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Topics:

What is concept description?

Data generalization and summarization-based

characterization

Analytical characterization: Analysis of attribute relevance

Mining class comparisons: Discriminating between

different classes

Mining descriptive statistical measures in large databases

Discussion

Summary

What is Concept Description?

Descriptive vs. predictive data mining

Descriptive mining: describes concepts or task-relevant

data sets in concise, summarative, informative,

discriminative forms

Predictive mining: Based on data and analysis,

constructs models for the database, and predicts the

trend and properties of unknown data

Concept description:

Characterization: provides a concise and succinct

summarization of the given collection of data

Comparison: provides descriptions comparing two or

more collections of data

4

Concept Description vs. OLAP

Concept description:

can handle complex data types of the

attributes and their aggregations

a more automated process

OLAP:

restricted to a small number of dimension and

measure types

user-controlled process

5

DATA GENERALIZATION AND

SUMMARIZATION-BASED

CHARACTERIZATION

6

Data Generalization and Summarizationbased

Characterization

Data generalization

A process which abstracts a large set of task-relevant

data in a database from a low conceptual levels to

higher ones.

Approaches:

Data cube approach(OLAP approach)

Attribute-oriented induction approach

1

2

3

4

5

Conceptual levels

7

Characterization: Data Cube Approach

Data are stored in data cube

Identify expensive computations

e.g., count( ), sum( ), average( ), max( )

Perform computations and store results in data

cubes

Generalization and specialization can be

performed on a data cube by roll-up and drilldown

An efficient implementation of data

generalization

8

Data Cube Approach (Cont…)

Limitations

can only handle data types of dimensions to

simple nonnumeric data and of measures to

simple aggregated numeric values .

Lack of intelligent analysis, can’t tell which

dimensions should be used and what levels

should the generalization reach

9

Attribute-Oriented Induction

Proposed in 1989 (KDD ‘89 workshop)

Not confined to categorical data nor particular measures.

How it is done?

Collect the task-relevant data (initial relation) using a

relational database query

Perform generalization by attribute removal or

attribute generalization.

Apply aggregation by merging identical, generalized

tuples and accumulating their respective counts

Interactive presentation with users

Basic Principles of Attribute-

Oriented Induction

Data focusing: task-relevant data, including dimensions, and

the result is the initial relation.

Attribute-removal: remove attribute A if there is a large set

of distinct values for A but (1) there is no generalization

operator on A, or (2) A’s higher level concepts are

expressed in terms of other attributes.

Attribute-generalization: If there is a large set of distinct

values for A, and there exists a set of generalization

operators on A, then select an operator and generalize A.

Attribute-threshold control: typical 2-8, specified/default.

Generalized relation threshold control: control the final

relation/rule size. see example

Attribute-Oriented Induction: Basic Algorithm

InitialRel: Query processing of task-relevant data, deriving

the initial relation.

PreGen: Based on the analysis of the number of distinct

values in each attribute, determine generalization plan for

each attribute: removal? or how high to generalize?

PrimeGen: Based on the PreGen plan, perform

generalization to the right level to derive a “prime

generalized relation”, accumulating the counts.

Presentation: User interaction: (1) adjust levels by drilling,

(2) pivoting, (3) mapping into rules, cross tabs,

visualization presentations.

12

Example

DMQL: Describe general characteristics of graduate

students in the Big-University database

use Big_University_DB

mine characteristics as “Science_Students”

in relevance to name, gender, major, birth_place,

birth_date, residence, phone#, gpa

from student

where status in “graduate”

Corresponding SQL statement:

Select name, gender, major, birth_place, birth_date,

residence, phone#, gpa

from student

where status in “Msc”, “MBA”, “PhD”

Class Characterization: An Example

Name Gender Major Birth-Place Birth_date Residence Phone # GPA

Jim

Woodman

M CS Vancouver,BC,

Canada

8-12-76 3511 Main St.,

Richmond

687-4598 3.67

Scott

Lachance

M CS Montreal, Que,

Canada

28-7-75 345 1st Ave.,

Richmond

253-9106 3.70

Laura Lee

…

F

…

Physics

…

Seattle, WA, USA

…

25-8-70

…

125 Austin Ave.,

Burnaby

…

420-5232

…

3.83

…

Removed Retained Sci,Eng,

Bus

Country Age range City Removed Excl,

VG,..

Gender Major Birth_region Age_range Residence GPA Count

M Science Canada 20-25 Richmond Very-good 16

F Science Foreign 25-30 Burnaby Excellent 22

… … … … … … …

Birth_Region

Gender

Canada Foreign Total

M 16 14 30

F 10 22 32

Total 26 36 62

Prime

Generalized

Relation

Initial

Relation

Presentation of Generalized Results

Generalized relation:

Relations where some or all attributes are generalized, with counts

or other aggregation values accumulated.

Cross tabulation:

Mapping results into cross tabulation form (similar to contingency

tables).

Visualization techniques:

Pie charts, bar charts, curves, cubes, and other visual forms.

Quantitative characteristic rules:

Mapping generalized result into characteristic rules with quantitative

information associated with it, e.g.,

_ ( ) ” “[ :53%] _ ( ) ” “[ :47%].

( ) ( )

birth region x Canada t birth region x foreign t

grad x male x

15

Presentation—Generalized Relation

16

Presentation—Crosstab

17

Implementation by Cube Technology

Construct a data cube on-the-fly for the given data

mining query

Facilitate efficient drill-down analysis

May increase the response time

A balanced solution: precomputation of “subprime”

relation

Use a predefined & precomputed data cube

Construct a data cube beforehand

Facilitate not only the attribute-oriented induction, but

also attribute relevance analysis, dicing, slicing, rollup

and drill-down

Cost of cube computation and the nontrivial storage

overhead

18

ANALYTICAL CHARACTERIZATION:

ANALYSIS OF ATTRIBUTE

RELEVANCE

19

Characterization vs. OLAP

Similarity:

Presentation of data summarization at multiple levels of

abstraction.

Interactive drilling, pivoting, slicing and dicing.

Differences:

Automated desired level allocation.

Dimension relevance analysis and ranking when there

are many relevant dimensions.

Sophisticated typing on dimensions and measures.

Analytical characterization: data dispersion analysis.

20

Attribute Relevance Analysis

Why?

Which dimensions should be included?

How high level of generalization?

Automatic VS. Interactive

Reduce # attributes; Easy to understand patterns

What?

statistical method for preprocessing data

filter out irrelevant or weakly relevant attributes

retain or rank the relevant attributes

relevance related to dimensions and levels

analytical characterization, analytical comparison

21

Attribute relevance analysis (cont’d)

How?

Data Collection

Analytical Generalization

Use information gain analysis (e.g., entropy or other

measures) to identify highly relevant dimensions and levels.

Relevance Analysis

Sort and select the most relevant dimensions and levels.

Attribute-oriented Induction for class description

On selected dimension/level

OLAP operations (e.g. drilling, slicing) on relevance

rules

22

Relevance Measures

Quantitative relevance measure determines the

classifying power of an attribute within a set of

data.

Methods

information gain (ID3)

gain ratio (C4.5)

gini index

2 contingency table statistics

uncertainty coefficient

23

Information-Theoretic Approach

Decision tree

each internal node tests an attribute

each branch corresponds to attribute value

each leaf node assigns a classification

ID3 algorithm

build decision tree based on training objects

with known class labels to classify testing

objects

rank attributes with information gain measure

minimal height

the least number of tests to classify an object

24

Top-Down Induction of Decision Tree

Attributes = Outlook, Temperature, Humidity, Wind

Outlook

Humidity Wind

sunny overcast rain

yes

no yes

high normal

no

strong weak

yes

PlayTennis = yes, no

25

Entropy and 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)

26

Example: Analytical Characterization

Task

Mine general characteristics describing graduate

students using analytical characterization

Given

attributes name, gender, major, birth_place, birth_date,

phone#, and gpa

Gen(ai) = concept hierarchies on ai

Ui = attribute analytical thresholds for ai

Ti = attribute generalization thresholds for ai

R = attribute relevance threshold

27

Example: Analytical Characterization (cont’d)

1. Data collection

target class: graduate student

contrasting class: undergraduate student

2. Analytical generalization using Ui

attribute removal

remove name and phone#

attribute generalization

generalize major, birth_place, birth_date and gpa

accumulate counts

candidate relation: gender, major, birth_country,

age_range and gpa

28

Example: Analytical characterization (2)

gender major birth_country age_range gpa count

M Science Canada 20-25 Very_good 16

F Science Foreign 25-30 Excellent 22

M Engineering Foreign 25-30 Excellent 18

F Science Foreign 25-30 Excellent 25

M Science Canada 20-25 Excellent 21

F Engineering Canada 20-25 Excellent 18

Candidate relation for Target class: Graduate students (=120)

gender major birth_country age_range gpa count

M Science Foreign <20 Very_good 18 F Business Canada <20 Fair 20 M Business Canada <20 Fair 22 F Science Canada 20-25 Fair 24 M Engineering Foreign 20-25 Very_good 22 F Engineering Canada <20 Excellent 24 Candidate relation for Contrasting class: Undergraduate students (=130) 29 Example: Analytical characterization (3) 3. Relevance analysis Calculate expected info required to classify an arbitrary tuple Calculate entropy of each attribute: e.g. major 0 9988 250 130 250 130 250 120 250 120130 120 I(s1,s 2 ) I( , ) log 2 log 2 . For major=”Science”: S11=84 S21=42 I(s11,s21)=0.9183 For major=”Engineering”: S12=36 S22=46 I(s12,s22)=0.9892 For major=”Business”: S13=0 S23=42 I(s13,s23)=0 Number of grad students in “Science” Number of undergrad students in “Science” 30 Example: Analytical Characterization (4) Calculate expected info required to classify a given sample if S is partitioned according to the attribute Calculate information gain for each attribute Information gain for all attributes 0 7873 250 42 250 82 250 126 E(major) I( s11,s21 ) I( s12,s22 ) I( s13,s23 ) . Gain(major) I(s1,s 2 ) E(major) 0.2115 Gain(gender) = 0.0003 Gain(birth_country) = 0.0407 Gain(major) = 0.2115 Gain(gpa) = 0.4490 Gain(age_range) = 0.5971 31 Example: Analytical characterization (5) 4. Initial working relation (W0) derivation R = 0.1 remove irrelevant/weakly relevant attributes from candidate relation => drop gender, birth_country

remove contrasting class candidate relation

5. Perform attribute-oriented induction on W0 using Ti

major age_range gpa count

Science 20-25 Very_good 16

Science 25-30 Excellent 47

Science 20-25 Excellent 21

Engineering 20-25 Excellent 18

Engineering 25-30 Excellent 18

Initial target class working relation W0: Graduate students

32

MINING CLASS COMPARISONS:

DISCRIMINATING BETWEEN

DIFFERENT CLASSES

Mining Class Comparisons

Comparison: Comparing two or more classes

Method:

Partition the set of relevant data into the target class and the

contrasting class(es)

Generalize both classes to the same high level concepts

Compare tuples with the same high level descriptions

Present for every tuple its description and two measures

support – distribution within single class

comparison – distribution between classes

Highlight the tuples with strong discriminant features

Relevance Analysis:

Find attributes (features) which best distinguish different classes

34

Example: Analytical comparison

Task

Compare graduate and undergraduate students using

discriminant rule.

DMQL query

use Big_University_DB

mine comparison as “grad_vs_undergrad_students”

in relevance to name, gender, major, birth_place, birth_date, residence, phone#, gpa

for “graduate_students”

where status in “graduate”

versus “undergraduate_students”

where status in “undergraduate”

analyze count%

from student

35

Example: Analytical comparison (2)

Given

attributes name, gender, major, birth_place,

birth_date, residence, phone# and gpa

Gen(ai) = concept hierarchies on attributes ai

Ui = attribute analytical thresholds for

attributes ai

Ti = attribute generalization thresholds for

attributes ai

R = attribute relevance threshold

36

Example: Analytical comparison (3)

1. Data collection

target and contrasting classes

2. Attribute relevance analysis

remove attributes name, gender, major, phone#

3. Synchronous generalization

controlled by user-specified dimension thresholds

prime target and contrasting class(es)

relations/cuboids

37

Example: Analytical comparison (4)

Birth_country Age_range Gpa Count%

Canada 20-25 Good 5.53%

Canada 25-30 Good 2.32%

Canada Over_30 Very_good 5.86%

… … … …

Other Over_30 Excellent 4.68%

Prime generalized relation for the target class: Graduate students

Birth_country Age_range Gpa Count%

Canada 15-20 Fair 5.53%

Canada 15-20 Good 4.53%

… … … …

Canada 25-30 Good 5.02%

… … … …

Other Over_30 Excellent 0.68%

Prime generalized relation for the contrasting class: Undergraduate students

38

Example: Analytical comparison (5)

4. Drill down, roll up and other OLAP operations

on target and contrasting classes to adjust levels

of abstractions of resulting description

5. Presentation

as generalized relations, crosstabs, bar charts,

pie charts, or rules

contrasting measures to reflect comparison

between target and contrasting classes

e.g. count%

39

Quantitative Discriminant Rules

Cj = target class

qa = a generalized tuple covers some tuples of class

but can also cover some tuples of contrasting class

d-weight

range: [0, 1]

quantitative discriminant rule form

m

i

a i

a j

count(q C )

d weight count(q C )

1

X, target_class(X)condition(X) [d : d_weight]

40

Example: Quantitative Discriminant Rule

Quantitative discriminant rule

where 90/(90+210) = 30%

Status Birth_country Age_range Gpa Count

Graduate Canada 25-30 Good 90

Undergraduate Canada 25-30 Good 210

Count distribution between graduate and undergraduate students for a generalized tuple

_ ( ) ” ” _ ( ) “25 30″ ( ) ” ” [ : 30%]

, _ ( )

birth country X Canada age range X gpa X good d

X graduate student X

41

Class Description

Quantitative characteristic rule

necessary

Quantitative discriminant rule

sufficient

Quantitative description rule

necessary and sufficient

1 [t :w1,d :w1]… [t :wn,d :wn]

condition (X) condition (X)

X, target_class(X)

n

X, target_class(X)condition(X) [d : d_weight]

X, target_class(X)condition(X) [t : t_weight]

42

Example: Quantitative Description Rule

Quantitative description rule for target class Europe

Location/item TV Computer Both_items

Count t-wt d-wt Count t-wt d-wt Count t-wt d-wt

Europe 80 25% 40% 240 75% 30% 320 100% 32%

N_Am 120 17.65% 60% 560 82.35% 70% 680 100% 68%

Both_

regions

200 20% 100% 800 80% 100% 1000 100% 100%

Crosstab showing associated t-weight, d-weight values and total number

(in thousands) of TVs and computers sold at AllElectronics in 1998

(item(X) “TV” )t : 25%,d : 40%[t : 75%,d : 30%]

X,Europe(X)

43

Mining Complex Data Objects:

Generalization of Structured Data

Set-valued attribute

Generalization of each value in the set into its corresponding

higher-level concepts

Derivation of the general behavior of the set, such as the

number of elements in the set, the types or value ranges in

the set, or the weighted average for numerical data

E.g., hobby = tennis, hockey, chess, violin, nintendo_games

generalizes to sports, music, video_games

List-valued or a sequence-valued attribute

Same as set-valued attributes except that the order of the

elements in the sequence should be observed in the

generalization

44

Generalizing Spatial and Multimedia Data

Spatial data:

Generalize detailed geographic points into clustered regions,

such as business, residential, industrial, or agricultural areas,

according to land usage

Require the merge of a set of geographic areas by spatial

operations

Image data:

Extracted by aggregation and/or approximation

Size, color, shape, texture, orientation, and relative positions

and structures of the contained objects or regions in the image

Music data:

Summarize its melody: based on the approximate patterns that

repeatedly occur in the segment

Summarized its style: based on its tone, tempo, or the major

musical instruments played

45

Generalizing Object Data

Object identifier: generalize to the lowest level of class in the

class/subclass hierarchies

Class composition hierarchies

generalize nested structured data

generalize only objects closely related in semantics to the current

one

Construction and mining of object cubes

Extend the attribute-oriented induction method

Apply a sequence of class-based generalization operators on

different attributes

Continue until getting a small number of generalized objects that

can be summarized as a concise in high-level terms

For efficient implementation

Examine each attribute, generalize it to simple-valued data

Construct a multidimensional data cube (object cube)

Problem: it is not always desirable to generalize a set of values to

single-valued data

46

An Example: Plan Mining by Divide & Conquer

Plan: a variable sequence of actions

E.g., Travel (flight):

Plan mining: extraction of important or significant generalized

(sequential) patterns from a planbase (a large collection of plans)

E.g., Discover travel patterns in an air flight database, or

find significant patterns from the sequences of actions in the repair

of automobiles

Method

Attribute-oriented induction on sequence data

A generalized travel plan: <small-big-small> Divide & conquer:Mine characteristics for each subsequence E.g., big: same airline, small-big: nearby region

47

A Travel Database for Plan Mining

Example: Mining a travel planbase

plan# action# departure depart_time arrival arrival_time airline …

1 1 ALB 800 JFK 900 TWA …

1 2 JFK 1000 ORD 1230 UA …

1 3 ORD 1300 LAX 1600 UA …

1 4 LAX 1710 SAN 1800 DAL …

2 1 SPI 900 ORD 950 AA …

. . . . . . . .

. . . . . . . .

. . . . . . . .

airport_code city state region airport_size …

1 1 ALB 800 …

1 2 JFK 1000 …

1 3 ORD 1300 …

1 4 LAX 1710 …

2 1 SPI 900 …

. . . . .

. . . . .

. . . . .

Travel plans table

Airport info table

48

Multidimensional Analysis

Strategy

Generalize the

planbase in

different

directions

Look for

sequential

patterns in the

generalized plans

Derive high-level

plans

A multi-D model for the planbase

49

Multidimensional Generalization

Plan# Loc_Seq Size_Seq State_Seq

1 ALB – JFK – ORD – LAX – SAN S – L – L – L – S N – N – I – C – C

2 SPI – ORD – JFK – SYR S – L – L – S I – I – N – N

. . .

. . .

. . .

Multi-D generalization of the planbase

Plan# Size_Seq State_Seq Region_Seq …

1 S – L+ – S N+ – I – C+ E+ – M – P+ …

2 S – L+ – S I+ – N+ M+ – E+ …

. . .

. . .

. . .

Merging consecutive, identical actions in plans

( ) ( ) [75%]

( , ,) _ ( , ) _ ( , )

region x region y

flight x y airport size x S airport size y L

50

Generalization-Based Sequence Mining

Generalize planbase in multidimensional way using

dimension tables

Use # of distinct values (cardinality) at each level to

determine the right level of generalization

(level-“planning”)

Use operators merge “+”, option “[]” to further generalize

patterns

Retain patterns with significant support

51

Generalized Sequence Patterns

AirportSize-sequence survives the min threshold (after

applying merge operator):

S-L+-S [35%], L+-S [30%], S-L+ [24.5%], L+ [9%]

After applying option operator:

[S]-L+-[S] [98.5%]

Most of the time, people fly via large airports to get to

final destination

Other plans: 1.5% of chances, there are other patterns:

S-S, L-S-L

52

MINING DESCRIPTIVE

STATISTICAL MEASURES IN LARGE

DATABASES

53

Mining Data Dispersion Characteristics

Motivation

To better understand the data: central tendency, variation

and spread

Data dispersion characteristics

median, max, min, quantiles, outliers, variance, etc.

Numerical dimensions correspond to sorted intervals

Data dispersion: analyzed with multiple granularities of

precision

Boxplot or quantile analysis on sorted intervals

Dispersion analysis on computed measures

Folding measures into numerical dimensions

Boxplot or quantile analysis on the transformed cube

54

Measuring the Central Tendency

Mean

Weighted arithmetic mean

Median: A holistic measure

Middle value if odd number of values, or average of the

middle two values otherwise

estimated by interpolation

Mode

Value that occurs most frequently in the data

Unimodal, bimodal, trimodal

Empirical formula:

n

i

i x

n

x

1

1

n

i

i

n

i

i i

w

w x

x

1

1

c

f

n f l

median L

median

)

/ 2 ( )

( 1

mean mode 3(mean median)

55

Measuring the Dispersion of Data

Quartiles, outliers and boxplots

Quartiles: Q1 (25th percentile), Q3 (75th percentile)

Inter-quartile range: IQR = Q3 – Q1

Five number summary: min, Q1, M, Q3, max

Boxplot: ends of the box are the quartiles, median is marked,

whiskers, and plot outlier individually

Outlier: usually, a value higher/lower than 1.5 x IQR

Variance and standard deviation

Variance s2: (algebraic, scalable computation)

Standard deviation s is the square root of variance s2

n

i

n

i

i i

n

i

i x

n

x

n

x x

n

s

1 1

2 2

1

2 2 [ 1 ( ) ]

1

( ) 1

1

1

56

Boxplot Analysis

Five-number summary of a distribution:

Minimum, Q1, M, Q3, Maximum

Boxplot

Data is represented with a box

The ends of the box are at the first and third

quartiles, i.e., the height of the box is IRQ

The median is marked by a line within the box

Whiskers: two lines outside the box extend to

Minimum and Maximum

57

Visualization of Data Dispersion: Boxplot Analysis

58

Mining Descriptive Statistical Measures in Large

Databases

Variance

Standard deviation: the square root of the variance

Measures spread about the mean

It is zero if and only if all the values are equal

Both the deviation and the variance are algebraic

2 2

1

2 2 1

1

( ) 1

1

1

i i

n

i

i x

n

x

n

x x

n

s

59

Histogram Analysis

Graph displays of basic statistical class descriptions

Frequency histograms

A univariate graphical method

Consists of a set of rectangles that reflect the counts or

frequencies of the classes present in the given data

60

Quantile Plot

Displays all of the data (allowing the user to assess both

the overall behavior and unusual occurrences)

Plots quantile information

For a data xi data sorted in increasing order, fi

indicates that approximately 100 fi% of the data are

below or equal to the value xi

61

Quantile-Quantile (Q-Q) Plot

Graphs the quantiles of one univariate distribution against

the corresponding quantiles of another

Allows the user to view whether there is a shift in going

from one distribution to another

62

Scatter plot

Provides a first look at bivariate data to see clusters of

points, outliers, etc

Each pair of values is treated as a pair of coordinates and

plotted as points in the plane

63

Loess Curve

Adds a smooth curve to a scatter plot in order to

provide better perception of the pattern of dependence

Loess curve is fitted by setting two parameters: a

smoothing parameter, and the degree of the

polynomials that are fitted by the regression

64

Graphic Displays of Basic Statistical Descriptions

Histogram: (shown before)

Boxplot: (covered before)

Quantile plot: each value xi is paired with fi indicating

that approximately 100 fi % of data are xi

Quantile-quantile (q-q) plot: graphs the quantiles of one

univariant distribution against the corresponding quantiles

of another

Scatter plot: each pair of values is a pair of coordinates

and plotted as points in the plane

Loess (local regression) curve: add a smooth curve to a

scatter plot to provide better perception of the pattern of

dependence

65

DISCUSSION

66

AO(Attribute Oriented) Induction vs.

Learning-from-example Paradigm

Difference in philosophies and basic assumptions

Positive and negative samples in learning-fromexample:

positive used for generalization, negative –

for specialization

Positive samples only in data mining: hence

generalization-based, to drill-down backtrack the

generalization to a previous state

Difference in methods of generalizations

Machine learning generalizes on a tuple by tuple basis

Data mining generalizes on an attribute by attribute

basis

67

Entire vs. Factored Version Space

68

Incremental and Parallel Mining of Concept

Description

Incremental mining: revision based on newly added data

DB

Generalize DB to the same level of abstraction in the

generalized relation R to derive R

Union R U R, i.e., merge counts and other statistical

information to produce a new relation R’

Similar philosophy can be applied to data sampling,

parallel and/or distributed mining, etc.

69

Summary

Concept description: characterization and discrimination

OLAP-based vs. attribute-oriented induction

Efficient implementation of AOI

Analytical characterization and comparison

Mining descriptive statistical measures in large

databases

Discussion

Incremental and parallel mining of description

Descriptive mining of complex types of data

70

Thank you !!!

Questions

71

Explain analytical characterization?

Methods of attribute relevance analysis?

How does analytical data

characterization/comparison performs?

From the descriptive statistics point of view, why is it

that additional statistical measures should be

introduced in describing central tendency and data

dispersion? Give an example.

In comparison with machine learning algorithm, why

is it that database-oriented concept description leads

to efficiency and scalability in large databases and

data warehouse?

72

Discuss why analytical data characterization is needed and

how it can be performed. Compare the result of two

induction methods with relevance analysis and without

relevance analysis.

Give three additional commonly used statistical measures

for the characterization of data dispersion and discuss how

they can be computed efficiently in large databases.

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