Download DM -Lect 4(updated) - Computer Science Unplugged

Data Mining:
Concepts and Techniques
May 1, 2017
Data Mining: Concepts and Techniques
1
Chapter 2: Data Preprocessing

Why preprocess the data?

Descriptive data summarization

Data cleaning

Data integration and transformation

Data reduction

Discretization and concept hierarchy generation

Summary
May 1, 2017
Data Mining: Concepts and Techniques
2
Major Tasks in Data Preprocessing

Data cleaning


Data integration


Normalization and aggregation
Data reduction


Integration of multiple databases, data cubes, or files
Data transformation


Fill in missing values, smooth noisy data, identify or remove
outliers, and resolve inconsistencies
Obtains reduced representation in volume but produces the same
or similar analytical results
Data discretization

May 1, 2017
Part of data reduction but with particular importance, especially
for numerical data
Data Mining: Concepts and Techniques
3
Forms of Data Preprocessing
May 1, 2017
Data Mining: Concepts and Techniques
4
Chapter 2: Data Preprocessing

Why preprocess the data?

Data cleaning

Data integration and transformation

Data reduction

Discretization and concept hierarchy generation

Summary
May 1, 2017
Data Mining: Concepts and Techniques
5
Data Integration




Data integration:
 Combines data from multiple sources into a coherent
store
Schema integration: e.g., A.cust-id  B.cust-#
 Integrate metadata from different sources
Entity identification problem:
 Identify real world entities from multiple data sources,
e.g., Bill Clinton = William Clinton
Detecting and resolving data value conflicts
 For the same real world entity, attribute values from
different sources are different
 Possible reasons: different representations, different
scales, e.g., metric vs. British units
May 1, 2017
Data Mining: Concepts and Techniques
6
Handling Redundancy in Data Integration

Redundant data occur often when integration of multiple
databases

Object identification: The same attribute or object
may have different names in different databases

Derivable data: One attribute may be a “derived”
attribute in another table, e.g., annual revenue

Redundant attributes may be able to be detected by
correlation analysis

Careful integration of the data from multiple sources may
help reduce/avoid redundancies and inconsistencies and
improve mining speed and quality
May 1, 2017
Data Mining: Concepts and Techniques
7
Correlation Analysis (Numerical Data)

Correlation coefficient (also called Pearson’s product
moment coefficient)
rA, B
( A  A)( B  B )  ( AB)  n A B



(n  1)AB
( n  1)AB
where n is the number of tuples, A and B are the respective
means of A and B, σA and σB are the respective standard deviation
of A and B, and Σ(AB) is the sum of the AB cross-product.


If rA,B > 0, A and B are positively correlated (A’s values
increase as B’s). The higher, the stronger correlation.
rA,B = 0: independent; rA,B < 0: negatively correlated
May 1, 2017
Data Mining: Concepts and Techniques
8
Correlation Analysis (Categorical Data)

Χ2 (chi-square) test
2
(
Observed

Expected
)
2  
Expected



The larger the Χ2 value, the more likely the variables are
related
The cells that contribute the most to the Χ2 value are
those whose actual count is very different from the
expected count
Correlation does not imply causality

# of hospitals and # of car-theft in a city are correlated

Both are causally linked to the third variable: population
May 1, 2017
Data Mining: Concepts and Techniques
9
Data Transformation

Smoothing: remove noise from data

Aggregation: summarization, data cube construction

Generalization: concept hierarchy climbing


Normalization: scaled to fall within a small, specified
range

min-max normalization

z-score normalization

normalization by decimal scaling
Attribute/feature construction

May 1, 2017
New attributes constructed from the given ones
Data Mining: Concepts and Techniques
10
Data Transformation: Normalization

Min-max normalization: to [new_minA, new_maxA]
v' 


v  minA
(new _ maxA  new _ minA)  new _ minA
maxA  minA
Ex. Let income range $12,000 to $98,000 normalized to [0.0,
73,600  12,000
(1.0  0)  0  0.716
1.0]. Then $73,000 is mapped to 98
,000  12,000
Z-score normalization (μ: mean, σ: standard deviation):
v' 


v  A

A
Ex. Let μ = 54,000, σ = 16,000. Then
Normalization by decimal scaling
v
v'  j
10
May 1, 2017
73,600  54,000
 1.225
16,000
Where j is the smallest integer such that Max(|ν’|) < 1
Data Mining: Concepts and Techniques
11
Standard Deviation



Mean doesn’t tell us a
lot about data set.
Different data sets can
have same mean.
Standard Deviation
(SD) of a data set is a
measure of how
spread out the data is.
n
s
(X
i 1
i
 X)
(n  1)
2
Example SD
SD
Mean = 10
Chapter 2: Data Preprocessing

Why preprocess the data?

Data cleaning

Data integration and transformation

Data reduction

Discretization and concept hierarchy generation

Summary
May 1, 2017
Data Mining: Concepts and Techniques
14
Data Reduction Strategies



Why data reduction?
 A database/data warehouse may store terabytes of data
 Complex data analysis/mining may take a very long time to run
on the complete data set
Data reduction
 Obtain a reduced representation of the data set that is much
smaller in volume but yet produce the same (or almost the
same) analytical results
Data reduction strategies
 Data cube aggregation:
 Dimensionality reduction — e.g., remove unimportant attributes
 Data Compression
 Numerosity reduction — e.g., fit data into models
 Discretization and concept hierarchy generation
May 1, 2017
Data Mining: Concepts and Techniques
15
Data Cube Aggregation


The lowest level of a data cube (base cuboid)

The aggregated data for an individual entity of interest

E.g., a customer in a phone calling data warehouse
Multiple levels of aggregation in data cubes


Reference appropriate levels


Further reduce the size of data to deal with
Use the smallest representation which is enough to
solve the task
Queries regarding aggregated information should be
answered using data cube, when possible
May 1, 2017
Data Mining: Concepts and Techniques
16
Attribute Subset Selection


Feature selection (i.e., attribute subset selection):
 Select a minimum set of features such that the
probability distribution of different classes given the
values for those features is as close as possible to the
original distribution given the values of all features
 reduce # of patterns in the patterns, easier to
understand
Heuristic methods (due to exponential # of choices):
 Step-wise forward selection
 Step-wise backward elimination
 Combining forward selection and backward elimination
 Decision-tree induction
May 1, 2017
Data Mining: Concepts and Techniques
17
Example of Decision Tree Induction
Initial attribute set:
{A1, A2, A3, A4, A5, A6}
A4 ?
A6?
A1?
Class 1
>
May 1, 2017
Class 2
Class 1
Class 2
Reduced attribute set: {A1, A4, A6}
Data Mining: Concepts and Techniques
18
Heuristic Feature Selection Methods


There are 2d possible sub-features of d features
Several heuristic feature selection methods:
 Best single features under the feature independence
assumption: choose by significance tests
 Best step-wise feature selection:
 The best single-feature is picked first
 Then next best feature condition to the first, ...
 Step-wise feature elimination:
 Repeatedly eliminate the worst feature
 Best combined feature selection and elimination
 Optimal branch and bound:
 Use feature elimination and backtracking
May 1, 2017
Data Mining: Concepts and Techniques
19
Data Compression



String compression
 There are extensive theories and well-tuned algorithms
 Typically lossless
 But only limited manipulation is possible without
expansion
Audio/video compression
 Typically lossy compression, with progressive
refinement
 Sometimes small fragments of signal can be
reconstructed without reconstructing the whole
Time sequence is not audio
 Typically short and vary slowly with time
May 1, 2017
Data Mining: Concepts and Techniques
20
Data Compression
Compressed
Data
Original Data
lossless
Original Data
Approximated
May 1, 2017
Data Mining: Concepts and Techniques
21
Dimensionality Reduction:
Wavelet Transformation
Haar2




Discrete wavelet transform (DWT): linear signal
processing, multi-resolutional analysis
Daubechie4
Compressed approximation: store only a small fraction of
the strongest of the wavelet coefficients
Similar to discrete Fourier transform (DFT), but better
lossy compression, localized in space
Method:

Length, L, must be an integer power of 2 (padding with 0’s, when
necessary)

Each transform has 2 functions: smoothing, difference

Applies to pairs of data, resulting in two set of data of length L/2

Applies two functions recursively, until reaches the desired length
May 1, 2017
Data Mining: Concepts and Techniques
22
DWT for Image Compression

Image
Low Pass
Low Pass
Low Pass
May 1, 2017
High Pass
High Pass
High Pass
Data Mining: Concepts and Techniques
23
Dimensionality Reduction: Principal
Component Analysis (PCA)




Given N data vectors from n-dimensions, find k ≤ n orthogonal
vectors (principal components) that can be best used to represent data
Steps
 Normalize input data: Each attribute falls within the same range
 Compute k orthonormal (unit) vectors, i.e., principal components
 Each input data (vector) is a linear combination of the k principal
component vectors
 The principal components are sorted in order of decreasing
“significance” or strength
 Since the components are sorted, the size of the data can be
reduced by eliminating the weak components, i.e., those with low
variance. (i.e., using the strongest principal components, it is
possible to reconstruct a good approximation of the original data
Works for numeric data only
Used when the number of dimensions is large
May 1, 2017
Data Mining: Concepts and Techniques
24
Principal Component Analysis
X2
Y1
Y2
X1
May 1, 2017
Data Mining: Concepts and Techniques
25
PCA Goal:
Removing Dimensional Redundancy
Dim 1
Dim 2
Dim 3
Dim 4
Dim 5
Dim 6
Dim 7
Dim 8
Dim 9
Dim 10
Dim 11
Dim 12
Analyzing 12
Dimensional data is
challenging !!!
PCA Goal:
Removing Dimensional Redundancy
Dim 1
Dim 2
Dim 3
Dim 4
Dim 5
Dim 6
Dim 7
Dim 8
Dim 9
Dim 10
Dim 11
Dim 12
But some dimensions
represent redundant
information. Can we
“reduce” these.
PCA Goal:
Removing Dimensional Redundancy
Dim 1
Dim 2
Dim 3
Dim 4
Dim 5
Dim 6
Lets assume we have a
“PCA black box” that can
reduce the correlating
dimensions.
Dim 7
Dim 8
Dim 9
Dim 10
Dim 11
Dim 12
Pass the 12 d data set
through the black box to
get a three dimensional
data set.
PCA Goal:
Removing Dimensional Redundancy
Dim 1
Dim 2
Dim 3
Dim 4
Dim 5
Dim 6
Dim 7
Dim 8
Dim 9
Given appropriate reduction,
analyzing the reduced dataset is
much more efficient than the
original “redundant” data.
PCA
Black box
Dim A
Dim B
Dim C
Pass the 12 d data set through the
black box to get a three dimensional
Dim 11
data set.
Dim 10
Dim 12
Mathematics inside PCA Black box: Bases


Lets now give the “black box” a mathematical form.
In linear algebra dimensions of a space are a linearly independent set
called “bases” that spans the space created by dimensions.

i.e. each point in that space is a linear combination of the bases set.

e.g. consider the simplest example of standard basis in Rn consisting
of the coordinate axes.
Every point in R3 is a linear combination
of the standard basis of R3
1 0 0
0 1 0
0 0 1
(2,3,3) = 2 (1,0,0) + 3(0,1,0) + 3 (0,0,1)
PCA Goal: Change of Basis

Assume X is the 6-dimensional data set given as
input
Dimensions
Data Points
x11
x12
x13
x14
x15
x16
x21 x22
X  x31 x32
x23
x33
x24
x34
x25
x35
x26 x2
x36  x3
x41 x42
x43
x44
x45
x46
x4
x51
x53
x54
x55
x56
x5
x52
x1
• A naïve basis for X is standard basis for R5 and hence
BX = X
• Here, we want to find a new (reduced) basis P such as
PX = Y
• Y will be the resultant reduced data set.
PCA Goal

Change of Basis
PX  Y
 p11
p
 21





 pm1
p12

p22

pm 2

p1m   x1   y1 
p2 m   x2   y2 
     
    
     
     
   
pmm   xm   ym 
• QUESTION: What is a good choice for P ?
– Lets park this question right now and revisit after
studying some related concepts
Background Stats/Maths




Mean and Standard Deviation
Variance and Covariance
Covariance Matrix
Eigenvectors and Eigenvalues
Mean and Standard Deviation

Population


Sample


Large data Set
Subset of population
Example




Consider Election Poll
Population is all the people in the country.
Sample is a subset of the population that the statistician measure.
By measuring only the sample you can work out for population
Cont’d

Take a sample dataset:
1


2 4 6 12 15 25 45 68 67 65 98
There is a number of things we can calculate about a
data set
E.g Mean
n
x
 Xi
i 1
n
Standard Deviation



Mean doesn’t tell us a
lot about data set.
Different data sets can
have same mean.
Standard Deviation
(SD) of a data set is a
measure of how
spread out the data is.
n
s
(X
i 1
i
 X)
(n  1)
2
Example SD
SD
Mean = 10
Variance


Variance is another
measure of the spread
of data in data set.
It is almost identical to
SD.
n
s 
2
(
X

X
)
 i
i 1
(n  1)
2
Covariance


SD and Variance are 1-dimensional
1-D data sets could be






Heights of all the people in the room
Salary of employee in a company
Marks in the quiz
However many datasets have more than 1-dimension
Our aim is to find any relationship between different
dimensions.
E.g. Finding relationship with students result and their
hour of study.
Covariance



Covariance is used for
this purpose
It is used to measure
relationship between 2Dimensions.
Covariance for higher
dimensions could be cov( X , y) 
calculated using
covariance matrix (see
next).
n
(X
i 1
i
 X )(Yi  Y )
(n  1)
Covariance Interpretation






We have data set for students study hour (H) and marks
achieved (M)
We find cov(H,M)
Exact value of covariance is not as important as the sign
(i.e. positive or negative)
+ve , both dimensions increase together
-ve , as one dimension increases other decreases
Zero, their exist no relationship
Covariance Matrix




Covariance is always measured between 2 – dim.
What if we have a data set with more than 2dim?
We have to calculate more than one covariance
measurement.
E.g. from a 3-dim data set (dimensions x,y,z) we
could cacluate cov(x,y) , cov(x,z) , cov(y,z)
Covariance Matrix



Can use covariance
matrix to find all the
possible covariance
Since
cov(a,b)=cov(b,a)
The matrix is
symmetrical about the
main diagonal
 cov( x, x) cov( x, y ) cov( x, z ) 


c   cov( y, x) cov( y, y ) cov( y, z ) 
 cov( z, x) cov( z, y ) cov( z, z ) 


Eigenvectors



Consider the two
multiplications between
a matrix and a vector
In first example the
resulting vector is not
an integer multiple of
the original vector.
Whereas in second
example, the resulting
vector is 4 times the
original matrix
 2 3   1  11

 x    
 2 1   3  5 
 2 3   3  12 
 3

        4   
 2 1  2   8 
 2
Eigenvectors and Eigenvalues

More formally defined


Let A be an n x n matrix. The vector v that
satisfies


Av  v
For some scalar
is called the eigenvector of
vector A and is the eigenvalue corresponding
to eigenvector v
Principal Component Analysis



PCA is a technique for identifying patterns in
data.
Also used to express data in such a way as to
highlight similarities and differences.
PCA are used to reduce the dimension in data
without losing the integrity of information.
Step by Step


Step 1:
 We need to have some data for PCA
Step 2:
 Subtract the mean from each of the data point
Step1 & Step2
Step3: Calculate the Covariance



Calculate the covariance matrix
Non-diagonal elements in the covariance matrix are
positive
So x , y variable increase together
 .616555556 .615444444 

cov  
 .615444444 .716555556 
Step 4: Calculate the eigenvectors and eigenvalues of
the covariance matrix

Since covariance matrix is square, we can
calculate the eigenvector and eigenvalues of the
matrix
.490833989 

eigenvalues  
1.28402771 
 .7351786 .67787339 

eigenvectors  
.677873 .735178656 
What does this all mean?
Data Points
Eigenvectors
Conclusion




Eigenvector give us information about the
pattern.
By looking at graph in previous slide. See how
one of the eigenvectors go through the middle of
the points.
Second eigenvector tells about another weak
pattern in data.
So by finding eigenvectors of covariance matrix
we are able to extract lines that characterize the
data.
Step 5:Chosing components and forming a
feature vector.




Highest eigenvalue is the principal component of
the data set.
In our example, the eigenvector with the largest
eigenvalue was the one that pointed down the
middle of the data.
So, once the eigenvectors are found, the next
step is to order them by eigenvectors, highest to
lowest.
This gives the components in order of
significance.
Cont’d




Now, here comes the idea of dimensionality
reduction and data compression
You can decide to ignore the components of least
significance.
You do lose some information, but if eigenvalues
are small you don’t lose much.
More formal stated (see next slide)
Cont’d




We have n – dimension
So we will find n eigenvectors
But if we chose only p first eigenvectors.
Then the final dataset has only p dimension



Step 6: Deriving the new dataset
Now, we have chosen
the components
  .6778  .7351


(eigenvectors) that we
want to keep.
  .7351 .67787 
We can write them in
Choice 1 with two eigenvectors
form of a matrix of
vectors
In our example we
have two eigenvectors,
So we have two
choices
Choice 2 with one eigenvectors
  .67787 



.
7351


Cont’d



To obtain the final dataset we will multiply the
above vector matrix transposed with the
transpose of original data matrix.
Final dataset will have data items in columns and
dimensions along rows.
So we have original data set represented in terms
of the vectors we chose.
Original data set represented using two
eigenvectors.
Original data set represented using one
eigenvectors.
PCA – Mathematical Working




Naïve Basis (I) of input matrix (X) spans a large
dimensional space.
Change of Basis (P) is required so that X can be
projected along a lower dimension space having
significant dimensions only.
A properly selected P will generate a projection Y.
Use this P to project the correlation matrix.
Lessen the number of Eigenvectors in P for a
reduced dimension projection.
PCA Procedures

Step 1


Step 2


Calculate the covariance matrix
Step 4


Subtract the mean
Step 3


Get data
Calculate the eigenvectors and eigenvalues of the covariance
matrix
Step 5

Choose components and form a feature vector
Numerosity Reduction



Reduce data volume by choosing alternative, smaller
forms of data representation
Parametric methods
 Assume the data fits some model, estimate model
parameters, store only the parameters, and discard
the data (except possible outliers)
 Example: Log-linear models—obtain value at a point
in m-D space as the product on appropriate marginal
subspaces
Non-parametric methods
 Do not assume models
 Major families: histograms, clustering, sampling
May 1, 2017
Data Mining: Concepts and Techniques
62
Data Reduction Method (1):
Regression and Log-Linear Models

Linear regression: Data are modeled to fit a straight line


Often uses the least-square method to fit the line
Multiple regression: allows a response variable Y to be
modeled as a linear function of multidimensional feature
vector

Log-linear model: approximates discrete
multidimensional probability distributions
May 1, 2017
Data Mining: Concepts and Techniques
63
Regress Analysis and Log-Linear Models



Linear regression: Y = w X + b
 Two regression coefficients, w and b, 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
Data Reduction Method (2): Histograms
35
Partitioning rules:
20
May 1, 2017
Data Mining: Concepts and Techniques
100000
90000
80000
0
MaxDiff: set bucket boundary
between each pair for pairs have
the β–1 largest differences
70000
V-optimal: with the least
15
histogram variance (weighted
10
sum of the original values that
5
each bucket represents)
60000

25
50000

Equal-frequency (or equaldepth)
40000

30
Equal-width: equal bucket range
30000

20000

Divide data into buckets and store 40
average (sum) for each bucket
10000

65
Data Reduction Method (3): Clustering

Partition data set into clusters based on similarity, and store cluster
representation (e.g., centroid and diameter) only

Can be very effective if data is clustered but not if data is “smeared”

Can have hierarchical clustering and be stored in multi-dimensional
index tree structures

There are many choices of clustering definitions and clustering
algorithms

Cluster analysis will be studied in depth in Chapter 7
May 1, 2017
Data Mining: Concepts and Techniques
66
Data Reduction Method (4): Sampling





Sampling: obtaining a small sample s to represent the
whole data set N
Allow a mining algorithm to run in complexity that is
potentially sub-linear to the size of the data
Choose a representative subset of the data
 Simple random sampling may have very poor
performance in the presence of skew
Develop adaptive sampling methods
 Stratified sampling:
 Approximate the percentage of each class (or
subpopulation of interest) in the overall database
 Used in conjunction with skewed data
Note: Sampling may not reduce database I/Os (page at a
time)
May 1, 2017
Data Mining: Concepts and Techniques
67
Sampling: with or without Replacement
Raw Data
May 1, 2017
Data Mining: Concepts and Techniques
68
Sampling: Cluster or Stratified Sampling
Raw Data
May 1, 2017
Cluster/Stratified Sample
Data Mining: Concepts and Techniques
69
Chapter 2: Data Preprocessing

Why preprocess the data?

Data cleaning

Data integration and transformation

Data reduction

Discretization and concept hierarchy generation

Summary
May 1, 2017
Data Mining: Concepts and Techniques
70
Discretization

Three types of attributes:

Nominal — values from an unordered set, e.g., color, profession

Ordinal — values from an ordered set, e.g., military or academic
rank


Continuous — real numbers, e.g., integer or real numbers
Discretization:

Divide the range of a continuous attribute into intervals

Some classification algorithms only accept categorical attributes.

Reduce data size by discretization

Prepare for further analysis
May 1, 2017
Data Mining: Concepts and Techniques
71
Discretization and Concept Hierarchy

Discretization

Reduce the number of values for a given continuous attribute by
dividing the range of the attribute into intervals


Interval labels can then be used to replace actual data values

Supervised vs. unsupervised

Split (top-down) vs. merge (bottom-up)

Discretization can be performed recursively on an attribute
Concept hierarchy formation

Recursively reduce the data by collecting and replacing low level
concepts (such as numeric values for age) by higher level concepts
(such as young, middle-aged, or senior)
May 1, 2017
Data Mining: Concepts and Techniques
72
Discretization and Concept Hierarchy
Generation for Numeric Data

Typical methods: All the methods can be applied recursively

Binning (covered above)


Histogram analysis (covered above)


Top-down split, unsupervised,
Top-down split, unsupervised
Clustering analysis (covered above)

Either top-down split or bottom-up merge, unsupervised

Entropy-based discretization: supervised, top-down split

Interval merging by 2 Analysis: unsupervised, bottom-up merge

Segmentation by natural partitioning: top-down split, unsupervised
May 1, 2017
Data Mining: Concepts and Techniques
73
Entropy-Based Discretization

Given a set of samples S, if S is partitioned into two intervals S1 and S2
using boundary T, the information gain after partitioning is
I (S , T ) 

| S1 |
|S |
Entropy( S1)  2 Entropy( S 2)
|S|
|S|
Entropy is calculated based on class distribution of the samples in the
set. Given m classes, the entropy of S1 is
m
Entropy( S1 )   pi log 2 ( pi )
i 1
where pi is the probability of class i in S1



The boundary that minimizes the entropy function over all possible
boundaries is selected as a binary discretization
The process is recursively applied to partitions obtained until some
stopping criterion is met
Such a boundary may reduce data size and improve classification
accuracy
May 1, 2017
Data Mining: Concepts and Techniques
74
Interval Merge by 2 Analysis

Merging-based (bottom-up) vs. splitting-based methods

Merge: Find the best neighboring intervals and merge them to form
larger intervals recursively

ChiMerge [Kerber AAAI 1992, See also Liu et al. DMKD 2002]

Initially, each distinct value of a numerical attr. A is considered to be
one interval

2 tests are performed for every pair of adjacent intervals

Adjacent intervals with the least 2 values are merged together,
since low 2 values for a pair indicate similar class distributions

This merge process proceeds recursively until a predefined stopping
criterion is met (such as significance level, max-interval, max
inconsistency, etc.)
May 1, 2017
Data Mining: Concepts and Techniques
75
Segmentation by Natural Partitioning

A simply 3-4-5 rule can be used to segment numeric data
into relatively uniform, “natural” intervals.

If an interval covers 3, 6, 7 or 9 distinct values at the
most significant digit, partition the range into 3 equiwidth intervals

If it covers 2, 4, or 8 distinct values at the most
significant digit, partition the range into 4 intervals

If it covers 1, 5, or 10 distinct values at the most
significant digit, partition the range into 5 intervals
May 1, 2017
Data Mining: Concepts and Techniques
76
Example of 3-4-5 Rule
count
Step 1:
Step 2:
-$351
-$159
Min
Low (i.e, 5%-tile)
msd=1,000
profit
High(i.e, 95%-0 tile)
Low=-$1,000
(-$1,000 - 0)
(-$400 - 0)
(-$200 -$100)
(-$100 0)
May 1, 2017
Max
High=$2,000
($1,000 - $2,000)
(0 -$ 1,000)
(-$400 -$5,000)
Step 4:
(-$300 -$200)
$4,700
(-$1,000 - $2,000)
Step 3:
(-$400 -$300)
$1,838
($1,000 - $2, 000)
(0 - $1,000)
(0 $200)
($1,000 $1,200)
($200 $400)
($1,200 $1,400)
($1,400 $1,600)
($400 $600)
($600 $800)
($800 $1,000)
($1,600 ($1,800 $1,800)
$2,000)
Data Mining: Concepts and Techniques
($2,000 - $5, 000)
($2,000 $3,000)
($3,000 $4,000)
($4,000 $5,000)
77
Concept Hierarchy Generation for Categorical Data

Specification of a partial/total ordering of attributes
explicitly at the schema level by users or experts


Specification of a hierarchy for a set of values by explicit
data grouping


{Urbana, Champaign, Chicago} < Illinois
Specification of only a partial set of attributes


street < city < state < country
E.g., only street < city, not others
Automatic generation of hierarchies (or attribute levels) by
the analysis of the number of distinct values

May 1, 2017
E.g., for a set of attributes: {street, city, state, country}
Data Mining: Concepts and Techniques
78
Automatic Concept Hierarchy Generation

Some hierarchies can be automatically generated based
on the analysis of the number of distinct values per
attribute in the data set
 The attribute with the most distinct values is placed
at the lowest level of the hierarchy
 Exceptions, e.g., weekday, month, quarter, year
15 distinct values
country
province_or_ state
365 distinct values
city
3567 distinct values
street
May 1, 2017
674,339 distinct values
Data Mining: Concepts and Techniques
79
Chapter 2: Data Preprocessing

Why preprocess the data?

Data cleaning

Data integration and transformation

Data reduction

Discretization and concept hierarchy
generation

May 1, 2017
Summary
Data Mining: Concepts and Techniques
80
Summary




Data preparation or preprocessing is a big issue for both
data warehousing and data mining
Discriptive data summarization is need for quality data
preprocessing
Data preparation includes

Data cleaning and data integration

Data reduction and feature selection

Discretization
A lot a methods have been developed but data
preprocessing still an active area of research
May 1, 2017
Data Mining: Concepts and Techniques
81
References

D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments. Communications
of ACM, 42:73-78, 1999

T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley & Sons, 2003

T. Dasu, T. Johnson, S. Muthukrishnan, V. Shkapenyuk. Mining Database Structure; Or, How to Build
a Data Quality Browser. SIGMOD’02.

H.V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the Technical
Committee on Data Engineering, 20(4), December 1997

D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999

E. Rahm and H. H. Do. Data Cleaning: Problems and Current Approaches. IEEE Bulletin of the
Technical Committee on Data Engineering. Vol.23, No.4

V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data Cleaning and
Transformation, VLDB’2001

T. Redman. Data Quality: Management and Technology. Bantam Books, 1992

Y. Wand and R. Wang. Anchoring data quality dimensions ontological foundations. Communications of
ACM, 39:86-95, 1996

R. Wang, V. Storey, and C. Firth. A framework for analysis of data quality research. IEEE Trans.
Knowledge and Data Engineering, 7:623-640, 1995
May 1, 2017
Data Mining: Concepts and Techniques
82