DCIT414: Data Mining and

Warehousing

Session 5 – Classification and Prediction

By
Solomon Mensah (PhD)

College of Education
School of Continuing and Distance Education
2014/2015 – 2016/2017
 Agenda
• What is classification? What is • Support Vector Machines (SVM)
prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 Classification vs. 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
• Prediction
– models continuous-valued functions, i.e., predicts unknown
or missing values
• Typical applications
– Credit approval
– Target marketing
– Medical diagnosis
– Fraud detection
 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
 Process (1): Model Construction

Classification
Algorithms
Training
Data

NAM E RANK YEARS TENURED Classifier

M ike Assistant Prof 3 no (Model)
M ary Assistant Prof 7 yes
Bill Professor 2 yes
Jim Associate Prof 7 yes
IF rank = ‘professor’
Dave Assistant Prof 6 no
OR years > 6
Anne Associate Prof 3 no
THEN tenured = ‘yes’
 Process (2): Using the Model in Prediction

Classifier

Testing
Data Unseen Data

(Jeff, Professor, 4)
NAM E RANK YEARS TENURED
Tom Assistant Prof 2 no Tenured?
M erlisa Associate Prof 7 no
George Professor 5 yes
Joseph Assistant Prof 7 yes
 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
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 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
 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
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 Decision Tree Induction: 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
Output: A Decision Tree for “buys_computer”

age?

<=30 overcast
31..40 >40

student? yes credit rating?

no yes excellent fair

no yes no yes
 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
 Attribute Selection Measure:
Information Gain
n Select the attribute with the highest information gain
n Let pi be the probability that an arbitrary tuple in D
belongs to class Ci, estimated by |Ci, D|/|D|
n Expected information (entropy) needed to classify a tuple
in D: m
Info ( D) = -å pi log 2 ( pi )
i =1

n Information needed (after using A to split D into v

v |D |
partitions) to classify D:
InfoA ( D) = å
j
´ I (D j )
j =1 |D|
n Information gained by branching on attribute A

Gain(A) = Info(D) - InfoA(D)

 Attribute Selection: Information Gain

g Class P: buys_computer = “yes”à9 5 4

Infoage ( D) = I (2,3) + I (4,0)
g Class N: buys_computer = “no”à5 14 14
9 9 5 5
Info( D) = I (9,5) = - log 2 ( ) - log 2 ( ) =0.940 5
14 14 14 14 + I (3,2) = 0.694
14
age pi ni I(pi, ni) 5
I (2,3)means “age <=30” has 5 out of
<=30 2 3 0.971 14 14 samples, with 2 yes’es and 3
31…40 4 0 0 no’s. Hence
>40 3 2 0.971
age income student credit_rating buys_computer Gain(age ) = Info ( D) - Infoage ( D) = 0.246
<=30 high no fair no
<=30 high no excellent no Similarly,
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 Gain(income) = 0.029
<=30 low yes fair yes
>40 medium yes fair yes
Gain( student ) = 0.152
<=30 medium yes excellent yes Gain(credit _ rating ) = 0.048
31…40 medium no excellent yes
31…40 high yes fair yes
>40 medium no excellent no
 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
 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
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 Bayesian Classification: Why?

• A statistical classifier: performs probabilistic prediction, i.e.,

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
 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), the probability that the
hypothesis holds given the observed data sample X
• 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) (posteriori probability), 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
 Bayesian Theorem
• Given training data X, posteriori probability of a hypothesis H,
P(H|X), follows the Bayes theorem

P(H | X) = P(X | H )P(H )

P(X)
• Informally, this can be written as
posteriori = likelihood x prior/evidence
• Predicts X belongs to C2 iff the probability P(Ci|X) is the highest
among all the P(Ck|X) for all the k classes
• Practical difficulty: require initial knowledge of many
probabilities, significant computational cost
https://www.statisticshowto.com/bayes-theorem-problems/
 Bayesian Theorem
• In most cases, you can’t just plug numbers into an equation; You
have to figure out what your “tests” and “events” are first.
• For two events, A and B, Bayes’ theorem allows you to figure
out p(A|B) (the probability that event A happened, given that
test B was positive) from p(B|A) (the probability that test B
happened, given that event A happened).
• It can be a little tricky to wrap your head around as technically
you’re working backwards; you may have to switch your tests
and events around, which can get confusing.
• An example should clarify what I mean by “switch the tests and
events around.”
https://www.statisticshowto.com/bayes-theorem-problems/
 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 = (x1,
x2, …, xn)
• Suppose there are m classes C1, C2, …, Cm.
• Classification is to derive the maximum posteriori, i.e., the
maximal P(Ci|X)
• This can be derived from Bayes’ theorem
P(X | C )P(C )
P(C | X) = i i
i P(X)
• Since P(X) is constant for all classes, only
P(C | X) = P(X| C )P(C )
i i i
needs to be maximized
 Derivation of Naïve Bayes Classifier
• A simplified assumption: attributes are conditionally
independent (i.e., no dependence
n
relation between attributes):
P( X | C i) = Õ P( x | C i) = P( x | C i) ´ P( x | C i) ´ ... ´ P( x | C i)
k 1 2 n
k =1
• This greatly reduces the computation cost: Only counts the
class distribution
• If Ak is categorical, P(xk|Ci) is the # of tuples in Ci having value xk
for Ak divided by |Ci, D| (# of tuples of Ci in D)
• If Ak is continous-valued, P(xk|Ci) is usually computed based on
Gaussian distribution with a mean μ and standard deviation σ

and P(xk|Ci) is 1 -
( x-µ )2

g ( x, µ , s ) = e 2s 2

2p s

P ( X | C i ) = g ( xk , µ Ci , s Ci )
 Naïve Bayesian Classifier: Training Dataset
age income studentcredit_rating
buys_compu
<=30 high no fair no
<=30 high no excellent no
Class: 31…40 high no fair yes
C1:buys_computer = ‘yes’ >40 medium no fair yes
C2:buys_computer = ‘no’ >40 low yes fair yes
>40 low yes excellent no
Data sample
X = (age <=30,
31…40 low yes excellent yes
Income = medium, <=30 medium no fair no
Student = yes <=30 low yes fair yes
Credit_rating = Fair) >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
 Naïve Bayesian Classifier: An Example
• P(Ci): P(buys_computer = “yes”) = 9/14 = 0.643
P(buys_computer = “no”) = 5/14= 0.357

• 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 0.667 = 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 = “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
n
P( X | C i ) = Õ P( x k | C i )
k =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
Prob(income = medium) = 991/1003
Prob(income = high) = 11/1003
– The “corrected” prob. estimates are close to their “uncorrected”
counterparts
 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
 Bayesian Belief 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
q Nodes: random variables
q Links: dependency
X Y q X and Y are the parents of Z, and Y is
the parent of P
Z q No dependency between Z and P
P q Has no loops or cycles
 Bayesian Belief Network: An Example
Family The conditional probability table
Smoker
History (CPT) for variable LungCancer:
(FH, S) (FH, ~S) (~FH, S) (~FH, ~S)

LC 0.8 0.5 0.7 0.1

LungCancer Emphysema ~LC 0.2 0.5 0.3 0.9

CPT shows the conditional probability for

each possible combination of its parents

PositiveXRay Dyspnea Derivation of the probability of a

particular combination of values of X,
from CPT:
n
Bayesian Belief Networks P( x1 ,..., xn ) = Õ P( xi | Parents(Y i ))
i =1
 Training Bayesian Networks
• Several scenarios:
– Given both the network structure and all variables
observable: learn only the CPTs
– Network structure known, some hidden variables: gradient
descent (greedy hill-climbing) method, analogous to neural
network learning
– Network structure unknown, all variables observable:
search through the model space to reconstruct network
topology
– Unknown structure, all hidden variables: No good
algorithms known for this purpose
• Ref. D. Heckerman: Bayesian networks for data mining
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 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 = yes
– Rule antecedent/precondition vs. rule consequent
• Assessment of a rule: coverage and accuracy
– ncovers = # of tuples covered by R
– ncorrect = # of tuples correctly classified by R
coverage(R) = ncovers /|D| /* D: training data set */
accuracy(R) = ncorrect / ncovers
• If more than one rule is 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 test)
– Class-based ordering: 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 or by experts
 Rule Extraction from a Decision Tree
age?

<=30 31..40 >40

n Rules are easier to understand than large trees
student? credit rating?
yes
n One rule is created for each path from the root
no yes excellent fair
to a leaf
no yes no yes
n Each attribute-value pair along a path forms a
conjunction: the leaf holds the class prediction
n Rules are mutually exclusive and exhaustive
• Example: Rule extraction from our buys_computer decision-tree
IF age = young AND student = no THEN buys_computer = no
IF age = young AND student = yes THEN buys_computer = yes
IF age = mid-age THEN buys_computer = yes
IF age = old AND credit_rating = excellent THEN buys_computer = yes
IF age = young AND credit_rating = fair THEN buys_computer = no
 Rule Extraction from the Training Data

• 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 Ci will cover many tuples
of Ci 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 examples 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
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 Classification: A Mathematical Mapping

• Classification:
– predicts categorical class labels
• E.g., Personal homepage classification
– xi = (x1, x2, x3, …), yi = +1 or –1
– x1 : # of a word “homepage”
– x2 : # of a word “welcome”
• Mathematically
– x Î X = Ân, y Î Y = {+1, –1}
– We want a function f: X à Y
 Linear Classification
• Binary Classification problem
• The data above the red line
belongs to class ‘x’
• The data below red line
x belongs to class ‘o’
x x
x x • Examples: SVM, Perceptron,
x Probabilistic Classifiers
x x x o
o
x o o
ooo
o o
o o o o
 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
 Perceptron & Winnow
• Vector: x, w
x2
• Scalar: x, y, w
Input: {(x1, y1), …}
Output: classification function f(x)
f(xi) > 0 for yi = +1
f(xi) < 0 for yi = -1
f(x) => wx + b = 0
or w1x1+w2x2+b = 0

• Perceptron: update W
additively
• Winnow: update W
multiplicatively
x1
 Classification by Backpropagation
• Backpropagation: A neural network learning algorithm
• Started by psychologists and neurobiologists to develop and
test computational analogues of neurons
• A neural network: A set of connected input/output units
where each connection has a weight associated with it
• During the learning phase, the network learns by adjusting
the weights so as to be able to predict the correct class label
of the input tuples
• Also referred to as connectionist learning due to the
connections between units
 Neural Network as a Classifier
• Weakness
– Long training time
– Require a number of parameters typically best determined empirically,
e.g., the network topology or ``structure."
– Poor interpretability: Difficult to interpret the symbolic meaning behind
the learned weights and of ``hidden units" in the network
• Strength
– High tolerance to noisy data
– Ability to classify untrained patterns
– Well-suited for continuous-valued inputs and outputs
– Successful on a wide array of real-world data
– Algorithms are inherently parallel
– Techniques have recently been developed for the extraction of rules
from trained neural networks
 A Neuron (= a perceptron)

- µk
x0 w0
x1 w1
å f
output y
xn wn
For Example
n
Input weight weighted Activation y = sign(å wi xi + µ k )
vector x vector w sum function i =0

• The n-dimensional input vector x is mapped into variable y by means of

the scalar product and a nonlinear function mapping
 A Multi-Layer Feed-Forward Neural Network

Output vector

Errj = O j (1 - O j )å Errk w jk
Output layer k
q j = q j + (l) Err j
wij = wij + (l ) Err j Oi
Hidden layer Err j = O j (1 - O j )(T j - O j )
wij 1
Oj = -I
1+ e j
Input layer
I j = å wij Oi + q j
i
Input vector: X
 How A Multi-Layer Neural Network Works?

• The inputs to the network correspond to the attributes measured for each
training tuple
• Inputs are fed simultaneously into the units making up the input layer
• They are then weighted and fed simultaneously to a hidden layer
• The number of hidden layers is arbitrary, although usually only one
• The weighted outputs of the last hidden layer are input to units making up
the output layer, which emits the network's prediction
• The network is feed-forward in that none of the weights cycles back to an
input unit or to an output unit of a previous layer
• From a statistical point of view, networks perform nonlinear regression:
Given enough hidden units and enough training samples, they can closely
approximate any function
 Defining a Network Topology
• First decide the network topology: # of units in the input layer, #
of hidden layers (if > 1), # of units in each hidden layer, and # of
units in the output layer
• Normalizing the input values for each attribute measured in the
training tuples to [0.0—1.0]
• One input unit per domain value, each initialized to 0
• Output, if for classification and more than two classes, one
output unit per class is used
• Once a network has been trained and its accuracy is
unacceptable, repeat the training process with a different
network topology or a different set of initial weights
 Backpropagation
• Iteratively process a set of training tuples & compare the network's
prediction with the actual known target value
• For each training tuple, the weights are modified to minimize the mean
squared error between the network's prediction and the actual target value
• Modifications are made in the “backwards” direction: from the output layer,
through each hidden layer down to the first hidden layer, hence
“backpropagation”
• Steps
– Initialize weights (to small random #s) and biases in the network
– Propagate the inputs forward (by applying activation function)
– Backpropagate the error (by updating weights and biases)
– Terminating condition (when error is very small, etc.)
 Backpropagation and Interpretability
• Efficiency of backpropagation: Each epoch (one interation through the
training set) takes O(|D| * w), with |D| tuples and w weights, but # of
epochs can be exponential to n, the number of inputs, in the worst case
• Rule extraction from networks: network pruning
– Simplify the network structure by removing weighted links that have the
least effect on the trained network
– Then perform link, unit, or activation value clustering
– The set of input and activation values are studied to derive rules
describing the relationship between the input and hidden unit layers
• Sensitivity analysis: assess the impact that a given input variable has on a
network output. The knowledge gained from this analysis can be
represented in rules
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 SVM—Support Vector Machines

• A new classification method for both linear and nonlinear data

• It uses a nonlinear mapping to transform the original training
data into a higher dimension
• With the new dimension, it searches for the linear optimal
separating hyperplane (i.e., “decision boundary”)
• With an appropriate nonlinear mapping to a sufficiently high
dimension, data from two classes can always be separated by a
hyperplane
• SVM finds this hyperplane using support vectors (“essential”
training tuples) and margins (defined by the support vectors)
 SVM—History and Applications
• Vapnik and colleagues (1992)—groundwork from Vapnik &
Chervonenkis’ statistical learning theory in 1960s
• Features: training can be slow but accuracy is high owing to
their ability to model complex nonlinear decision boundaries
(margin maximization)
• Used both for classification and prediction
• Applications:
– handwritten digit recognition, object recognition, speaker
identification, benchmarking time-series prediction tests
 SVM—General Philosophy

Small Margin Large Margin

Support Vectors
SVM—Margins and Support Vectors
SVM—When Data Is Linearly Separable

Let data D be (X1, y1), …, (X|D|, y|D|), where Xi is the set of training tuples
associated with the class labels yi
There are infinite lines (hyperplanes) separating the two classes but we want to
find the best one (the one that minimizes classification error on unseen data)
SVM searches for the hyperplane with the largest margin, i.e., maximum
marginal hyperplane (MMH)
 SVM—Linearly Separable
n A separating hyperplane can be written as
W●X+b=0
where W={w1, w2, …, wn} is a weight vector and b a scalar (bias)
n For 2-D it can be written as
w0 + w1 x1 + w2 x2 = 0
n The hyperplane defining the sides of the margin:
H1: w0 + w1 x1 + w2 x2 ≥ 1 for yi = +1, and
H2: w0 + w1 x1 + w2 x2 ≤ – 1 for yi = –1
n Any training tuples that fall on hyperplanes H1 or H2 (i.e., the
sides defining the margin) are support vectors
n This becomes a constrained (convex) quadratic optimization
problem: Quadratic objective function and linear constraints à
Quadratic Programming (QP) à Lagrangian multipliers
 Why Is SVM Effective on High Dimensional Data?

n The complexity of trained classifier is characterized by the # of

support vectors rather than the dimensionality of the data
n The support vectors are the essential or critical training examples —
they lie closest to the decision boundary (MMH)
n If all other training examples are removed and the training is
repeated, the same separating hyperplane would be found
n The number of support vectors found can be used to compute an
(upper) bound on the expected error rate of the SVM classifier, which
is independent of the data dimensionality
n Thus, an SVM with a small number of support vectors can have good
generalization, even when the dimensionality of the data is high
 A2

SVM—Linearly Inseparable

Transform the original input data into a higher dimensional

A1
n

space

n Search for a linear separating hyperplane in the new space

 SVM—Kernel functions
n Instead of computing the dot product on the transformed data tuples,
it is mathematically equivalent to instead applying a kernel function
K(Xi, Xj) to the original data, i.e., K(Xi, Xj) = Φ(Xi) Φ(Xj)
n Typical Kernel Functions

n SVM can also be used for classifying multiple (> 2) classes and for
regression analysis (with additional user parameters)
 SVM vs. Neural Network
• SVM • Neural Network
– Deterministic algorithm – Nondeterministic algorithm
– Nice Generalization – Generalizes well but
doesn’t have strong
properties mathematical foundation
– Hard to learn – learned in – Can easily be learned in
batch mode using incremental fashion
quadratic programming – To learn complex
techniques functions—use multilayer
perceptron (not that trivial)
– Using kernels can learn
very complex functions
 SVM Related Links
• SVM Website

– http://www.kernel-machines.org/

• Representative implementations

– LIBSVM: an efficient implementation of SVM, multi-class classifications,

nu-SVM, one-class SVM, including also various interfaces with java,
python, etc.

– SVM-light: simpler but performance is not better than LIBSVM, support

only binary classification and only C language

– SVM-torch: another recent implementation also written in C.

 SVM—Introduction Literature
• “Statistical Learning Theory” by Vapnik: extremely hard to understand,
containing many errors too.
• C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern
Recognition. Knowledge Discovery and Data Mining, 2(2), 1998.
– Better than the Vapnik’s book, but still written too hard for introduction,
and the examples are so not-intuitive
• The book “An Introduction to Support Vector Machines” by N. Cristianini and
J. Shawe-Taylor
– Also written hard for introduction, but the explanation about the
mercer’s theorem is better than above literatures
• The neural network book by Haykins
– Contains one nice chapter of SVM introduction
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 Associative Classification
• Associative classification
– Association rules are generated and analyzed for use in classification
– Search for strong associations between frequent patterns (conjunctions of
attribute-value pairs) and class labels
– Classification: Based on evaluating a set of rules in the form of
P1 ^ p2 … ^ pl à “Aclass = C” (conf, sup)
• Why effective?
– It explores highly confident associations among multiple attributes and may
overcome some constraints introduced by decision-tree induction, which
considers only one attribute at a time
– In many studies, associative classification has been found to be more
accurate than some traditional classification methods, such as C4.5
 Typical Associative Classification Methods

• CBA (Classification By Association: Liu, Hsu & Ma, KDD’98)

– Mine association possible rules in the form of
• Cond-set (a set of attribute-value pairs) à class label
– Build classifier: Organize rules according to decreasing precedence based on
confidence and then support
• CMAR (Classification based on Multiple Association Rules: Li, Han, Pei, ICDM’01)
– Classification: Statistical analysis on multiple rules
• CPAR (Classification based on Predictive Association Rules: Yin & Han, SDM’03)
– Generation of predictive rules (FOIL-like analysis)
– High efficiency, accuracy similar to CMAR
• RCBT (Mining top-k covering rule groups for gene expression data, Cong et al. SIGMOD’05)
– Explore high-dimensional classification, using top-k rule groups
– Achieve high classification accuracy and high run-time efficiency
Associative Classification May Achieve High Accuracy and
Efficiency (Cong et al. SIGMOD05)
 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, dist(X1, X2)
• Target function could be discrete- or real- valued
• For discrete-valued, 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 + . . .
_
+ .
 Discussion on the k-NN Algorithm
• k-NN for real-valued prediction for a given unknown tuple
– Returns 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 xq 1
wº
• Give greater weight to closer neighbors d ( xq , x )2
i
• 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
 Genetic Algorithms (GA)
• Genetic Algorithm: based on an analogy to biological evolution
• An initial population is created consisting of randomly generated rules
– Each rule is represented by a string of bits
– E.g., if A1 and ¬A2 then C2 can be encoded as 100
– If an attribute has k > 2 values, k bits can be used
• Based on the notion of survival of the fittest, a new population is formed to
consist 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
• The process continues until a population P evolves when each rule in P
satisfies a prespecified threshold
• Slow but easily parallelizable
 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 (which stores the differences between
attribute values for each pair of data tuples) is used to reduce the
computation intensity
 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, and these sums are combined
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 What Is Prediction?
• (Numerical) prediction is similar to classification
– construct a model
– use model to predict continuous or ordered value for a given input
• Prediction is different from classification
– Classification refers to predict categorical class label
– Prediction models continuous-valued functions
• Major method for prediction: regression
– model the relationship between one or more independent or predictor
variables and a dependent or response variable
• Regression analysis
– Linear and multiple regression
– Non-linear regression
– Other regression methods: generalized linear model, Poisson regression,
log-linear models, regression trees
 Linear Regression
• Linear regression: involves a response variable y and a single predictor
variable x
y = w0 + w1 x
where w0 (y-intercept) and w1 (slope) are regression coefficients
• Method of least squares: estimates the best-fitting straight line
| D|

å (x - x )( yi - y )
w = i =1
i
w = y-w x
1 | D|
0 1
å (x - x) i =1
i
2

• Multiple linear regression: involves more than one predictor variable

– Training data is of the form (X1, y1), (X2, y2),…, (X|D|, y|D|)
– Ex. For 2-D data, we may have: y = w0 + w1 x1+ w2 x2
– Solvable by extension of least square method or using SAS, S-Plus
– Many nonlinear functions can be transformed into the above
 Nonlinear Regression
• Some nonlinear models can be modeled by a polynomial function
• A polynomial regression model can be transformed into linear
regression model. For example,
y = w0 + w1 x + w2 x2 + w3 x3
convertible to linear with new variables: x2 = x2, x3= x3
y = w0 + w1 x + w2 x2 + w3 x3
• Other functions, such as power function, can also be transformed
to linear model
• Some models are intractable nonlinear (e.g., sum of exponential
terms)
– possible to obtain least square estimates through extensive
calculation on more complex formulae
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 C1 C2
Classifier Accuracy Measures C1 True positive False negative
C2 False positive True negative

classes buy_computer = yes buy_computer = no total recognition(%)

buy_computer = yes 6954 46 7000 99.34
buy_computer = no 412 2588 3000 86.27
total 7366 2634 10000 95.52

• 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, CMi,j, an entry in a confusion matrix, indicates # of tuples in
class i 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
 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. yi and the predicted value yi’
– Absolute error: | yi – yi’|
– Squared error: (yi – yi’)2
• Test error (generalization error): the average loss over the test set
d d

– Mean absolute error: å | y - yMean

i =1
'| squared error:
i i å( y - y ')
i =1
i i
2

d d
d

– Relative absolute error:

d

å | y -Relative
y '|
i squared error:
i
å ( yi - yi ' ) 2
i =1
i =1
d d
å| y
i =1
i -y|
å(y
i =1
i - y)2
The mean squared-error exaggerates the presence of outliers
Popularly use (square) root mean-square error, similarly, root relative
squared error
 Evaluating the Accuracy of a Classifier or Predictor (I)

• 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 sampling: 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 k mutually exclusive subsets, each
approximately equal size
– At i-th iteration, use Di as test set and others as training set
– Leave-one-out: k folds where k = # of tuples, for small sized data
– Stratified cross-validation: folds are stratified so that class dist. in each
fold is approx. the same as that in the initial data
 Evaluating the Accuracy of a Classifier or Predictor (II)

• 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 boostrap methods, and a common one is .632 boostrap
– Suppose we are given a data set of d tuples. The data set is sampled d times, with
replacement, resulting in a training set of d samples. The data tuples that did not
make it into the training set end up forming the test set. About 63.2% of the
original data will end up in the bootstrap, and the remaining 36.8% will form the
test set (since (1 – 1/d)d ≈ e-1 = 0.368)
– Repeat the sampling procedue k times, overall accuracy of the model:
k
acc( M ) = å (0.632 ´ acc( M i )test _ set +0.368 ´ acc( M i )train _ set )
i =1
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 Ensemble Methods: Increasing the Accuracy

• Ensemble methods
– Use a combination of models to increase accuracy
– Combine a series of k learned models, M1, M2, …, Mk, with
the aim of creating an improved model M*
• Popular ensemble methods
– Bagging: averaging the prediction over a collection of
classifiers
– Boosting: weighted vote with a collection of classifiers
– Ensemble: combining a set of heterogeneous classifiers
 Bagging: Boostrap Aggregation
• Analogy: Diagnosis based on multiple doctors’ majority vote
• Training
– Given a set D of d tuples, at each iteration i, a training set Di of d tuples is
sampled with replacement from D (i.e., boostrap)
– A classifier model Mi is learned for each training set Di
• Classification: classify an unknown sample X
– Each classifier Mi returns its class prediction
– The bagged classifier M* counts the votes and assigns the class with the
most votes to X
• Prediction: can be applied to the prediction of continuous values by taking
the average value of each prediction for a given test tuple
• Accuracy
– Often significant better than a single classifier derived from D
– For noise data: not considerably worse, more robust
– Proved improved accuracy in prediction
 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 is iteratively learned
– After a classifier Mi is learned, the weights are updated to allow the
subsequent classifier, Mi+1, to pay more attention to the training tuples
that were misclassified by Mi
– The final M* combines the votes of each individual classifier, where the
weight of each classifier's vote is a function of its accuracy
• The boosting algorithm can be extended for the prediction of continuous
values
• 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, (X1, y1), …, (Xd, yd)
• Initially, all the weights of tuples are set the same (1/d)
• Generate k classifiers in k rounds. At round i,
– Tuples from D are sampled (with replacement) to form a training set Di
of the same size
– Each tuple’s chance of being selected is based on its weight
– A classification model Mi is derived from Di
– Its error rate is calculated using Di as a test set
– If a tuple is misclssified, its weight is increased, o.w. it is decreased
• Error rate: err(Xj) is the misclassification error of tuple Xj. Classifier Mi
error rate is the sum of the weights of the misclassified tuples:
d
error ( M i ) = å w j ´ err ( X j )
j
• The weight of classifier Mi’s vote is 1 - error ( M i )
log
error ( M i )
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 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
n Vertical axis represents
• The area under the ROC curve is a measure of
the true positive rate
the accuracy of the model
n Horizontal axis rep. the
• Rank the test tuples in decreasing order: the false positive rate
one that is most likely to belong to the positive
n The plot also shows a
class appears at the top of the list diagonal line
• The closer to the diagonal line (i.e., the closer n A model with perfect
the area is to 0.5), the less accurate is the accuracy will have an
model area of 1.0
 Classification and Prediction

• What is classification? What is • Support Vector Machines (SVM)

prediction? • Associative classification
• Issues regarding classification and • Other classification methods
prediction • Prediction
• Classification by decision tree • Accuracy and error measures
induction
• Ensemble methods
• Bayesian classification
• Model selection
• Rule-based classification
• Summary
• Classification by back propagation
 Summary (I)
• Classification and prediction are two forms of data analysis that can be used
to extract models 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), associative
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.
 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
Thank you