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University of Helsinki/Dept. of CS
Pirjo Moen
Concept description
Descriptive vs. predictive data mining
Clustering
Descriptive mining:
28.2.
∗ describe concepts or task-relevant data sets in
Introduction 17.1.
University of Helsinki/Dept. of CS
Pirjo Moen
Association rules 14.3.
20.1.
KDD Process
Concept description 31.1.
Conclusions 4.4.
Data mining methods – Spring 2005
informative, or
discriminative
Predictive mining:
∗ based on data and analysis, construct models
for the database, and predict the trend and
properties of unknown data
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Pirjo Moen
summarative,
form
Exam
12.4.
Classification 14.2.
concise,
Concept description – Contents
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Pirjo Moen
What is concept description?
Characterization:
What is concept description?
∗ provide a concise summarization of
the given collection of data
Data generalization
Analytical characterization
Mining class comparisons
Comparison:
∗ provide descriptions comparing two
or more collections of data
Mining descriptive statistical measures
Summary
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University of Helsinki/Dept. of CS
Pirjo Moen
University of Helsinki/Dept. of CS
Pirjo Moen
Concept description vs. OLAP
Data cube approach
Computations and results in data cubes
Concept description:
Strengths:
∗ can handle complex data types of
the attributes and their aggregations
∗ an efficient implementation of data generalization
∗ a more automated process
∗ computation of various kinds of measures, e.g., count( ) or sum( )
∗ roll-up and drill-down
OLAP:
Limitations:
∗ restricted to a small number of
dimension and measure types
∗ only dimensions of simple non-numeric data and measures of simple
aggregated numeric values
∗ user-controlled process
∗ lack of intelligent analysis
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Pirjo Moen
Data generalization
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Pirjo Moen
Attribute-oriented induction
Data focusing:
Data generalization:
∗ collect the task-relevant data (initial
relation)
∗ summarization-based characterization
∗ a process which abstracts a large set of task-relevant data in a database
from a low conceptual levels to higher ones
Data generalization:
1
Conceptual levels
∗ attribute removal or
2
3
∗ attribute generalization
4
Data aggregation
5
∗ approaches:
∗ by merging identical, generalized tuples
and accumulating their respective counts
data cube approach (OLAP approach)
attribute-oriented induction (AOI)
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Presentation of the generalized relation
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Pirjo Moen
Data generalization in AOI
Example of class characterization
DMQL: Describe general characteristics of graduate students in the
Big-University database
Two methods for generalization:
∗ attribute-removal:
use B ig_U niv ersity _ D B
no generalization operator on A
m ine charact erist ics as “ Scien ce_Stu dents”
A’s higher level concepts are expressed in
terms of other attributes
in relev ance t o nam e, gender, major, birth_place, birt h_dat e, residence,
phone# , gpa
∗ attribute-generalization
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Pirjo Moen
f rom student
a generalization operator exists
w here st atus in “ graduate”
Attribute generalization control:
Corresponding SQL statement:
∗ attribute threshold control
select nam e, gen der, m ajor, birth_place, birth_date, residence, phone# , gpa
∗ generalized relation threshold control
from st udent
w here stat us in {“ M sc” , “ M B A ” , “ PhD ” }
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Pirjo Moen
Presentation of generalized results
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Pirjo Moen
Example of class characterization (2)
Initial relation
Generalized relation:
∗ a relation where some or all attributes are generalized, with counts or
other aggregation values accumulated
Cross tabulation:
∗ mapping results into cross tabulation form
Name
Gender
Jim Woodman
M
Scott Lachance
M
Laura Lee
F
...
..
Major
CS
CS
Physics
...
Generalized relation
Visualization techniques:
Birth_place
Vancouver, BC, Canada
Montreal, Que, Canada
Seattle, WA, USA
...
Birth_date
08.12.76
28.07.75
25.08.70
...
Residence
3511 Main St., Richmond
345 1st Ave., Richmond
125 Austin Ave., Burnaby
...
Gender Major Birth_region Age_range
M
Science
Canada
20-25
F
Science
Foreign
25-30
...
...
...
...
Phone#
687-4598
253-9106
420-5232
...
Residence
Gpa
Richmond Very-good
Burnaby
Excellent
...
...
Gpa
3,67
3,7
3,83
...
Count
16
22
...
∗ pie charts, bar charts, curves, cubes, and other visual forms
Cross tabulation
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t:w
....
X t:w
Canada
16
10
26
Foreign
14
22
36
Total
30
32
62
m
1
1
Gender / Birth_region
M
F
Total
condition X
condition
X, target_class X
Quantitative characteristic rules:
m
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Pirjo Moen
University of Helsinki/Dept. of CS
Pirjo Moen
Example of class characterization (3)
Analytical characterization (2)
Bar chart
Cross tabulation
G / B_p Canada Foreign
M
16
14
F
10
22
Total
26
36
Gender and birth place
Total
30
32
62
What is attribute relevance analysis?
65
60
∗ Statistical method for preprocessing data
55
50
45
40
Canada
Foreign
Total
35
30
25
15
∗ Analytical characterization, analytical comparison
10
5
0
F
Total
M
retain or rank the relevant attributes
∗ Relevance related to dimensions and levels
20
Quantitative
characteristic rule
filter out irrelevant or weakly relevant attributes
birth region x
grad x male x
birthregion x Canada t :53 %
Foreign t : 47 %
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Pirjo Moen
Analytical characterization
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Pirjo Moen
Analytical characterization (3)
How attribute relevance analysis is done?
Preprocessing for class characterization or
comparison
∗ Data collection
∗ Analytical generalization
∗ Need for attribute relevance analysis
Why attribute relevance analysis?
∗ Which dimensions should be included?
∗ Relevance analysis
∗ How high level of generalization?
∗ Automatic vs. interactive
sort and select the most relevant dimensions and
levels
∗ Attribute-oriented induction for class
description
∗ Reduce number of attributes
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use, for example, information gain analysis to
identify highly relevant dimensions and levels
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on selected dimension/level
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Pirjo Moen
Example of analytical characterization
Relevance measures
Quantitative relevance measure determines
the classifying power of an attribute within
a set of data.
∗ information gain (ID3)
∗ concept hierarchies of attributes
∗ gini index
∗ attribute analytical threshold for each attribute
contingency table statistics
∗ attribute generalization threshold for each attribute
∗ uncertainty coefficient
∗ attribute relevance threshold
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Pirjo Moen
Entropy and information gain
i
m
2
m
i 1
s
log
i
2
s
I s ,... , s
1j
mj
1
2
m
∗ attribute generalization
generalize major, birth_ place, birt h_date and gpa
accumulate counts
I s ,s , . . . ,s
remove nam e and phone#
mj
s
1 j
1
∗ contrasting class: undergraduate students
∗ attribute removal
Information gained by partitioning on the attribute A
Gain A
∗ target class: graduate students
...
s
s
E A
j
University of Helsinki/Dept. of CS
Pirjo Moen
2. Analytical generalization using attribute analytical thresholds
Entropy of the attribute A with values {a1,a2,…,av}
v
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1. Data collection
Information measures expected information required to classify any
arbitrary tuple
s
s
1
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Example of analytical characterization (2)
A data set S contains si tuples of class Ci for i = {1, …, m}
I s ,s , . . . ,s
Given
∗ attributes: nam e, gender, m ajor, birt h_place, birth_date, p hone# , and gpa
∗ gain ratio (C4.5)
2
Task
∗ mine general characteristics describing graduate students using analytical
characterization
Methods:
∗
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Pirjo Moen
E A
∗ candidate relation: gender, major, birth_count ry , age_ran ge and gpa
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University of Helsinki/Dept. of CS
Example of analytical characterization (3)
120)
11
Major
Science
Business
Business
Science
Engineering
Engineering
Birth_country
Foreign
Canada
Canada
Canada
Foreign
Canada
Age_range
< 20
< 20
< 20
20-25
20-25
< 20
Gpa
Very good
Fair
Fair
Fair
Very good
Excellent
13
42
I s ,s
250
22
23
0. 7873
1
I s ,s
2
E major
0. 2115
information gain for all the attributes:
Gain(gender) = 0.0003
Gain(gpa) = 0.4490
Gain(birth_country) = 0.0407
Gain(age_range) = 0.5971
Gain(major) = 0.2115
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12
Gain major
Count
18
20
22
24
22
24
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82
I s ,s
250
information gain for attribute major:
130)
Gender
M
F
M
F
M
F
21
∗ calculate information gain for each attribute
Undergraduate students (
126
I s ,s
250
E major
Count
16
22
18
25
21
18
Gpa
Very good
Excellent
Excellent
Excellent
Excellent
Excellent
Gender
Major
Birth_country Age_range
M
Science
Canada
20-25
F
Science
Foreign
25-30
M
Engineering
Foreign
25-30
F
Science
Foreign
25-30
M
Science
Canada
20-25
F
Engineering
Canada
20-25
Example of analytical characterization (5)
∗ calculate expected information required to classify a given sample, if the
data set is partitioned according to the attribute (i.e., entropy)
Graduate students (
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Example of analytical characterization (4)
Example of analytical characterization (6)
3. Relevance analysis
4. Initial working relation (W0) derivation
∗ attribute relevance treshold 0.1
1
2
2
130
130
log
250
250
120
120
log
250
250
I 120 , 130
I s ,s
∗ calculate expected information required to classify an arbitrary tuple
2
∗ remove irrelevant/weakly relevant attributes from candidate relation
=> drop gender, birth_country
0 . 9988
∗ remove contrasting class candidate relation
∗ calculate entropy of each attribute; start by calculating expected
information for each value of the attribute
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
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Major
Age_range
Gpa
Science
20-25
Very_good
Science
25-30
Excellent
Science
20-25
Excellent
Engineering
20-25
Excellent
Engineering
25-30
Excellent
Count
16
47
21
18
18
W0: graduate students
5. Perform attribute-oriented induction on W0 using attribute
generalization thresholds
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Pirjo Moen
Example of analytical comparison (2)
Comparison: comparing two or more classes
Method:
Mining class comparisons
University of Helsinki/Dept. of CS
Pirjo Moen
∗ Partition the set of relevant data into the target class and the contrasting
class(es)
∗ attributes: nam e, gender, m ajor, birt h_place,
birt h_dat e, resid ence, phone# and gpa
∗ Generalize both classes to the same high level concepts
∗ concept hierarchies on all attributes
∗ Compare tuples with the same high level descriptions
∗ attribute analytical threshold for each
attribute
support: distribution within single class
∗ Present for every tuple its description and two measures:
comparison: distribution between classes
∗ attribute generalization threshold for each
attribute
∗ attribute relevance threshold
∗ Highlight the tuples with strong discriminant features
Relevance analysis: find attributes (features) which best distinguish
different classes
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Example of analytical comparison
Given
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Example of analytical comparison (3)
Task: Compare graduate and undergraduate students using
discriminant rule
DMQL query:
1. Data collection
∗ target and contrasting classes
use B ig_U niv ersity _D B
2. Attribute relevance analysis
mine com parison as “ grad_v s_undergrad_st udent s”
in relev ance to nam e, gend er, m ajor, birth_place, birth_ date, residence,
∗ remove attributes name, gender, m ajor, phone#
phone#, gpa
for “ g raduate_st udent s”
w here st atus in “ gradu ate”
3. Synchronous generalization
v ersus “ undergraduat e_st udent s”
∗ controlled by user-specified dimension
thresholds
w here st atus in “ undergraduat e”
analy ze count %
∗ prime target and contrasting class(es) relations
from st udent
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University of Helsinki/Dept. of CS
Pirjo Moen
Example of analytical comparison (4)
Quantitative discriminant rules
Generalized relation for graduate students
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%
…
…
…
…
Foreign
Over_30 Excellent 4.68%
Cj = target class
qa = a generalized tuple that covers some tuples of class Cj
d_weight
count q
d_weight
C
a
j
m
count q
a
C
i
1
i
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quantitative discriminant rules:
X, target_class X
condition X
d: d_weight
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Quantitative discriminant rules (2)
Count distribution for graduate and undergraduate students
Status
Birth_country Age_range Gpa
Graduate
Canada
25-30
Good
Undergraduate
Canada
25-30
Good
Count
90
210
Birth_country X Canada
Age_range X 25-30
Gpa X Good
d: 30%
5. Drill down, roll up and other OLAP
operations on target and contrasting
classes to adjust levels of abstractions of
resulting description
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graduate
X, Status X
Quantitative discriminant rule
∗ contrasting measures to reflect comparison
between target and contrasting classes, e.g.
count%
∗ as generalized relations, crosstabs, bar
charts, pie charts, or rules
4. Presentation
Example of analytical comparison (5)
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Pirjo Moen
∗ range: [0, 1]
Count%
5.53%
4.53%
…
5.02%
…
0.68%
Birth_country Age_range Gpa
Canada
15-20
Fair
Canada
15-20
Good
…
…
…
Canada
25-30
Good
…
…
…
Foreign
Over_30 Excellent
Generalized relation for undergraduate students
∗ can also cover some tuples of contrasting class
Pirjo Moen
where 90/(90+210) = 30%
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Median
m
∗ numerical data:
m
1
m
∗ other types of data: estimated by interpolation
Mode
t : w , d : w'
....
X t : w , d : w'
1
1
1
m
∗ value that occurs most frequently in the data
condition X
condition
otherwise, average of the middle two values
d:w
....
X d:w
1
condition X
condition
Quantitative description rule (necessary and sufficient)
X, target_class X
middle value, if odd number of values,
Quantitative discriminant rule (sufficient)
m
1
Mean or weighted arithmetic mean
t:w
....
X t:w
condition X
condition
1
X, target_class X
Measuring the central tendency
Quantitative characteristic rule (necessary)
Class descriptions
X, target_class X
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m
m
∗ unimodal, bimodal, trimodal; multimodal
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Motivation
Measuring the dispersion of data
∗ to better understand the data: central
tendency, variation and spread
∗ inter-quartile range: IQR = Q3 – Q1
Central tendency measures:
∗ five number summary: min, Q1, M, Q3, max
∗ boxplot: ends of the box are the quartiles, median is
marked, whiskers; outliers plotted individually
Data dispersion measures:
∗ quartiles, outliers, variance, etc.
Quartiles, outliers and boxplots
∗ quartiles: Q1 (25th percentile), Q3 (75th percentile)
∗ mean, median, max, min etc.
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Pirjo Moen
Mining descriptive statistical measures
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∗ outlier: usually, a value higher/lower than 1.5 x IQR
Graphical presentation of statistical class
descriptions
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Pirjo Moen
Example of a boxplot
i
2
x
2
i
i
1
1
n
2
1
n 1
x
x
n
1
n 1
2
s
Variance
Measuring the dispersion of data (2)
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x
i
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
databases
scalable in large
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Boxplot analysis
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Visualization of data dispersion
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 IQR
∗ the median is marked by a line within the box
∗ whiskers: two lines outside the box extend to
minimum and maximum
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Pirjo Moen
University of Helsinki/Dept. of CS
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Quantile-quantile plot
Scatter plot
Loess curve
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Displays all of the data (allowing the user to assess both the overall
behavior and unusual occurrences)
Plots quantile information
∗ For a data xi sorted in increasing order, a precentage fi indicates that
approximately 100 fi% of the data are below or equal to the value xi
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Quantile plot
Quantile plot
Histograms
Presentation of class descriptions
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Consists of a set of rectangles that reflect the counts or frequencies
of the classes present in the given data
Graphs the quantiles of one univariate distribution against the
corresponding quantiles of another
Quantile-quantile plot
A univariate graphical method
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Histograms
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Allows the user to view whether there is a shift in going from one
distribution to another
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Pirjo Moen
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Pirjo Moen
Provides a first look at bivariate data to see clusters of points,
outliers, etc.
Typical machine learning methods for concept description follow a
learning-from-examples paradigm.
Data mining vs. machine learning
Scatter plot
Each pair of values is treated as a pair of coordinates and plotted as
points in the plane.
Difference in philosophies and basic assumptions:
∗ in learning-from-examples: positive used for generalization, negative for
specialization
The size of the set of training examples
∗ in data mining: generalization-based; specialization implemented by
backtracking 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
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Incremental mining of concept description
Adds a smooth curve to a scatter plot in order to provide better
perception of the pattern of dependence.
Loess (local regression) curve is fitted by setting two parameters:
Incremental mining: revision based on
newly added data DB
∗ Generalize DB to the same level of
abstraction as in the generalized relation R to
derive R
Loess curve
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∗ a smoothing parameter, and
∗ the degree of the polynomials that are fitted by the regression.
R, i.e., merge counts and other
∗ Union R
statistical information to produce a new
relation R’
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Similar philosophy can be applied to data
sampling, parallel and/or distributed
mining, etc.
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Pirjo Moen
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Pirjo Moen
References (2)
Summary
Concept description: characterization and
discrimination
Analytical characterization and comparison
OLAP-based and attribute-oriented
induction
Mining descriptive statistical measures in
large database
E. Knorr and R. Ng. Algorithms for mining distance-based outliers in large datasets. VLDB'98, New York, NY,
Aug. 1998.
H. Liu and H. Motoda. Feature Selection for Knowledge Discovery and Data Mining. Kluwer Academic
Publishers, 1998.
R. S. Michalski. A theory and methodology of inductive learning. In Michalski et al., editor, Machine Learning: An
Artificial Intelligence Approach, Vol. 1, Morgan Kaufmann, 1983.
T. M. Mitchell. Version spaces: A candidate elimination approach to rule learning. IJCAI'97, Cambridge, MA.
T. M. Mitchell. Generalization as search. Artificial Intelligence, 18:203-226, 1982.
T. M. Mitchell. Machine Learning. McGraw Hill, 1997.
J. R. Quinlan. Induction of decision trees. Machine Learning, 1:81-106, 1986.
D. Subramanian and J. Feigenbaum. Factorization in experiment generation. AAAI'86, Philadelphia, PA, Aug.
1986.
Presentation of descriptions
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References
Thanks
Y. Cai, N. Cercone, and J. Han. Attribute-oriented induction in relational databases. In G. Piatetsky-Shapiro and
W. J. Frawley, editors, Knowledge Discovery in Databases, pages 213-228. AAAI/MIT Press, 1991.
C. Carter and H. Hamilton. Efficient attribute-oriented generalization for knowledge discovery from large
databases. IEEE Trans. Knowledge and Data Engineering, 10:193-208, 1998.
S. Chaudhuri and U. Dayal. An overview of data warehousing and OLAP technology. ACM SIGMOD Record,
26:65-74, 1997
W. Cleveland. Visualizing Data. Hobart Press, Summit NJ, 1993.
J. L. Devore. Probability and Statistics for Engineering and the Science, 4th ed. Duxbury Press, 1995.
T. G. Dietterich and R. S. Michalski. A comparative review of selected methods for learning from examples. In
Michalski et al., editor, Machine Learning: An Artificial Intelligence Approach, Vol. 1, pages 41-82. Morgan
Kaufmann, 1983.
J. Gray, S. Chaudhuri, A. Bosworth, A. Layman, D. Reichart, M. Venkatrao, F. Pellow, and H. Pirahesh. Data
cube: A relational aggregation operator generalizing group-by, cross-tab and sub-totals. Data Mining and
Knowledge Discovery, 1:29-54, 1997.
J. Han, Y. Cai, and N. Cercone. Data-driven discovery of quantitative rules in relational databases. IEEE Trans.
Knowledge and Data Engineering, 5:29-40, 1993.
J. Han and Y. Fu. Exploration of the power of attribute-oriented induction in data mining. In U.M. Fayyad, G.
Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy, editors, Advances in Knowledge Discovery and Data Mining,
pages 399-421. AAAI/MIT Press, 1996.
R. A. Johnson and D. A. Wichern. Applied Multivariate Statistical Analysis, 3rd ed. Prentice Hall, 1992.
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Thank you for
Jiawei Han from Simon Fraser University
for his slides
which greatly helped in preparing this lecture!
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