IF IF age = old AND credit_rating = excellent IF age age = mid-age = young AND credit_rating = fair THEN buys_computer = yes THEN buys_computer = yes THEN buys_computer = no

>40

credit rating?

excellent fair yes 51

Rule Induction: Sequential Covering Method

     Sequential covering algorithm: Extracts rules directly from training data Typical sequential covering algorithms: FOIL, AQ, CN2, RIPPER Rules are learned sequentially , each for a given class C i will cover many tuples of C i but none (or few) of the tuples of other classes Steps:  Rules are learned one at a time   Each time a rule is learned, the tuples covered by the rules are removed The process repeats on the remaining tuples unless termination condition , e.g., when no more training tuples or when the quality of a rule returned is below a user-specified threshold Comp. w. decision-tree induction: learning a set of rules simultaneously 52

Sequential Covering Algorithm

while

(enough target tuples left) generate a rule remove positive target tuples satisfying this rule Examples covered Examples covered by Rule 2 by Rule 1 Examples covered by Rule 3

Positive examples

How to Learn-One-Rule?

   Start with the most general rule possible: condition = empty Adding new attributes by adopting a greedy depth-first strategy  Picks the one that most improves the rule quality Rule-Quality measures: consider both coverage and accuracy Rule increases accuracy 54

Rule-Quality measures

 Choosing accuracy only between two rules  Rules R1 and R2 for class loan_decisision = accept     “a” represents tuples of class “accept” and “r” represents tuples of class “reject” Rule R1 correctly classifies 38/40 tuples it covers, with accuracy 95% Rule R2 correctly classifies 2 tuples it covers, with accuracy 100% R2 has greater accuracy than R1 but is not better because of small coverage 55

Rule-Quality measures

 FOIL: a sequential covering algorithm that learns first-order logic rules (complex due to variables)  Concerned with propositional rules instead (variable-free)    Tuples of class for which we are learning rules – positive tuples pos - # of positive tuples covered by R FOIL (& RIPPER) assesses information gain by extending condition

FOIL

Gain



pos

'  (log 2

pos pos

'  '

neg

'  log 2

pos pos



neg

) It favors rules that have high accuracy and cover many positive tuples 56

A statistical test of significance

  Statistical test of significance to determine if the apparent effect of a rule is not attributed to chance Compare observed distribution among classes of tuples covered by a rule with the expected distribution that would result if the rule made predictions at random   m = # of classes, f i = observed frequency, e i = expected frequency The statistic has  2 distribution with m-1 degrees of freedom Higher likelihood ratio => significant difference in the number of correct predictions made by our rule in comparison with a “random guesser” 57

Rule Pruning

   A rule is pruned by removing a conjunct (attribute test) A rule R is pruned if pruned version has greater quality assessed on an independent set of tuples Rule pruning based on an independent set of test tuples

FOIL

Prune

(

) 

pos



neg pos



neg

Pos/neg are # of positive/negative tuples covered by R.

If FOIL_Prune is higher for the pruned version of R, prune R 58

Rule Generation

 To generate a rule

while

(true) find the best predicate

foil-gain(

) > threshold

then

add

to current rule

else

break

=1&&

&&A8

=1 Positive examples Negative examples 59

Chapter 8. Classification: Basic Concepts

Model Evaluation and Selection

    Evaluation metrics: How can we measure accuracy? Other metrics to consider?

Use test set of class-labeled tuples instead of training set when assessing accuracy Methods for estimating a classifier’s accuracy:  Holdout method, random subsampling   Comparing classifiers:  Confidence intervals  Cross-validation Bootstrap Cost-benefit analysis and ROC Curves 61

Evaluation Measures

    True positives (TP) : These refer to the positive tuples that were correctly labeled by the classifier True negatives (TN) : these are the negative tuples that were correctly labeled by the classifier False positives (FP) : These are the negative tuples that were incorrectly labeled as positive (e.g. tuples of class buys_computer = no for which the classifier predicted buys_computer = yes) False negatives (FN) : These are the positive tuples that were mislabeled as negatives (e.g. tuples of class buys_computer = yes for which the classifier predicted buys_computer = no) 62

Classifier Evaluation Metrics: Accuracy & Error Rate

Confusion Matrix:

Actual class\Predicted class C 1 ~C 1 C 1

True Positives (TP) False Positives (FP)

~C 1

False Negatives (FN) True Negatives (TN)

Total

P’ N’

Total

P N P+N

Classifier Accuracy, or recognition rate: percentage of test set tuples that are correctly classified, Error rate: misclassification rate, 1 – accuracy , or

Classifier Evaluation Metrics: Example - Confusion Matrix

Actual class\Predicted class buy_computer = yes buy_computer = yes

6954

buy_computer = no Total Recognition(%)

7000 99.34

buy_computer = no Total

412

7366

2588

2634 3000 10000   Given

m

classes, an entry,

CM i,j

matrix indicates # of tuples in class labeled by the classifier as class

j.

in a confusion

i

that were May be extra rows/columns to provide totals or recognition rate per class.

86.27

95.42

Classifier Evaluation Metrics: Sensitivity and Specificity

 Class Imbalance Problem:  one class may be medical data

rare

, e.g. fraud detection data,  significant

majority of the negative class

of the positive class and minority  Sensitivity: True Positive recognition rate,   sensitivity = 𝑇𝑃 𝑃 Specificity: True Negative recognition rate, specificity = 𝑇𝑁 𝑁 Accuracy as a function of sensitivity and specificity: accuracy = sensitivity 𝑃 (𝑃+𝑁) + specificity 𝑁 (𝑃+𝑁) 65

Classifier Evaluation Metrics: Precision and Recall

 Precision: exactness – what % of tuples that the classifier labeled as positive are actually positive?

precision = 𝑇𝑃 𝑇𝑃+𝐹𝑃  Recall: completeness – what % of positive tuples did the classifier label as positive?

recall = 𝑇𝑃 𝑇𝑃+𝐹𝑁 = 𝑇𝑃 𝑃   Perfect score is 1.0

Inverse relationship between precision & recall 66

Classifier Evaluation Metrics: Example

Actual class\Predicted class cancer = yes cancer = no Total cancer = yes

90 140

230 cancer = no

210 9560

9770 Total Recognition(%) 300 9700 10000 30.00

sensitivity 98.56

specificity 96.40

accuracy

Precision

30.00% = 90/230 = 39.13%;

Recall

= 90/300 = 67

Classifier Evaluation Metrics:

and

F ß

Measures



F measure (

and recall,

F 1

-score): harmonic mean of precision F = 2  𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛  𝑟𝑒𝑐𝑎𝑙𝑙 𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛+ 𝑟𝑒𝑐𝑎𝑙𝑙 

  

 is a non-negative integer weighted measure of precision and recall assigns  precision, times as much weight to recall as to F  = 1+ 𝛽 2 ×𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 × 𝑟𝑒𝑐𝑎𝑙𝑙 𝛽 2 ×𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛+ 𝑟𝑒𝑐𝑎𝑙𝑙  Commonly used F  measures are F 2 (which weights weights precision twice as much as recall) (which 68

 

Evaluating Classifier Accuracy: Holdout & Cross-Validation Methods

Holdout method

 Given data is randomly partitioned into two independent sets    Training set (e.g., 2/3) for model construction Test set (e.g., 1/3) for accuracy estimation Random subsampling: a variation of holdout  Repeat holdout k times, accuracy = avg. of the accuracies obtained Cross-validation ( k -fold, where k = 10 is most popular)  Randomly partition the data into approximately equal size k mutually exclusive subsets, each   At i -th iteration, use D i as test set and others as training set Leave-one-out: k folds where k = # of tuples, for small sized data, i.e. only one sample is “left out” at a time for the test set  *Stratified cross-validation*: folds are stratified so that class distribution in each fold is approximately the same as that in the initial data 69

 

Evaluating the Classifier Accuracy: Bootstrap

Bootstrap

  Works well with small data sets Samples the given training tuples uniformly with replacement  i.e., each time a tuple is selected, it is equally likely to be selected again and re-added to the training set Several bootstrap methods, and a common one is .632 boostrap   A data set with d tuples is sampled d times, with replacement, resulting in a training set of training set end up forming the test set. About 63.2% of the original data end up in the bootstrap, and the remaining 36.8% form the test set (since (1 – 1/d) d ≈ e -1 d samples. The data tuples that did not make it into the = 0.368) Repeat the sampling procedure k model:

acc

(

) 

i k

  1 ( 0 .

632 

acc

times, overall accuracy of the (

M i

)

test

set

 0 .

368 

acc

(

M i

)

train

set

) 70

Estimating Confidence Intervals: Classifier Models M

vs. M

    Suppose we have 2 classifiers, M 1 is best?

and M 2 . Which Use 10-fold cross-validation to obtain

𝑒𝑟𝑟

(M 1 ) and

𝑒𝑟𝑟

(M 2 ) These mean error rates are just on the true population of

future estimates

data cases of error What if the difference between the 2 error rates is just attributed to

chance

  Use a test of statistical significance Obtain confidence limits for our mean error estimates 71

     

Estimating Confidence Intervals: Null Hypothesis

For each model, perform 10-fold cross-validation, say 10 times, each time using a different 10-fold partitioning of data Average the 10 error rates obtained each for M 1 get the mean error rates for each model and M 2 Assume samples follow a t distribution with

k–1

of freedom (here,

k=10

) to

degrees

Use t-test (or Student’s t-test) as the significance test Null Hypothesis: M 1 | 𝑒𝑟𝑟 (M 1 ) 𝑒𝑟𝑟 (M 2 )| = 0 & M 2 are the same, i.e., If we can reject null hypothesis, then   conclude that the difference between M

statistically significant

Chose model with lower error rate 1 & M 2 is 72

Estimating Confidence Intervals: t-test

 If only 1 test set available:pairwise comparison    For i th round of 10-fold cross-validation, the same cross partitioning is used to obtain

err(M

)

i and

err(M

)

i Average over 10 rounds to get 𝑒𝑟𝑟 (M 1 ) and 𝑒𝑟𝑟 (M 2 )

t-test computes t-statistic with

of freedom:

k-1

degrees

where  If 2 test sets available: use non-paired t-test where where k 1 & k 2 are # of cross-validation samples used for M 1 & M 2 , resp.

Estimating Confidence Intervals: Table for t-distribution

   Symmetric

Significance

level, e.g,

sig = 0.05

M 1 or & M 2

5%

means are

significantly different

for 95% of population

Confidence

limit,

z = sig/2

Estimating Confidence Intervals: Statistical Significance

 Are M 1   & M 2 Compute significantly different?

t.

Select

significance level

(e.g.

sig = 5%)

Consult table for t-distribution: Find corresponding to

t value k-1 degrees of freedom

(here, 9)  t-distribution is symmetric – typically upper % points of distribution shown → look up value for confidence

limit

z=sig/2

(here, 0.025)   If t > z or t < -z, then t value lies in rejection region:  Reject null hypothesis that mean error rates of M 1 same & M 2 are  Conclude: statistically significant difference between M 1 & M 2 Otherwise, conclude that any difference is chance.

Model Selection: ROC Curves

      ROC (Receiver Operating Characteristics) curves: for visual comparison of classification models Originated from signal detection theory Shows the trade-off between the true positive rate and the false positive rate The area under the ROC curve is a measure of the accuracy of the model Rank the test tuples in decreasing order: the one that is most likely to belong to the positive class appears at the top of the list The closer to the diagonal line (i.e., the closer the area is to 0.5), the less accurate is the model     Vertical axis represents the true positive rate Horizontal axis rep. the false positive rate The plot also shows a diagonal line A model with perfect accuracy will have an area of 1.0

Issues Affecting Model Selection

     

Accuracy

 classifier accuracy: predicting class label

Speed

 time to construct the model (training time)  time to use the model (classification/prediction time) Robustness: handling noise and missing values Scalability: efficiency in disk-resident databases

Interpretability

 understanding and insight provided by the model Other measures, e.g., goodness of rules, such as decision tree size or compactness of classification rules

Chapter 8. Classification: Basic Concepts

Ensemble Methods: Increasing the Accuracy

 Ensemble methods  Use a combination of models to increase accuracy    A class labeled prediction is returned by the ensemble based on the votes from individual classifiers Combine a series of k learned models, M 1 , M 2 , …, M k , with the aim of creating an improved model M* A given data set D is used to create k training sets D 1 , D 2 , …, D k , where D i is used to generate classifier M i 79

Ensemble Methods

  Popular ensemble methods  Bagging: averaging the prediction over a collection of classifiers   Boosting: weighted vote with a collection of classifiers Random forests An ensemble is more accurate than its base classifiers and yields better results when there is diversity in the models 80

Ensemble Methods

 Example: A 2-class problem described by two attributes x1 and x2  The problem has a linear decision boundary   (a) decision boundary of a decision tree classifier (b) decision boundary of an ensemble of decision tree classifiers 81

Bagging: Bootstrap Aggregation

     Analogy: Diagnosis based on multiple doctors’ majority vote Training  Given a set D of d tuples, at each iteration i , a training set D tuples is sampled with replacement from D (i.e., bootstrap) i of d  A classifier model M i is learned for each training set D i Classification: classify an unknown sample X   Each classifier M i returns its class prediction, which counts as one vote The bagged classifier M* counts the votes and assigns the class with the most votes to X Bagging can be applied to the prediction of continuous values by taking the average value of each prediction for a given test tuple Accuracy   Often significantly better than a single classifier derived from D For noise data: not considerably worse, more robust  Increased accuracy: composite model reduces variance of individual classifiers 82

Boosting

    Analogy: Consult several doctors, based on a combination of weighted diagnoses—weight assigned based on the previous diagnosis accuracy How boosting works?

 Weights are assigned to each training tuple    A series of k classifiers are iteratively learned After a classifier M i is learned, the weights are updated to allow the subsequent classifier, M i+1 , to pay more attention to the training tuples that were misclassified by M i The final M* combines the votes of each individual classifier, where the weight of each classifier's vote is a function of its accuracy Boosting algorithm can be extended for numeric prediction.

Comparing with bagging: Boosting tends to achieve greater accuracy, but it also risks overfitting the model to misclassified data.

Adaboost (Freund and Schapire, 1997)

       Given a set of d class-labeled tuples, (X

, y 1 ), …, (X

, y d ), where y i class label of tuple X i Initially, all the weights of tuples are set the same (1/d) Generate k classifiers in k rounds. At round i, is the   Tuples from D are sampled (with replacement) to form a training set D i of size d Each tuple’s chance of being selected is based on its weight    A classification model M i is derived from D i Its error rate is calculated using D i as a test set If a tuple is misclassified, its weight is increased, o.w. it is decreased Error rate: err(X

) is the misclassification error of tuple X

. Classifier M i error rate is the sum of the weights of the misclassified tuples:

error

(

M i

) 



j w j



err

(

X j

) If the tuple was misclassified, then err(X

) = 1, otherwise it is 0 If performance of classifier M i Generate a new D i is poor, i.e. err(X

) > 0.5, abandon M training set from which we derive a new M i i 84

Adaboost

       If a tuple in round i was correctly classified, its weight is multiplied by error(M i )/(1-error(M i )) Once the weights of all the correctly classified tuples are updated, weights for all tuples are normalized To normalize a weight, multiply by sum of old weights divided by sum of new weights As a result, weights of misclassified tuples are increased and weights of correctly classified tuples are decreased 1 

error

(

M i

) The weight of classifier M assigned class c to X i ’s vote is log

error

(

M i

) The class with the highest sum is the predicted class for tuple X 85

Random Forests

    If each classifier in the ensemble is a decision tree classifier, then the collection of classifiers is a forest Individual decision trees are generated using a random selection of attributes at each node to determine the split During classification, each tree votes and the most popular class is returned Given a training set D of d tuples, for each iteration i (i=1, 2,…, k) a training set D i of d tuples is sampled with replacement from D  Let F be # of attributes to determine the split at each node  To construct M i , randomly select, at each node, F attributes as candidates for the split at the node   Trees are grown to maximize size and are not pruned Random forests formed with random input selection are called Forest-RI 86

Random Forests

   Forest-RC uses random linear combination of the input attributes It creates new attributes that are a linear combination of the existing attributes    An attribute is generated by specifying L, the number of original attributes to be combined At a given node, L attributes are randomly selected and added together with coefficients that are uniform random numbers on [-1,1] F linear combinations are generated and a search is made over these for the best split  These types of random forests are useful with few attributes available to reduce correlation between individual classifiers Accuracy: comparable with Adaboost, more robust to errors and outliers 87

Chapter 8. Classification: Basic Concepts

   

Class Imbalance Problem

Given two-class data, the data are class imbalanced if the main class of interest (positive class) is represented by only a few tuples, while the majority of tuples represent the negative class For multiclass imbalanced data, the data distribution of each class differs substantially where, again, the main class or classes of interest are rare The class-imbalance problem is closely related to cost sensitive learning wherein the costs of errors, per class, are not equal Example: False diagnosis of a cancerous patient as healthy (false negative) is more costly than false diagnosis of a healthy person with cancer (false positive) 89

Class Imbalance Problem

    Algorithms that give equal costs to false positives and false negatives are not suitable for class-imbalanced data Oversampling works by resampling the positive tuples so that the resulting training set contains an equal number of positive tuples so that the resulting training set contains an equal number of positive and negative tuples Undersampling negative tuples works by decreasing the number of  It randomly eliminates tuples from the majority (negative) class until there are equal number of positive and negative tuples Both oversampling represented and undersampling change the training data distribution so that rare (positive) class is well

Class Imbalance Problem

  Threshold-moving  approach does not involve any sampling It applies to classifiers that, given an input tuple, return a continuous output value    For an input tuple X, such a classifier returns as output a mapping f(X)  [0,1] Rather than manipulating the training tuples, this method returns classification decision based on the output values In the simplest approach, tuples for which f(X) some threshold, f are considered positive, while all other tuples are considered negative  t, for  In general, threshold-moving moves the threshold t, so that the rare class tuples are easier to classify Ensemble methods have also been applied to the problem

Chapter 8. Classification: Basic Concepts

Summary (I)

    Classification is a form of data analysis that extracts models describing important data classes. Effective and scalable methods have been developed for decision tree induction, Naive Bayesian classification, rule based classification, and many other classification methods.

Evaluation metrics precision, recall,

F

include: accuracy, sensitivity, specificity, measure, and

F

ß measure.

Stratified k-fold cross-validation is recommended for accuracy estimation. Bagging and boosting can be used to increase overall accuracy by learning and combining a series of individual models.

Summary (II)

    Significance tests and ROC curves are useful for model selection.

There have been numerous comparisons of the different classification methods; the matter remains a research topic.

No single method has been found to be superior over all others for all data sets.

Issues such as accuracy, training time, robustness, scalability, and interpretability must be considered and can involve trade-offs, further complicating the quest for an overall superior method.

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C. M. Bishop, Neural Networks for Pattern Recognition. Oxford University Press, 1995.

L. Breiman, J. Friedman, R. Olshen, and C. Stone. Classification and Regression Trees. Wadsworth International Group, 1984.

C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery , 2(2): 121-168, 1998. P. K. Chan and S. J. Stolfo. Learning arbiter and combiner trees from partitioned data for scaling machine learning. KDD'95.

H. Cheng, X. Yan, J. Han, and C.-W. Hsu,

Discriminative Frequent Pattern Analysis for Effective Classification

, ICDE'07.

H. Cheng, X. Yan, J. Han, and P. S. Yu,

Direct Discriminative Pattern Mining for Effective Classification

, ICDE'08.

W. Cohen. Fast effective rule induction. ICML'95.

G. Cong, K.-L. Tan, A. K. H. Tung, and X. Xu. Mining top-k covering rule groups for gene expression data. SIGMOD'05.

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          A. J. Dobson. An Introduction to Generalized Linear Models. Chapman & Hall, 1990.

G. Dong and J. Li. Efficient mining of emerging patterns: Discovering trends and differences. KDD'99.

R. O. Duda, P. E. Hart, and D. G. Stork. Pattern Classification, 2ed. John Wiley, 2001 U. M. Fayyad. Branching on attribute values in decision tree generation. AAAI’94.

Y. Freund and R. E. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. J. Computer and System Sciences, 1997.

J. Gehrke, R. Ramakrishnan, and V. Ganti. Rainforest: A framework for fast decision tree construction of large datasets. VLDB’98.

J. Gehrke, V. Gant, R. Ramakrishnan, and W.-Y. Loh, BOAT -- Optimistic Decision Tree Construction. SIGMOD'99 .

T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer-Verlag, 2001.

D. Heckerman, D. Geiger, and D. M. Chickering. Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 1995.

W. Li, J. Han, and J. Pei, CMAR: Accurate and Efficient Classification Based on Multiple Class-Association Rules, ICDM'01. 96

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complexity, and training time of thirty-three old and new classification

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M. Mehta, R. Agrawal, and J. Rissanen. SLIQ : A fast scalable classifier for data mining. EDBT'96.

T. M. Mitchell. Machine Learning. McGraw Hill, 1997. S. K. Murthy, Automatic Construction of Decision Trees from Data: A Multi- Disciplinary Survey, Data Mining and Knowledge Discovery 2(4): 345-389, 1998 J. R. Quinlan. Induction of decision trees. Machine Learning , 1:81-106, 1986. J. R. Quinlan and R. M. Cameron-Jones. FOIL: A midterm report. ECML’93.

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Old Slides follow:

100

Chapter 6. Classification and Prediction

      What is classification? What is prediction?

prediction Classification by decision tree induction Bayesian classification Rule-based classification Classification by back propagation April 26, 2020          Support Vector Machines (SVM) Lazy learners (or learning from your neighbors) Frequent-pattern-based classification Other classification methods Prediction Accuracy and error measures Ensemble methods Model selection Summary Data Mining: Concepts and Techniques

Chapter 8. Classification: Basic Concepts

    Classification: Basic Concepts   What Is Classification?

General Approach to Classification Decision Tree Induction  Decision Tree Induction     Attribute Selection Measures Tree Pruning Rainforest: Scalability and Decision Tree Induction Visual Mining for Decision-Tree Induction Bayes Classification Methods  Bayes Theorem  Naive Bayes Classification  Statistical Foundation of Classification Rule-Based Classification   Using IF-THEN Rules for Classification Rule Extraction from a Decision Tree  Rule Induction Using a Sequential Covering Algorithm     April 26, 2020 Model Evaluation and Selection  Evaluation Metric     Holdout Method and Random Subsampling Cross-validation Bootstrap Estimating Confidence Intervals  Comparing Classifiers Based on Cost-Benefit and ROC Curves Techniques to Improve Classification Accuracy: Ensemble Methods   Why does ensemble increase classi¯cation accuracy?

Bagging   Boosting and AdaBoost Random Forest Handling Different Kinds of Cases in Classification  Class Imbalance Problems: Classification of Skewed Data   Multiclass Classification Cost-Sensitive Learning   Active Learning Transfer Learning Summary Data Mining: Concepts and Techniques

Issues: Data Preparation

   Data cleaning  Preprocess data in order to reduce noise and handle missing values Relevance analysis (feature selection)  Remove the irrelevant or redundant attributes Data transformation  Generalize and/or normalize data April 26, 2020 Data Mining: Concepts and Techniques

Issues: Evaluating Classification Methods

      Accuracy   classifier accuracy: predicting class label predictor accuracy: guessing value of predicted attributes Speed  time to construct the model (training time)  time to use the model (classification/prediction time) Robustness: handling noise and missing values Scalability: efficiency in disk-resident databases Interpretability  understanding and insight provided by the model Other measures, e.g., goodness of rules, such as decision tree size or compactness of classification rules April 26, 2020 Data Mining: Concepts and Techniques

Gain Ratio for Attribute Selection (C4.5)

(MK:contains errors)

SplitInfo A

(

)  

j v

  1 | |

D j D

| |  log 2 ( | |

D D j

| | )  GainRatio(A) = Gain(A)/SplitInfo(A) Ex.



SplitInfo A

(

)   4 14  log 2 4 ( 14 )  6 14  log 2 6 ( 14 )  4 14  gain_ratio(income) = 0.029/0.926 = 0.031

log 2 4 ( 14 )  0 .

926 The attribute with the maximum gain ratio is selected as the splitting attribute April 26, 2020 Data Mining: Concepts and Techniques

Gini index (CART, IBM IntelligentMiner)

  Ex. D has 9 tuples in buys_computer = “yes” and 5 in “no”

gini

(

)  1  9 2  5 2  0 .

459 14 14 Suppose the attribute income partitions D into 10 in D 1 : {low, medium} and 4 in D 2

gini income

 {

low

medium

} (

)  10 14  

Gini

(

1 )  4 14  

Gini

(

1 )    but gini {medium,high} is 0.30 and thus the best since it is the lowest All attributes are assumed continuous-valued May need other tools, e.g., clustering, to get the possible split values Can be modified for categorical attributes April 26, 2020 Data Mining: Concepts and Techniques

Classifier Accuracy Measures

Real class\Predicted class C 1 ~C 1 C 1 True positive False positive ~C 1 False negative True negative Real class\Predicted class buy_computer = yes buy_computer = yes 6954 buy_computer = no 46 total 7000 recognition(%) 99.34

buy_computer = no 412 2588 3000 86.27

total 7366 2634 10000 95.42

  Accuracy of a classifier M, acc(M): percentage of test set tuples that are correctly classified by the model M   Error rate (misclassification rate) of M = 1 – acc(M) Given m classes, of tuples in class i CM i,j , an entry in a confusion matrix, indicates # that are labeled by the classifier as class j Alternative accuracy measures (e.g., for cancer diagnosis) sensitivity = t-pos/pos /* true positive recognition rate */ specificity = t-neg/neg /* true negative recognition rate */ precision = t-pos/(t-pos + f-pos) accuracy = sensitivity * pos/(pos + neg) + specificity * neg/(pos + neg)  This model can also be used for cost-benefit analysis April 26, 2020 Data Mining: Concepts and Techniques

Predictor Error Measures

   Measure predictor accuracy: measure how far off the predicted value is from the actual known value Loss function: measures the error betw. y i  Absolute error: | y i – y i ’|  Squared error: (y i – y i ’) 2 and the predicted value y ’ i Test error (generalization error): the average loss over the test set 

Mean absolute error: Mean squared error:

(

y i



y i

  1

  1 ) 2 

i d

  1

d i d



 1

i d

  1 |

y i



| The mean squared-error exaggerates the presence of outliers

i d

  1 ( (

y i y i

 

y i

' )

) 2 2 Popularly use (square) root mean-square error, similarly, root relative squared error April 26, 2020 Data Mining: Concepts and Techniques

Summary (I)

   Classification and prediction used to extract models are two forms of data analysis that can be describing important data classes or to predict future data trends. Effective and scalable methods have been developed for decision trees induction, Naive Bayesian classification, Bayesian belief network, rule based classifier, Backpropagation, Support Vector Machine (SVM), pattern-based classification, nearest neighbor classifiers, and case-based reasoning , and other classification methods such as genetic algorithms , rough set and fuzzy set approaches.

Linear, nonlinear, and generalized linear models of regression can be used for prediction . Many nonlinear problems can be converted to linear problems by performing transformations on the predictor variables. Regression trees and model trees are also used for prediction. April 26, 2020 Data Mining: Concepts and Techniques

Summary (II)

     Stratified k-fold cross-validation is a recommended method for accuracy estimation. Bagging and boosting can be used to increase overall accuracy by learning and combining a series of individual models. Significance tests and ROC curves are useful for model selection There have been numerous comparisons of the different classification and prediction methods , and the matter remains a research topic No single method has been found to be superior over all others for all data sets Issues such as accuracy, training time, robustness, interpretability, and scalability must be considered and can involve trade-offs, further complicating the quest for an overall superior method April 26, 2020 Data Mining: Concepts and Techniques