CHAPTER 7 CLASSIFICATIONS

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CHAPTER 7
CLASSIFICATIONS
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Topics
 What is classification? What is prediction?
 Issues regarding classification and prediction
 Classification by decision tree induction
 Bayesian Classification
 Classification by Neural Networks
 Classification by Support Vector Machines (SVM)
 Classification based on concepts from association rule
mining
 Other Classification Methods
 Prediction
 Classification accuracy
 Summary
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 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
 Prediction:
 models continuous-valued functions, i.e., predicts
unknown or missing values
 Typical Applications
 credit approval
 target marketing
 medical diagnosis
 treatment effectiveness analysis
Classification vs. Prediction
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Classification—A Two-Step Process
 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 over-fitting
will occur
 If the accuracy is acceptable, use the model to classify data
tuples whose class labels are not known
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Classification Process (1): Model
Construction
Training
Data
NAME RANK YEARS TENURED
Mike Assistant Prof 3 no
Mary Assistant Prof 7 yes
Bill Professor 2 yes
Jim Associate Prof 7 yes
Dave Assistant Prof 6 no
Anne Associate Prof 3 no
Classification
Algorithms
IF rank = ‘professor’
OR years > 6
THEN tenured = ‘yes’
Classifier
(Model)
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Classification Process (2): Use the
Model in Prediction
Classifier
Testing
Data
NAME RANK YEARS TENURED
Tom Assistant Prof 2 no
Merlisa Associate Prof 7 no
George Professor 5 yes
Joseph Assistant Prof 7 yes
Unseen Data
(Jeff, Professor, 4)
Tenured?
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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
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ISSUES REGARDING
CLASSIFICATION AND
PREDICTION
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Issues Regarding Classification and Prediction
(1): 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
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Issues regarding classification and prediction
(2): Evaluating Classification Methods
 Predictive accuracy
 Speed and scalability
 time to construct the model
 time to use the model
 Robustness
 handling noise and missing values
 Scalability
 efficiency in disk-resident databases
 Interpretability:
 understanding and insight provided by the model
 Goodness of rules
 decision tree size
 compactness of classification rules
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CLASSIFICATION BY DECISION
TREE INDUCTION
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Training Dataset
age income student credit_rating buys_computer
<=30 high no fair no
<=30 high no excellent no
31…40 high no fair yes
40 medium no fair yes
40 low yes fair yes
40 low yes excellent no
31…40 low yes excellent yes
<=30 medium no fair no <=30 low yes fair yes 40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes 40 medium no excellent no This follows an example from Quinlan’s ID3 13 Output: A Decision Tree for “buys_computer” age? overcast student? credit rating? no yes excellent fair <=30 >40
no yes no yes
yes
30..40
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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)
 Examples are partitioned recursively based on selected attributes
 Test 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
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Attribute Selection Measure:
Information Gain (ID3/C4.5)
 Select the attribute with the highest information gain
 S contains si tuples of class Ci for i = 1, …, m
 information measures info required to classify any
arbitrary tuple
 entropy of attribute A with values a1,a2,…,av
 information gained by branching on attribute A
s
log s
s
I( s ,s ,…,s ) s m i
i
i
1 2 m 2
1 
 
I( s ,…,s )
s
E(A) s … s j mj
v
j
j mj
1
1
1 

 

Gain(A)  I(s1,s 2,…,sm) E(A)
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Attribute Selection by Information
Gain Computation
 Class P: buys_computer = “yes”
 Class N: buys_computer = “no”
 I(p, n) = I(9, 5) =0.940
 Compute the entropy for age:
means “age <=30” has 5 out of 14 samples, with 2 yes’es and 3 no’s. Hence Similarly, age pi ni I(pi, ni) <=30 2 3 0.971 30…40 4 0 0 40 3 2 0.971 (3,2) 0.694 14 5 (4,0) 14 (2,3) 4 14 ( ) 5     I E age I I ( _ ) 0.048 ( ) 0.151 ( ) 0.029    Gain credit rating Gain student Gain income age income student credit_rating buys_computer Gain(age)  I ( p,n)  E(age)  0.246 <=30 high no fair no <=30 high no excellent no 31…40 high no fair yes 40 medium no fair yes 40 low yes fair yes 40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes 40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes 40 medium no excellent no (2,3) 14 5 I 17 Other Attribute Selection Measures  Gini index (CART, IBM IntelligentMiner)  All attributes are assumed continuous-valued  Assume there exist several possible split values for each attribute  May need other tools, such as clustering, to get the possible split values  Can be modified for categorical attributes 18 Gini Index (IBM IntelligentMiner)  If a data set T contains examples from n classes, gini index, gini(T) is defined as where pj is the relative frequency of class j in T.  If a data set T is split into two subsets T1 and T2 with sizes N1 and N2 respectively, the gini index of the split data contains examples from n classes, the gini index gini(T) is defined as  The attribute provides the smallest ginisplit(T) is chosen to split the node (need to enumerate all possible splitting points for each attribute).     n j gini T p j 1 ( ) 1 2 ( ) ( ) ( 2) 2 1 1 gini T N gini T N N gini T N split   19 Extracting Classification Rules from Trees  Represent the knowledge in the form of IF-THEN rules  One rule is created for each path from the root to a leaf  Each attribute-value pair along a path forms a conjunction  The leaf node holds the class prediction  Rules are easier for humans to understand  Example IF age = “<=30” AND student = “no” THEN buys_computer = “no” IF age = “<=30” AND student = “yes” THEN buys_computer = “yes” IF age = “31…40” THEN buys_computer = “yes” IF age = “>40” AND credit_rating = “excellent” THEN buys_computer =
“yes”
IF age = “<=30” AND credit_rating = “fair” THEN buys_computer = “no” 20 Avoid Overfitting in Classification  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” 21 Approaches to Determine the Final Tree Size  Separate training (2/3) and testing (1/3) sets  Use cross validation, e.g., 10-fold cross validation  Use all the data for training  but apply a statistical test (e.g., chi-square) to estimate whether expanding or pruning a node may improve the entire distribution  Use minimum description length (MDL) principle  halting growth of the tree when the encoding is minimized 22 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 23 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 24 Scalable Decision Tree Induction Methods in Data Mining Studies  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 (VLDB’98 — Gehrke, Ramakrishnan & Ganti)  separates the scalability aspects from the criteria that determine the quality of the tree  builds an AVC-list (attribute, value, class label) 25 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. 26 Presentation of Classification Results 27 Visualization of a Decision Tree in SGI/MineSet 3.0 28 Interactive Visual Mining by Perception-Based Classification (PBC) 29 BAYESIAN CLASSIFICATION 30 Bayesian Classification: Why?  Probabilistic learning: Calculate explicit probabilities for hypothesis, among the most practical approaches to certain types of learning problems  Incremental: Each training example can incrementally increase/decrease the probability that a hypothesis is correct. Prior knowledge can be combined with observed data.  Probabilistic prediction: Predict multiple hypotheses, weighted by their probabilities  Standard: Even when Bayesian methods are computationally intractable, they can provide a standard of optimal decision making against which other methods can be measured 31 Bayesian Theorem: Basics  Let X be a data sample whose class label is unknown  Let H be a hypothesis that X belongs to class C  For classification problems, determine P(H/X): the probability that the hypothesis holds given the observed data sample X  P(H): prior probability of hypothesis H (i.e. the initial probability before we observe any data, reflects the background knowledge)  P(X): probability that sample data is observed  P(X|H) : probability of observing the sample X, given that the hypothesis holds 32 Bayesian Theorem  Given training data X, posteriori probability of a hypothesis H, P(H|X) follows the Bayes theorem  Informally, this can be written as posterior =likelihood x prior / evidence  MAP (maximum posteriori) hypothesis  Practical difficulty: require initial knowledge of many probabilities, significant computational cost ( ) ( | ) ( | ) ( ) P X P H X  P X H P H argmax ( | ) argmaxP(D|h)P(h). h H P h D MAP h H h     33 Naïve Bayes Classifier  A simplified assumption: attributes are conditionally independent:  The product of occurrence of say 2 elements x1 and x2, given the current class is C, is the product of the probabilities of each element taken separately, given the same class P([y1,y2],C) = P(y1,C) * P(y2,C)  No dependence relation between attributes  Greatly reduces the computation cost, only count the class distribution.  Once the probability P(X|Ci) is known, assign X to the class with maximum P(X|Ci)P(Ci)   n k P X Ci P xk Ci 1 ( | ) ( | ) 34 Training dataset age income student credit_rating buys_computer <=30 high no fair no <=30 high no excellent no 30…40 high no fair yes 40 medium no fair yes 40 low yes fair yes 40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes 40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes 40 medium no excellent no Class: C1:buys_computer= ‘yes’ C2:buys_computer= ‘no’ Data sample X =(age<=30, Income=medium, Student=yes Credit_rating= Fair) 35 Naïve Bayesian Classifier: Example  Compute P(X/Ci) 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|Ci) : P(X|buys_computer=“yes”)= 0.222 x 0.444 x 0.667 x 0.0.667 =0.044 P(X|buys_computer=“no”)= 0.6 x 0.4 x 0.2 x 0.4 =0.019 P(X|Ci)P(Ci ) : P(X|buys_computer=“yes”) * P(buys_computer=“yes”)=0.028 P(X|buys_computer=“yes”) * P(buys_computer=“yes”)=0.007 X belongs to class “buys_computer=yes” 36 Naïve Bayesian Classifier: Comments  Advantages :  Easy to implement  Good results obtained in most of the cases  Disadvantages  Assumption: class conditional independence , therefore loss of accuracy  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?  Bayesian Belief Networks 37 Bayesian Networks  Bayesian belief network allows a subset of the variables conditionally independent  A graphical model of causal relationships  Represents dependency among the variables  Gives a specification of joint probability distribution X Y Z P Nodes: random variables Links: dependency X,Y are the parents of Z, and Y is the parent of P No dependency between Z and P Has no loops or cycles 38 Bayesian Belief Network: An Example Family History LungCancer PositiveXRay Smoker Emphysema Dyspnea LC ~LC (FH, S) (FH, ~S) (~FH, S) (~FH, ~S) 0.8 0.2 0.5 0.5 0.7 0.3 0.1 0.9 Bayesian Belief Networks The conditional probability table for the variable LungCancer: Shows the conditional probability for each possible combination of its parents   n i P z zn P zi Parents Zi 1 ( 1,…, ) ( | ( )) 39 Learning Bayesian Networks  Several cases  Given both the network structure and all variables observable: learn only the CPTs  Network structure known, some hidden variables: method of gradient descent, analogous to neural network learning  Network structure unknown, all variables observable: search through the model space to reconstruct graph topology  Unknown structure, all hidden variables: no good algorithms known for this purpose  D. Heckerman, Bayesian networks for data mining 40 CLASSIFICATION BY NEURAL NETWORKS 41  Classification:  predicts categorical class labels  Typical Applications  credit history, salary-> credit approval ( Yes/No)
 Temp, Humidity –> Rain (Yes/No)
Classification
Mathematically
( )
:
0,1 , 0,1
y h x
h X Y
x X n y Y


   
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Linear Classification
 Binary Classification
problem
 The data above the red
line belongs to class ‘x’
 The data below red line
belongs to class ‘o’
 Examples – SVM,
Perceptron, Probabilistic
Classifiers
x
x x
x
x x
x
x
x
x oo
o
o
o
o
o
o
o o
o
o
o
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Discriminative Classifiers
 Advantages
 prediction accuracy is generally high
 (as compared to Bayesian methods – in general)
 robust, works when training examples contain errors
 fast evaluation of the learned target function
 (Bayesian networks are normally slow)
 Criticism
 long training time
 difficult to understand the learned function (weights)
 (Bayesian networks can be used easily for pattern discovery)
 not easy to incorporate domain knowledge
 (easy in the form of priors on the data or distributions)
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Neural Networks
 Analogy to Biological Systems (Indeed a great example
of a good learning system)
 Massive Parallelism allowing for computational
efficiency
 The first learning algorithm came in 1959 (Rosenblatt)
who suggested that if a target output value is provided
for a single neuron with fixed inputs, one can
incrementally change weights to learn to produce these
outputs using the perceptron learning rule
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A Neuron
 The n-dimensional input vector x is mapped into
variable y by means of the scalar product and a
nonlinear function mapping
k
f
weighted
sum
Input
vector x
output y
Activation
function
weight
vector w

w0
w1
wn
x0
x1
xn
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A Neuron
k
f
weighted
sum
Input
vector x
output y
Activation
function
weight
vector w

w0
w1
wn
x0
x1
xn
y sign( )
For Example
n
i 0
i i k x w    

Multi-Layer Perceptron
Output nodes
Input nodes
Hidden nodes
Output vector
Input vector: xi
wij
  
i
I j wijOi  j
j I j e
O  

1
1
Errj  Oj (1Oj )(Tj Oj )
jk
k
Errj  Oj (1Oj )Errkw
wij  wij  (l)ErrjOi
 j  j  (l)Errj
Network Training
 The ultimate objective of training
 obtain a set of weights that makes almost all the
tuples in the training data classified correctly
 Steps
 Initialize weights with random values
 Feed the input tuples into the network one by one
 For each unit
 Compute the net input to the unit as a linear combination
of all the inputs to the unit
 Compute the output value using the activation function
 Compute the error
 Update the weights and the bias
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CLASSIFICATION BY
SUPPORT VECTOR MACHINES (SVM)
SVM – Support Vector Machines
Support Vectors
Small Margin Large Margin
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SVM – Cont.
 Linear Support Vector Machine
Given a set of points with label
The SVM finds a hyperplane defined by the pair (w,b)
(where w is the normal to the plane and b is the distance from the
origin)
s.t.
y x w b i N i i (   )  1 1,…,
n
i x  y 1,1 i  
x – feature vector, b- bias, y- class label, ||w|| – margin
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SVM – Cont.
 What if the data is not linearly separable?
 Project the data to high dimensional space where it is
linearly separable and then we can use linear SVM –
(Using Kernels)
-1 0 +1
– +
(0,0) (1,0)
(0,1) +
+
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Non-Linear SVM

?

b
w
x
i
Classification using SVM (w,b)
( , ) 0
?
K x w  b i
In non linear case we can see this as
Kernel – Can be thought of as doing dot product
in some high dimensional space
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Example of Non-linear SVM
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Results
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SVM vs. Neural Network
 SVM
 Relatively new concept
 Nice Generalization
properties
 Hard to learn – learned
in batch mode using
quadratic programming
techniques
 Using kernels can learn
very complex functions
 Neural Network
 Quiet Old
 Generalizes well but
doesn’t have strong
mathematical foundation
 Can easily be learned in
incremental fashion
 To learn complex
functions – use
multilayer perceptron
(not that trivial)
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SVM Related Links
 http://svm.dcs.rhbnc.ac.uk/
 http://www.kernel-machines.org/
 C. J. C. Burges.
A Tutorial on Support Vector Machines for Pattern Recognitio
n.
Knowledge Discovery and Data Mining , 2(2), 1998.
 SVMlight – Software (in C)
http://ais.gmd.de/~thorsten/svm_light
 BOOK: An Introduction to Support Vector Machines
N. Cristianini and J. Shawe-Taylor
Cambridge University Press
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CLASSIFICATION BASED ON
CONCEPTS FROM
ASSOCIATION RULE MINING
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Association-Based Classification
 Several methods for association-based classification
 ARCS: Quantitative association mining and clustering
of association rules (Lent et al’97)
 It beats C4.5 in (mainly) scalability and also accuracy
 Associative classification: (Liu et al’98)
 It mines high support and high confidence rules in the form of
“cond_set => y”, where y is a class label
 CAEP (Classification by aggregating emerging patterns)
(Dong et al’99)
 Emerging patterns (EPs): the itemsets whose support
increases significantly from one class to another
 Mine Eps based on minimum support and growth rate
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OTHER CLASSIFICATION METHODS
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Other Classification Methods
 k-nearest neighbor classifier
 case-based reasoning
 Genetic algorithm
 Rough set approach
 Fuzzy set approaches
63
Instance-Based Methods
 Instance-based learning:
 Store training examples and delay the processing
(“lazy evaluation”) until a new instance must be
classified
 Typical approaches
 k-nearest neighbor approach
 Instances represented as points in a Euclidean
space.
 Locally weighted regression
 Constructs local approximation
 Case-based reasoning
 Uses symbolic representations and knowledgebased
inference
64
The k-Nearest Neighbor Algorithm
 All instances correspond to points in the n-D space.
 The nearest neighbor are defined in terms of
Euclidean distance.
 The target function could be discrete- or real- valued.
 For discrete-valued, the k-NN returns the most
common value among the k training examples nearest
to xq.
 Vonoroi diagram: the decision surface induced by 1-
NN for a typical set of training examples.
.
_
+
_ xq
+
_ _
+
_
_
+
.
.
.
. .
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Discussion on the k-NN Algorithm
 The k-NN algorithm for continuous-valued target functions
 Calculate the mean values of the k nearest neighbors
 Distance-weighted nearest neighbor algorithm
 Weight the contribution of each of the k neighbors
according to their distance to the query point xq
 giving greater weight to closer neighbors
 Similarly, for real-valued target functions
 Robust to noisy data by averaging k-nearest neighbors
 Curse of dimensionality: distance between neighbors could
be dominated by irrelevant attributes.
 To overcome it, axes stretch or elimination of the least
relevant attributes.
w
d xq xi
 1
( , )2
66
Case-Based Reasoning
 Also uses: lazy evaluation + analyze similar instances
 Difference: Instances are not “points in a Euclidean space”
 Example: Water faucet problem in CADET (Sycara et al’92)
 Methodology
 Instances represented by rich symbolic descriptions
(e.g., function graphs)
 Multiple retrieved cases may be combined
 Tight coupling between case retrieval, knowledge-based
reasoning, and problem solving
 Research issues
 Indexing based on syntactic similarity measure, and
when failure, backtracking, and adapting to additional
cases
67
Remarks on Lazy vs. Eager Learning
 Instance-based learning: lazy evaluation
 Decision-tree and Bayesian classification: eager evaluation
 Key differences
 Lazy method may consider query instance xq when deciding how to
generalize beyond the training data D
 Eager method cannot since they have already chosen global
approximation when seeing the query
 Efficiency: Lazy – less time training but more time predicting
 Accuracy
 Lazy method effectively uses a richer hypothesis space since it uses
many local linear functions to form its implicit global approximation
to the target function
 Eager: must commit to a single hypothesis that covers the entire
instance space
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Genetic Algorithms
 GA: based on an analogy to biological evolution
 Each rule is represented by a string of bits
 An initial population is created consisting of randomly
generated rules
 e.g., IF A1 and Not A2 then C2 can be encoded as 100
 Based on the notion of survival of the fittest, a new
population is formed to consists of the fittest rules and
their offsprings
 The fitness of a rule is represented by its classification
accuracy on a set of training examples
 Offsprings are generated by crossover and mutation
69
Rough Set Approach
 Rough sets are used to approximately or “roughly”
define equivalent classes
 A rough set for a given class C is approximated by two
sets: a lower approximation (certain to be in C) and an
upper approximation (cannot be described as not
belonging to C)
 Finding the minimal subsets (reducts) of attributes (for
feature reduction) is NP-hard but a discernibility matrix
is used to reduce the computation intensity
70
Fuzzy Set
Approaches
 Fuzzy logic uses truth values between 0.0 and 1.0 to
represent the degree of membership (such as using fuzzy
membership graph)
 Attribute values are converted to fuzzy values
 e.g., income is mapped into the discrete categories
low, medium, high with fuzzy values calculated
 For a given new sample, more than one fuzzy value may
apply
 Each applicable rule contributes a vote for membership in
the categories
 Typically, the truth values for each predicted category are
summed
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PREDICTION
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What Is Prediction?
 Prediction is similar to classification
 First, construct a model
 Second, use model to predict unknown value
 Major method for prediction is regression
 Linear and multiple regression
 Non-linear regression
 Prediction is different from classification
 Classification refers to predict categorical class label
 Prediction models continuous-valued functions
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 Predictive modeling: Predict data values or construct
generalized linear models based on the database data.
 One can only predict value ranges or category distributions
 Method outline:
 Minimal generalization
 Attribute relevance analysis
 Generalized linear model construction
 Prediction
 Determine the major factors which influence the prediction
 Data relevance analysis: uncertainty measurement,
entropy analysis, expert judgement, etc.
 Multi-level prediction: drill-down and roll-up analysis
Predictive Modeling in Databases
74
 Linear regression: Y =  +  X
 Two parameters ,  and  specify the line and are to
be estimated by using the data at hand.
 using the least squares criterion to the known values of
Y1, Y2, …, X1, X2, ….
 Multiple regression: Y = b0 + b1 X1 + b2 X2.
 Many nonlinear functions can be transformed into the
above.
 Log-linear models:
 The multi-way table of joint probabilities is
approximated by a product of lower-order tables.
 Probability: p(a, b, c, d) = ab acad bcd
Regress Analysis and Log-Linear
Models in Prediction
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Locally Weighted Regression
 Construct an explicit approximation to f over a local region
surrounding query instance xq.
 Locally weighted linear regression:
 The target function f is approximated near xq using the
linear function:
 minimize the squared error: distance-decreasing weight K
 the gradient descent training rule:
 In most cases, the target function is approximated by a
constant, linear, or quadratic function.
f(x)  w w a (x) wnan(x) 0 1 1 
E xq f x f x
x k nearest neighbors of xq
( ) ( ( ) ( )) K d xq x
  ( ( , ))

1 
2
2
wj K d xq x f x f x a j x
x k nearest neighbors of xq
 

  ( ( , ))(( ( ) ( )) ( )
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Prediction: Numerical Data
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Prediction: Categorical Data
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CLASSIFICATION ACCURACY
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Classification Accuracy: Estimating Error
Rates
 Partition: Training-and-testing
 use two independent data sets, e.g., training set
(2/3), test set(1/3)
 used for data set with large number of samples
 Cross-validation
 divide the data set into k subsamples
 use k-1 subsamples as training data and one subsample
as test data—k-fold cross-validation
 for data set with moderate size
 Bootstrapping (leave-one-out)
 for small size data
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Bagging and Boosting
 General idea
Training data
Altered Training data
Altered Training data
……..
Aggregation ….
Classifier C
Classification method (CM)
CM
Classifier C1
CM
Classifier C2
Classifier C*
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Bagging
 Given a set S of s samples
 Generate a bootstrap sample T from S. Cases in S may not
appear in T or may appear more than once.
 Repeat this sampling procedure, getting a sequence of k
independent training sets
 A corresponding sequence of classifiers C1,C2,…,Ck is
constructed for each of these training sets, by using the
same classification algorithm
 To classify an unknown sample X,let each classifier predict
or vote
 The Bagged Classifier C* counts the votes and assigns X to
the class with the “most” votes
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Boosting Technique — Algorithm
 Assign every example an equal weight 1/N
 For t = 1, 2, …, T Do
 Obtain a hypothesis (classifier) h(t) under w(t)
 Calculate the error of h(t) and re-weight the examples
based on the error . Each classifier is dependent on the
previous ones. Samples that are incorrectly predicted
are weighted more heavily
 Normalize w(t+1) to sum to 1 (weights assigned to
different classifiers sum to 1)
 Output a weighted sum of all the hypothesis, with each
hypothesis weighted according to its accuracy on the
training set
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Bagging and Boosting
 Experiments with a new boosting algorithm,
freund et al (AdaBoost )
 Bagging Predictors, Brieman
 Boosting Naïve Bayesian Learning on large subset
of MEDLINE, W. Wilbur
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Summary
 Classification is an extensively studied problem (mainly in
statistics, machine learning & neural networks)
 Classification is probably one of the most widely used
data mining techniques with a lot of extensions
 Scalability is still an important issue for database
applications: thus combining classification with database
techniques should be a promising topic
 Research directions: classification of non-relational data,
e.g., text, spatial, multimedia, etc..
May 27, 2020 Data Mining: Concepts and Techniques 85
Thank you !!!
Questions
86
Based on the figure below, what is the valid production
rule for the decision tree.
Teaching Job
Application?
Yes No
Temp
above
90?
Decision=wear
formal dress
No Yes
Decision=wear slacks Decision=wear jeans
87
Make a decision tree with root node Type from the data in the table below. The
first row contains attribute names. Each row after the first represents the values for
one data instance. The output attribute is Class.
Scale Type Color Texture Class
One One Light slick A
Two One Dark slick A
Two Two Dark slick B
Two One Light slick B
One Two Light slick C
88
Unsupervised evaluation can be internal or external. Why is it that Comparing the sum of
squared error differences between instances and their corresponding cluster centers for each
alternative clustering is an internal method for evaluating alternative clustering produced by the
K-Means algorithm? Explain your answer.
Why is it that sensitivity analysis is a neural network explanation technique used to determine
the relative importance of individual input attributes.
Explain why a feed-forward neural network is said to be fully connected when all nodes at one
layer are connected to all nodes in the next higher layer.
The probability of 60% that a person owns a sports car is given a subscription at least one
automotive magazine. 5% of the adult population subscribes at least one automotive magazine.
35% is the probability of a person owning a sports car given that they don’t subscribe any
automotive magazine. Use the information given together with Bayes theorem to compute the
probability that a person subscribes at least one automotive magazine owned a sports car.

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