Data Mining: Concepts and Techniques (3rd ed.)- Chapter 3 preprocessing

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Data Mining:
Concepts and Techniques
(3rd ed.)
— Chapter 3 —
Jiawei Han, Micheline Kamber, and Jian Pei
University of Illinois at Urbana-Champaign &
Simon Fraser University
©2013 Han, Kamber & Pei. All rights reserved.

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Chapter 3: Data Preprocessing
 Data Preprocessing: An Overview
 Data Quality
 Major Tasks in Data Preprocessing
 Data Cleaning
 Data Integration
 Data Reduction
 Data Transformation and Data Discretization
 Summary

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Data Quality: Why Preprocess the Data?
 Measures for data quality: A multidimensional view
 Accuracy: correct or wrong, accurate or not
 Completeness: not recorded, unavailable, …
 Consistency: some modified but some not, dangling, …
 Timeliness: timely update?
 Believability: how trustable the data are correct?
 Interpretability: how easily the data can be
understood?

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Major Tasks in Data Preprocessing
 Data cleaning
 Fill in missing values, smooth noisy data, identify or remove
outliers, and resolve inconsistencies
 Data integration
 Integration of multiple databases, data cubes, or files
 Data reduction
 Dimensionality reduction
 Numerosity reduction
 Data compression
 Data transformation and data discretization
 Normalization
 Concept hierarchy generation

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 Data Quality
 Data Cleaning
 Data Reduction
 Summary

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Data Cleaning
 Data in the Real World Is Dirty: Lots of potentially incorrect data,
e.g., instrument faulty, human or computer error, transmission error
 incomplete: lacking attribute values, lacking certain attributes of
interest, or containing only aggregate data
 e.g., Occupation = “ ” (missing data)
 noisy: containing noise, errors, or outliers
 e.g., Salary = “−10” (an error)
 inconsistent: containing discrepancies in codes or names, e.g.,
 Age = “42”, Birthday = “03/07/2010”
 Was rating “1, 2, 3”, now rating “A, B, C”
 discrepancy between duplicate records
 Intentional (e.g., disguised missing data)
 Jan. 1 as everyone’s birthday?

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Incomplete (Missing) Data
 Data is not always available
 E.g., many tuples have no recorded value for several
attributes, such as customer income in sales data
 Missing data may be due to
 equipment malfunction
 inconsistent with other recorded data and thus deleted
 data not entered due to misunderstanding
 certain data may not be considered important at the time
of entry
 not register history or changes of the data
 Missing data may need to be inferred

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How to Handle Missing Data?
 Ignore the tuple: usually done when class label is missing (when
doing classification)—not effective when the % of missing values
per attribute varies considerably
 Fill in the missing value manually: tedious + infeasible?
 Fill in it automatically with
 a global constant : e.g., “unknown”, a new class?!
 the attribute mean
 the attribute mean for all samples belonging to the same
class: smarter
 the most probable value: inference-based such as Bayesian
formula or decision tree

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Noisy Data
 Noise: random error or variance in a measured variable
 Incorrect attribute values may be due to
 faulty data collection instruments
 data entry problems
 data transmission problems
 technology limitation
 inconsistency in naming convention
 Other data problems which require data cleaning
 duplicate records
 incomplete data
 inconsistent data

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How to Handle Noisy Data?
 Binning
 first sort data and partition into (equal-frequency) bins
 then one can smooth by bin means, smooth by bin median,
smooth by bin boundaries, etc.
 Regression
 smooth by fitting the data into regression functions
 Clustering
 detect and remove outliers
 Combined computer and human inspection
 detect suspicious values and check by human (e.g., deal
with possible outliers)

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Data Cleaning as a Process
 Data discrepancy detection
 Use metadata (e.g., domain, range, dependency, distribution)
 Check field overloading
 Check uniqueness rule, consecutive rule and null rule
 Use commercial tools
 Data scrubbing: use simple domain knowledge (e.g., postal code,
spell-check) to detect errors and make corrections
 Data auditing: by analyzing data to discover rules and relationship to
detect violators (e.g., correlation and clustering to find outliers)
 Data migration and integration
 Data migration tools: allow transformations to be specified
 ETL (Extraction/Transformation/Loading) tools: allow users to specify
transformations through a graphical user interface
 Integration of the two processes
 Iterative and interactive (e.g., Potter’s Wheels)

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 Data Quality
 Data Cleaning
 Data Reduction
 Summary

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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

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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 and covariance analysis
 Careful integration of the data from multiple sources may help
reduce/avoid redundancies and inconsistencies and improve
mining speed and quality

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Correlation Analysis (Nominal 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

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Chi-Square Calculation: An Example
 Χ2 (chi-square) calculation (numbers in parenthesis are expected
counts calculated based on the data distribution in the two
categories)
(250 90) 2 (50 210)
2 (200 360)
2 (1000 840)
2
2 
 It shows that like_science_fiction and play_chess are correlated
in the group
507.93
840
360
210
90







 
Play chess Not play chess Sum (row)
Like science fiction 250(90) 200(360) 450
Not like science fiction 50(210) 1000(840) 1050
Sum(col.) 300 1200 1500

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Correlation Analysis (Numeric Data)
 Correlation coefficient (also called Pearson’s product moment
coefficient)
a b nAB
( )
  
( )( )
1 1

 

, ( 1)


  ( 1) 
A B
n
i i i
n
i i i
a A b B
r
A B n
A B
n

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(aibi) 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; rAB < 0: negatively correlated

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Visually Evaluating Correlation
Scatter plots
showing the
similarity from
–1 to 1.

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Correlation (viewed as linear
relationship)
 Correlation measures the linear relationship between
objects
 To compute correlation, we standardize data objects,
A and B, and then take their dot product
a' (a mean(A)) / std(A) k k  
b' (b mean(B)) / std(B) k k  
correlation(A,B)  A'B'

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Covariance (Numeric Data)
 Covariance is similar to correlation
Correlation coefficient:
where n is the number of tuples, and are the respective mean or
A B
expected values of A and B, σA and σB are the respective standard deviation
of A and B
 Positive covariance: If CovA,B > 0, then A and B both tend to be larger than their
expected values
 Negative covariance: If CovA,B < 0 then if A is larger than its expected value, B is
likely to be smaller than its expected value
 Independence: CovA,B = 0 but the converse is not true:
 Some pairs of random variables may have a covariance of 0 but are not
independent. Only under some additional assumptions (e.g., the data follow
multivariate normal distributions) does a covariance of 0 imply independence

Co-Variance: An Example
 It can be simplified in computation as
 Suppose two stocks A and B have the following values in one week: (2, 5), (3,
8), (5, 10), (4, 11), (6, 14).
 Question: If the stocks are affected by the same industry trends, will their
prices rise or fall together?
 E(A) = (2 + 3 + 5 + 4 + 6)/ 5 = 20/5 = 4
 E(B) = (5 + 8 + 10 + 11 + 14) /5 = 48/5 = 9.6
 Cov(A,B) = (2×5+3×8+5×10+4×11+6×14)/5 − 4 × 9.6 = 4
 Thus, A and B rise together since Cov(A, B) > 0.

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 Data Quality
 Data Cleaning
 Data Reduction
 Summary

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Data Reduction Strategies
 Data reduction: Obtain a reduced representation of the data set that is much
smaller in volume but yet produces the same (or almost the same) analytical
results
 Why data reduction? — A database/data warehouse may store terabytes of
data. Complex data analysis may take a very long time to run on the
complete data set.
 Data reduction strategies
 Dimensionality reduction, e.g., remove unimportant attributes
 Wavelet transforms
 Principal Components Analysis (PCA)
 Feature subset selection, feature creation
 Numerosity reduction (some simply call it: Data Reduction)
 Regression and Log-Linear Models
 Histograms, clustering, sampling
 Data cube aggregation
 Data compression

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Data Reduction 1: Dimensionality
Reduction
 Curse of dimensionality
 When dimensionality increases, data becomes increasingly sparse
 Density and distance between points, which is critical to clustering,
outlier analysis, becomes less meaningful
 The possible combinations of subspaces will grow exponentially
 Dimensionality reduction
 Avoid the curse of dimensionality
 Help eliminate irrelevant features and reduce noise
 Reduce time and space required in data mining
 Allow easier visualization
 Dimensionality reduction techniques
 Wavelet transforms
 Principal Component Analysis
 Supervised and nonlinear techniques (e.g., feature selection)

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Mapping Data to a New Space
 Fourier transform
 Wavelet transform
Two Sine Waves Two Sine Waves + Noise Frequency

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What Is Wavelet Transform?
 Decomposes a signal into
different frequency subbands
 Applicable to n-dimensional
signals
 Data are transformed to
preserve relative distance
between objects at different
levels of resolution
 Allow natural clusters to
become more distinguishable
 Used for image compression

Haar2 Daubechie4
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Wavelet Transformation
 Discrete wavelet transform (DWT) for linear signal processing,
multi-resolution analysis
 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

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Wavelet Decomposition
 Wavelets: A math tool for space-efficient hierarchical
decomposition of functions
 S = [2, 2, 0, 2, 3, 5, 4, 4] can be transformed to S^ = [23/4, -11/4,
1/2, 0, 0, -1, -1, 0]
 Compression: many small detail coefficients can be replaced by
0’s, and only the significant coefficients are retained

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Why Wavelet Transform?
 Use hat-shape filters
 Emphasize region where points cluster
 Suppress weaker information in their boundaries
 Effective removal of outliers
 Insensitive to noise, insensitive to input order
 Multi-resolution
 Detect arbitrary shaped clusters at different scales
 Efficient
 Complexity O(N)
 Only applicable to low dimensional data

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Principal Component Analysis (PCA)
 Find a projection that captures the largest amount of variation in
x2
e
x1
data
 The original data are projected onto a much smaller space, resulting
in dimensionality reduction. We find the eigenvectors of the
covariance matrix, and these eigenvectors define the new space

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Principal Component Analysis (Steps)
 Given N data vectors from n-dimensions, find k ≤ n orthogonal vectors
(principal components) that can be best used to represent data
 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

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Attribute Subset Selection
 Another way to reduce dimensionality of data
 Redundant attributes
 Duplicate much or all of the information contained in one or
more other attributes
 E.g., purchase price of a product and the amount of sales
tax paid
 Irrelevant attributes
 Contain no information that is useful for the data mining
task at hand
 E.g., students' ID is often irrelevant to the task of predicting
students' GPA

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Heuristic Search in Attribute Selection
 There are 2d possible attribute combinations of d attributes
 Typical heuristic attribute selection methods:
 Best single attribute under the attribute independence
assumption: choose by significance tests
 Best step-wise feature selection:
 The best single-attribute is picked first
 Then next best attribute condition to the first, ...
 Step-wise attribute elimination:
 Repeatedly eliminate the worst attribute
 Best combined attribute selection and elimination
 Optimal branch and bound:
 Use attribute elimination and backtracking

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Attribute Creation (Feature Generation)
 Create new attributes (features) that can capture the
important information in a data set more effectively than the
original ones
 Three general methodologies
 Attribute extraction
 Domain-specific
 Mapping data to new space (see: data reduction)
 E.g., Fourier transformation, wavelet transformation,
manifold approaches (not covered)
 Attribute construction
 Combining features (see: discriminative frequent
patterns in Chapter on “Advanced Classification”)
 Data discretization

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Data Reduction 2: Numerosity
Reduction
 Reduce data volume by choosing alternative, smaller forms of
data representation
 Parametric methods (e.g., regression)
 Assume the data fits some model, estimate model
parameters, store only the parameters, and discard the
data (except possible outliers)
 Ex.: 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, …

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Parametric Data Reduction:
Regression and Log-Linear Models
 Linear regression
 Data 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

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Regression Analysis
 Regression analysis: A collective name for
techniques for the modeling and analysis of
numerical data consisting of values of a
dependent variable (also called response
variable or measurement) and of one or more
independent variables (aka. explanatory
variables or predictors)
 The parameters are estimated so as to give a
"best fit" of the data
 Most commonly the best fit is evaluated by
using the least squares method, but other
criteria have also been used
y
y = x + 1
x
X1
Y1
Y1’
 Used for prediction (including
forecasting of time-series
data), inference, hypothesis
testing, and modeling of causal
relationships

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Regress Analysis and Log-Linear
 Linear regression: Y = w X + b
Models
 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:
 Approximate discrete multidimensional probability distributions
 Estimate the probability of each point (tuple) in a multi-dimensional
space for a set of discretized attributes, based on a smaller subset of
dimensional combinations
 Useful for dimensionality reduction and data smoothing

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Histogram Analysis
 Divide data into buckets and
store average (sum) for each
bucket
 Partitioning rules:
 Equal-width: equal bucket
range
 Equal-frequency (or equal-depth)
40
35
30
25
20
15
10
5
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000

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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 10

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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
 Key principle: Choose a representative subset of the data
 Simple random sampling may have very poor performance
in the presence of skew
 Develop adaptive sampling methods, e.g., stratified
sampling:
 Note: Sampling may not reduce database I/Os (page at a time)

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Types of Sampling
 Simple random sampling
 There is an equal probability of selecting any particular item
 Sampling without replacement
 Once an object is selected, it is removed from the population
 Sampling with replacement
 A selected object is not removed from the population
 Stratified sampling:
 Partition the data set, and draw samples from each partition
(proportionally, i.e., approximately the same percentage of
the data)
 Used in conjunction with skewed data

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Sampling: With or without Replacement
Raw Data

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Sampling: Cluster or Stratified
Sampling
Raw Data Cluster/Stratified Sample

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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
 Further reduce the size of data to deal with
 Reference appropriate levels
 Use the smallest representation which is enough to solve
the task
 Queries regarding aggregated information should be answered
using data cube, when possible

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Data Reduction 3: 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
 Dimensionality and numerosity reduction may also be
considered as forms of data compression

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Data Compression
Original Data Compressed
Data
lossless
Original Data
Approximated

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 Data Quality
 Data Cleaning
 Data Reduction
 Summary

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Data Transformation
 A function that maps the entire set of values of a given attribute to a new
set of replacement values s.t. each old value can be identified with one of
the new values
 Methods
 Smoothing: Remove noise from data
 Attribute/feature construction
 New attributes constructed from the given ones
 Aggregation: Summarization, data cube construction
 Normalization: Scaled to fall within a smaller, specified range
 min-max normalization
 z-score normalization
 normalization by decimal scaling
 Discretization: Concept hierarchy climbing

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Normalization
 Min-max normalization: to [new_minA, new_maxA]
v' ( _  _ )  _
A A A
v min
A
 Ex. Let income range $12,000 to $98,000 normalized to [0.0, 1.0].
Then $73,000 is mapped to
73,600 
12,000
 Z-score normalization (μ: mean, σ: standard deviation):
v A

 Ex. Let μ = 54,000, σ = 16,000. Then
 Normalization by decimal scaling
(1.0 0) 0 0.716
98,000 12,000
  

A A
new max new min new min
max 
min


A
v

'
73,600 54,000
'  Where j is the smallest integer such that Max(|ν’|) < 1
j
v
v
10
1.225
16,000



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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
 Numeric—real numbers, e.g., integer or real numbers
 Discretization: Divide the range of a continuous attribute into intervals
 Interval labels can then be used to replace actual data values
 Reduce data size by discretization
 Supervised vs. unsupervised
 Split (top-down) vs. merge (bottom-up)
 Discretization can be performed recursively on an attribute
 Prepare for further analysis, e.g., classification

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Data Discretization Methods
 Typical methods: All the methods can be applied recursively
 Binning
 Top-down split, unsupervised
 Histogram analysis
 Top-down split, unsupervised
 Clustering analysis (unsupervised, top-down split or bottom-up
merge)
 Decision-tree analysis (supervised, top-down split)
 Correlation (e.g., 2) analysis (unsupervised, bottom-up
merge)

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Simple Discretization: Binning
 Equal-width (distance) partitioning
 Divides the range into N intervals of equal size: uniform grid
 if A and B are the lowest and highest values of the attribute, the width of
intervals will be: W = (B –A)/N.
 The most straightforward, but outliers may dominate presentation
 Skewed data is not handled well
 Equal-depth (frequency) partitioning
 Divides the range into N intervals, each containing approximately same
number of samples
 Good data scaling
 Managing categorical attributes can be tricky

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Binning Methods for Data Smoothing
 Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34
* Partition into equal-frequency (equi-depth) bins:
- Bin 1: 4, 8, 9, 15
- Bin 2: 21, 21, 24, 25
- Bin 3: 26, 28, 29, 34
* Smoothing by bin means:
- Bin 1: 9, 9, 9, 9
- Bin 2: 23, 23, 23, 23
- Bin 3: 29, 29, 29, 29
* Smoothing by bin boundaries:
- Bin 1: 4, 4, 4, 15
- Bin 2: 21, 21, 25, 25
- Bin 3: 26, 26, 26, 34

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Discretization Without Using Class
Labels
(Binning vs. Clustering)
Data Equal interval width (binning)
Equal frequency (binning) K-means clustering leads to better results

57
Discretization by Classification &
Correlation Analysis
 Classification (e.g., decision tree analysis)
 Supervised: Given class labels, e.g., cancerous vs. benign
 Using entropy to determine split point (discretization point)
 Top-down, recursive split
 Details to be covered in Chapter “Classification”
 Correlation analysis (e.g., Chi-merge: χ2-based discretization)
 Supervised: use class information
 Bottom-up merge: find the best neighboring intervals (those
having similar distributions of classes, i.e., low χ2 values) to merge
 Merge performed recursively, until a predefined stopping condition

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Concept Hierarchy Generation
 Concept hierarchy organizes concepts (i.e., attribute values)
hierarchically and is usually associated with each dimension in a data
warehouse
 Concept hierarchies facilitate drilling and rolling in data warehouses to
view data in multiple granularity
 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 youth, adult, or senior)
 Concept hierarchies can be explicitly specified by domain experts
and/or data warehouse designers
 Concept hierarchy can be automatically formed for both numeric and
nominal data—For numeric data, use discretization methods shown

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Concept Hierarchy Generation
for Nominal Data
 Specification of a partial/total ordering of attributes explicitly at
the schema level by users or experts
 street < city < state < country
 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
 E.g., only street < city, not others
 Automatic generation of hierarchies (or attribute levels) by the
analysis of the number of distinct values
 E.g., for a set of attributes: {street, city, state, country}

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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
country
province_or_ state
city
street
15 distinct values
365 distinct values
3567 distinct values
674,339 distinct values

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 Data Quality
 Data Cleaning
 Data Reduction
 Summary

62
Summary
 Data quality: accuracy, completeness, consistency, timeliness,
believability, interpretability
 Data cleaning: e.g. missing/noisy values, outliers
 Data integration from multiple sources:
 Entity identification problem; Remove redundancies; Detect
inconsistencies
 Data reduction
 Dimensionality reduction; Numerosity reduction; Data
compression
 Data transformation and data discretization
 Normalization; Concept hierarchy generation

63
References
 D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments.
Comm. of ACM, 42:73-78, 1999
 T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley, 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), Dec. 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
 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

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