Transcript Lecture 10 - Lenoir

Lecture 7 Classification
ITCS 6163
Chapter 7. Classification and
Prediction
•
•
•
•
•
•
•
What is classification? What is prediction?
Classification by decision tree induction
Bayesian Classification
Other Classification Methods (SVM)
Classification accuracy
Prediction
Summary
Classification problem
• Given:
– Tuples each assigned a class level.
• Develop a model for each class
– Example:
– Good creditor : (age in [25,40]) AND (income > 50K)
AND (status = MARRIED)
• Applications:
– Credit approval (good, bad)
– Store locations (good, fair, poor)
– Emergency situations (emergency, non-emergency)
Classification vs. Prediction
• Classification:
– predicts categorical class labels
– 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—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: 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
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
Chapter 7. Classification and
Prediction
•
•
•
•
•
•
•
What is classification? What is prediction?
Classification by decision tree induction
Bayesian Classification
Other Classification Methods
Classification accuracy
Prediction
Summary
Classification by Decision Tree
Induction
• Decision tree
–
–
–
–
A flow-chart-like tree structure
Internal node denotes a test on an attribute
Branch represents an outcome of the test
Leaf nodes represent class labels or class distribution
• Decision tree generation consists of two phases
– Tree construction
• At start, all the training examples are at the root
• Partition examples recursively based on selected attributes
– Tree pruning
• Identify and remove branches that reflect noise or outliers
• Use of decision tree: Classifying an unknown sample
– Test the attribute values of the sample against the decision tree
Training Dataset
This
follows
an
example
from
Quinlan’s
ID3
age
<=30
<=30
30…40
>40
>40
>40
31…40
<=30
<=30
>40
<=30
31…40
31…40
>40
income student credit_rating
high
no fair
high
no excellent
high
no fair
medium
no fair
low
yes fair
low
yes excellent
low
yes excellent
medium
no fair
low
yes fair
medium
yes fair
medium
yes excellent
medium
no excellent
high
yes fair
medium
no excellent
buys_computer
no
no
yes
yes
yes
no
yes
no
yes
yes
yes
yes
yes
no
Output: A Decision Tree for
“buys_computer”
age?
<=30
student?
overcast
30..40
yes
>40
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
Decision trees
Training set
Salary Education
10000 HS
40000 C
15000 C
75000 G
18000 G
Salary < 20000
Class
R
Y
N
A
R
A
Education = G
A
A
N
Y
A
R
Decision trees
• Pros:
– Fast.
– Rules easy to interpret.
– High dimensional data
• Cons:
– No correlations
– Axis-parallel cuts.
Decision trees(cont.)
• Machine learning:
– ID3 (Quinlan86)
– C4.5 (Quinlan93 )
– CART (Breiman, Friedman, Olshen, Stone,
Classification and Regression Trees 1984)
• Database:
– SLIQ (Metha, Agrawal and Rissanen, EDBT96)
– SPRINT (Shafer, Agrawal, Metha, VLDB96)
– Rainforest (Gherke, Ramakrishnan, Ghanti
VLDB98)
Decision trees
• Finding the best tree is NP-Hard
• We look at non-backtracking algorithms (never
look back at a previous decision)
• Assume we have a test with n outcomes that
partitions T into subsets T1, T2,…, Tn
If the test is to be evaluated without exploring
subsequent dimensions of the Ti’s, the only
information available for guidance is the
distribution of classes in T and its subsets.
Decision tree algorithms
• Building phase:
– Recursively split nodes using best splitting
attribute and value for node
• Pruning phase:
– Smaller (yet imperfect) tree achieves better
prediction accuracy.
– Prune leaf nodes recursively to avoid overfitting.
Predictor variables (attributes)
• Numerically ordered: values are ordered and they
can be represented in real line. ( E.g., salary.)
• Categorical: takes values from a finite set not
having any natural ordering. (E.g., color.)
• Ordinal: takes values from a finite set whose
values posses a clear ordering, but the distances
between them are unknown. (E.g., preference
scale: good, fair, bad.)
Binary Splits
Recursive (binary) partitioning
– Univariate split on numerically ordered or
ordinal X
X <= c
– on categorical X X  A
– Linear combination on numerical
 ai Xi <= c
c and A are chosen to maximize separation.
Some probability...
S = cases
freq(Ci,S) = # cases in S that belong to Ci
Gain entropic meassure:
Prob(“this case belongs to Ci”) = freq(Ci,S)/|S|
Information conveyed:
-log (freq(Ci,S)/|S|)
Entropy = expected information =
-  (freq(Ci,S)/|S|) log (freq(Ci,S)/|S|) = info(S)
Gain
Test X:
infoX (T) =  |Ti|/T info(Ti)
gain(X) = info (T) - infoX(T)
Example
Outlook
sunny
sunny
sunny
sunny
sunny
overcast
overcast
overcast
overcast
rain
rain
rain
rain
rain
Temp
75
80
85
72
69
72
83
64
81
71
65
75
68
70
Humidity Windy
70
90
85
95
70
90
78
65
75
80
70
80
80
96
Class
Y
Y
N
N
N
Y
N
Y
N
Y
Y
Y
N
N
gainOutlook = 0.94-0.64= 0.3
gainWindy = 0.94-0.278= 0.662
Play
Don't
Don't
Don't
Play
Play
Play
Play
Play
Don't
Don't
Play
Play
Play
Info(T) (9 play, 5 don’t)
info(T) = -9/14log(9/14)5/14log(5/14) = 0.94 (bits)
Test Windy
Test:
outlook
infowindy==
info
Outlook
5/14
(-2/5 log(2/5)-3/5log(3/7))
log(3/5))+
7/14(-4/7log(4/7)-3/7
4/14 (-4/4 log(4/4)) +
+7/14(-5/7log(5/7)-2/7log(2/(7))
5/14 (-3/5 log(3/5) - 2/5 log(2/5))
= 0.278
= 0.64 (bits)
Windy is a better test
Problem with Gain
Strong bias towards test with many outcomes.
Example: Z = Name
|Ti| = 1 (each name unique)
infoZ (T) =  1/|T| (- 1/N log (1/N))  0
Maximal gain!! (but useless division--- overfitting--)
Split
Split-info (X) = -  |Ti|/|T| log (|Ti|/|T|)
gain-ratio(X) = gain(X)/split-info(X)
Gain <= log(k)
Split <= log(n)
ratio small
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”
OVERFITTING
• Decision trees can grow so long that there is
a leaf for each training example.
• Extremes:
– Overfitted: “Whatever I haven’t seen can’t be
classified”
– Too General: “If it is green, it is a tree”
Avoid Overfitting in
Classification
• The generated tree may overfit the training data
– Too many branches, some may reflect anomalies due to
noise or outliers
– Result is in 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”
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
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
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)
SPRINT
For large data sets.
Age
23
17
43
68
32
20
Car Type
Family
Sports
Sports
Family
Truck
Family
Age < 25
Risk
H
H
H
L
L
H
Car = Sports
H
H
L
Gini Index (IBM IntelligentMiner)
• If a data set T contains examples from n classes, gini index, gini(T)
n
is defined as gini(T ) 1 
p 2j
j 1
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
N1 gini( )  N 2 gini( )
(
T
)

gini split
T1
T2
N
N
• The attribute provides the smallest ginisplit(T) is chosen to split the
node (need to enumerate all possible splitting points for each
attribute).
SPRINT
Partition (S)
if all points of S are in the same class
return;
else
for each attribute A do
evaluate_splits on A;
use best split to partition into S1,S2;
Partition(S1);
Partition(S2);
SPRINT Data Structures
Age
23
17
43
68
32
20
Training
set
Age
Age
17
20
23
32
43
68
Risk
H
H
H
L
H
L
Attribute lists
Tuple
1
5
0
4
3
2
Car Type
Family
Sports
Sports
Family
Truck
Family
Car
Risk
H
H
H
L
L
H
Car Type
Family
Sports
Sports
Family
Truck
Family
Risk
H
H
H
L
L
H
Tuple
0
1
2
3
4
5
Age
17
20
23
32
43
68
Risk
H
H
H
L
H
L
Tuple
1
5
0
4
3
2
Car Type
Family
Sports
Family
Age < 27.5
Risk
H
H
H
L
L
H
Tuple
0
1
2
3
4
5
Group2
Group1
Age
17
20
23
Splits
Car Type
Family
Sports
Sports
Family
Truck
Family
Risk
H
H
H
Tuple
1
5
0
Risk
H
H
H
Tuple
0
1
5
Age
32
43
68
Car Type
Sports
Family
Truck
Risk
L
H
L
Risk
H
L
L
Tuple
4
2
3
Tuple
2
3
4
Histograms
For continuous attributes
Associated with node (Cabove, Cbelow)
to process
already processed
Example
Age
17
20
23
32
43
68
Risk
H
H
H
L
H
L
Tuple
1
5
0
4
3
2
HH
CbCb
CaCa
ginisplit0 = 0.444
LL
23410
12034
0210
2012
ginisplit1= 0.156
ginisplit2= 0.333
gini
ginisplit3
=
0/6gini(S1)
gini(S1)
gini(S1)+3/6
+4/6
+ 6/6
gini(S2)
gini(S2)
gini(S2)
split2
split0=3/6
gini
==2/6
=4/6
=5/6
=6/6
1/6
gini(S1)
gini(S1)
+2/6
+1/6
+0/6
+5/6
gini(S2)
gini(S2)
split1
split4
split5
ginisplit3= 0.222
gini(S1)
gini(S2)=
[(2/2)
[(4/6)22 ]+(2/6)
= 00 22]]==0.444
gini(S1)
==111---[(3/3)
[(1/1)
[(3/4)
[(4/5)
[(4/6)
]=
+(1/4)
+(1/5)
+(2/6)
0.375
0.320
ginisplit4= 0.416
2 +(2/4)2
gini(S2)
[(2/4)
0.5
gini(S2) =
= 11 -- [(1/3)
[(3/4)2 +(2/3)
[(1/2)
[(1/1)
+(2/4)
]+(1/2)
= 0 2 ]] =
= 0.444
0.1875
0.5
ginisplit5= 0.222
ginisplit6= 0.444
Age <= 18.5
Splitting categorical attributes
Single scan through the attribute list collecting
counts on count matrix for each combination of
class label + attribute value
Example
Car Type
Family
Sports
Sports
Family
Truck
Family
Risk
H
H
H
L
L
H
Tuple
0
1
2
3
4
5
ginisplit(family)= 0.444
ginisplit((sports) )= 0.333
H
Family
Sports
Truck
L
2
2
0
1
0
1
gini
==1/6
3/6
gini(S1)
++5/6
3/6
gini(S2)
gini
2/6
gini(S1)
4/6
gini(S2)
split((sports)
ginisplit(family)
=
gini(S1)
+
gini(S2)
split(truck)
2
+ (1/3)2] = 4/9
2
gini(S1)
=
1
[(2/3)
2
gini(S1)
=
1
[(2/2)
]
gini(S1) = 1 - [(1/1) ] =
= 00
2
+
2
2
+
2 = 4/9
gini(S2)
=
1[(2/3)
(1/3)
2
+
gini(S2)
=
1[(2/4)
(2/4)
gini(S2) = 1- [(4/5) (1/5)2]]] =
= 0.5
0.32
ginisplit(truck) )= 0.266
Car Type = Truck
Example (2 attributes)
Age
17
20
23
32
43
68
Risk
H
H
H
L
H
L
Car Type
Family
Sports
Sports
Family
Truck
Family
Tuple
1
5
0
4
3
2
Risk
H
H
H
L
L
H
Tuple
0
1
2
3
4
5
The winner is Age <= 18.5
Y
H
N
Age
20
23
32
43
68
Risk
H
H
L
H
L
Tuple
5
0
4
3
2
Car Type
Family
Risk
H
Tuple
0
Sports
Family
Truck
Family
H
L
L
H
2
3
4
5
Performing the split
• Create 2 child nodes
• Split attribute lists for winning attribute
• For the remaining
– Insert Tuple Ids in Hash Table (which child)
– Scan lists of attributes and probe hash table
(may be too large and need several steps).
Drawbacks
• Large explosion of space (possibly tripling
the size of database).
• Costly Hash-Join.
Chapter 7. Classification and
Prediction
•
•
•
•
•
•
•
What is classification? What is prediction?
Classification by decision tree induction
Bayesian Classification
Other methods (SVM)
Classification accuracy
Prediction
Summary
Bayesian
Theorem
• Given training data D, posteriori probability of a
hypothesis h, P(h|D) follows the Bayes theorem
P(h | D)  P(D | h)P(h)
P(D)
• MAP (maximum posteriori) hypothesis
h
 arg max P(h | D)  arg max P(D | h)P(h).
MAP
hH
hH
• Practical difficulty: require initial knowledge of
many probabilities, significant computational cost
Naïve Bayes Classifier (I)
• A simplified assumption: attributes are
conditionally independent:
n
P( C j |V )  P( C j ) P( v i | C j )
i 1
• Greatly reduces the computation cost, only
count the class distribution.
Naive Bayesian Classifier (II)
• Given a training set, we can compute the probabilities
O u tlo o k
su n n y
o verc ast
rain
T em p reatu re
hot
m ild
cool
P
2 /9
4 /9
3 /9
2 /9
4 /9
3 /9
N
3 /5
0
2 /5
2 /5
2 /5
1 /5
H u m id ity P
h ig h
3 /9
n o rm al
6 /9
N
4 /5
1 /5
W in d y
tru e
false
3 /5
2 /5
3 /9
6 /9
Example
Outlook
sunny
sunny
sunny
sunny
sunny
overcast
overcast
overcast
overcast
rain
rain
rain
rain
rain
Temp
75
80
85
72
69
72
83
64
81
71
65
75
68
70
Humidity Windy
70
90
85
95
70
90
78
65
75
80
70
80
80
96
Class
Y
Y
N
N
N
Y
N
Y
N
Y
Y
Y
N
N
Play
Don't
Don't
Don't
Play
Play
Play
Play
Play
Don't
Don't
Play
Play
Play
E ={outlook = sunny, temp =
[64,70], humidity= [65,70],
windy = y} =
{E1,E2,E3,E4}
Pr[“Play”/E] = (Pr[E1/Play] x
Pr[E2/Play] x Pr[E3/Play] x
Pr[E4/Play] x Pr[Play]) / Pr[E] =
(2/9x 3/9 x 3/9 x 4/9x 9/14)/Pr[E]
= 0.007/Pr[E]
Pr[“Don’t”/E] = (3/5 x 2/5 x 1/5 x 3/5 x 5/14)/Pr[E] = 0.010/Pr[E]
With E: Pr[“Play”/E] = 41 %, Pr[“Don’t”/E] = 59 %
Bayesian Belief Networks (I)
Family
History
Smoker
(FH, S) (FH, ~S)(~FH, S) (~FH, ~S)
LungCancer
Emphysema
LC
0.8
0.5
0.7
0.1
~LC
0.2
0.5
0.3
0.9
The conditional probability table
for the variable LungCancer
PositiveXRay
Dyspnea
Bayesian Belief Networks
Bayesian Belief Networks (II)
• Bayesian belief network allows a subset of the
variables conditionally independent
• A graphical model of causal relationships
• Several cases of learning Bayesian belief networks
– Given both network structure and all the variables: easy
– Given network structure but only some variables
– When the network structure is not known in advance
Another Example (Friedman &
Goldzsmidt)
Variables : Burglary, Earthquake, Alarm, Neighbor call, Radio
announcement.
Burglary and Earthquake are independent (P(BE) = P(B)*P(E))
Burglary and Radio announcement are independent given
Earthquake (P(BR/E) = P(B/E)*P(R/E))
So, P(A,R,E,B)=P(A|R,E,B)*P(R|E,B)*P(E|B)*P(B)
can be reduced to:
P(A,R,E,B) = P(A|E,B)*P(R|E)*P(E)*P(B)
Example (cont.)
Earthquake
Burglary
Alarm
Radio announc.
Neigh. call
Example (cont.)
Associated with each node is a set of conditional probability
distributions. For example, the "Alarm" node might have the
following probability distribution
E
B
P(A/EB)
P(!A/EB)
E
E
!E
!E
B
!B
B
!B
0.90
0.20
0.90
0.01
0.10
0.80
0.10
0.99
Chapter 7. Classification and
Prediction
•
•
•
•
•
•
•
•
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Methods
Classification accuracy
Prediction
Summary
Extending linear classification
Problem: all the algorithms we covered (plus many other
ones) can only represent linear boundaries between classes
Age <= 25 <-
-> Age > 25
Too
simplistic for
many real
cases
Nonlinear class boundaries
Support vector machines (SVM)-- a misnomer, since they are
algorithms, not machines-Idea: use a non-linear mapping and transform the space into a
new space.
Example:
x = w1a13 + w2 a12 a2 + w3 a1 a22 + w4 a23
SVMs
Based on an algorithm that finds a maximum marginal
hyperplane (linear model).
Shortest line
connecting the
hulls
Maximum
margin
hyperplane
Support
vectors
Convex
hull:
(tightest
enclosing
polygon)
SVMs (cont.)
• We have assumed that the two classes are linearly separable,
so their convex hulls cannot overlap.
• The maximum margin hyperplane (MMH) is the one that is
as far away as possible from both convex hulls. It is orthogonal
to the shortest line connecting the hulls.
• The instances closest to the MMH (minimum distance to the
line) are called support vectors (SV). (At least one for each
class, often more.)
– Given the SVs, we can easily construct the MLH.
– All other training points can be deleted without any
effect on the MMH
SVMs (cont.)
A hyperplane that separates the two classes can be written as:
x = w0 + w1a1 + w2 a2
for a two-attribute case.
However, the equation that defines the MMH, can be defined in
terms of the SVs. Write the class value y of a training instance
(point) as 1 (yes) or -1 (no). Then the MMH is:
x = b +  i yi a(i). a
i  SVs
yi = class value of the point a(i); b and i are numerical values
to be determined; a is a test point.
SVMs (cont.)
So, now…
Use the training values to determine b and i for
x = b +  i yi a(i). a
i  SVs
Dot product
Standard optimization problem: constrained quadratic optimization
(off-the-shelf software packages to solve this: Fletcher, Practical
Methods of Optimization, 1987)
Chapter 7. Classification and
Prediction
•
•
•
•
•
•
•
•
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Methods
Classification accuracy
Prediction
Summary
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 sub-sample as
test data --- k-fold cross-validation
– for data set with moderate size
• Bootstrapping (leave-one-out)
– for small size data
Boosting and Bagging
• Boosting increases classification accuracy
– Applicable to decision trees or Bayesian
classifier
• Learn a series of classifiers, where each
classifier in the series pays more attention to
the examples misclassified by its
predecessor
• Boosting requires only linear time and
constant space
Chapter 7. Classification and
Prediction
•
•
•
•
•
•
•
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Classification accuracy
Prediction
Summary
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
Predictive Modeling in
Databases
• 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
Regress Analysis and Log-Linear
Models in Prediction
• 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
Chapter 7. Classification and
Prediction
•
•
•
•
•
•
•
•
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Classification Methods
Classification accuracy
Prediction
Summary
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..