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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
3
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
4
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 (1Oj )(Tj Oj )
jk
k
Errj Oj (1Oj )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
0
?
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
57
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
61
OTHER CLASSIFICATION METHODS
62
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
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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
+
_ _
+
_
_
+
.
.
.
. .
65
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
68
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
71
PREDICTION
72
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
73
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 acad bcd
Regress Analysis and Log-Linear
Models in Prediction
75
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
( ( , ))(( ( ) ( )) ( )
76
Prediction: Numerical Data
77
Prediction: Categorical Data
78
CLASSIFICATION ACCURACY
79
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
82
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
83
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
84
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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