1.6.data preprocessing

2
Introduction
 Real World databases
 Huge size
 Noisy, Missing and Inconsistent
 Data Preprocessing
 Data Cleaning
 Data Integration
 Data Transformation
 Data Reduction

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Need for Data Preprocessing
 Incomplete Data
 Lacking certain attributes of interest
 May not have been considered important during data entry
 Equipment Malfunctioning
 Deleted due to clashes with other data
 Only aggregate data maybe present

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 Noisy data
 Incorrect attribute values
 Errors or outliers e.g., Salary=“-10”
 Data collection instruments – faulty
 Data entry errors
 Transmission errors – limited buffer size
 Inconsistent
 Containing discrepancies in codes or names e.g., Age=“42”
Birthdate=“03/07/1997”
 Different data sources
 Functional dependency violation (e.g., modify some linked
data)
 Duplicate records also need data cleaning

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 Quality data
 Quality decisions must be based on quality data
 e.g., duplicate or missing data may cause incorrect or even
misleading statistics.
 Data warehouse needs consistent integration of quality data
 Data extraction, cleaning, and transformation
comprises the majority of the work of building a data
warehouse

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Major Tasks in Data Preprocessing
 Data cleaning
 Fill in missing values
 Smooth noisy data
 Identify or remove outliers
 Resolve inconsistencies
 Data integration
 Integration of multiple databases, data cubes, or files
 Attributes may have different names
 Eliminating redundancies
 Some attributes can be inferred from others

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Major Tasks in Data Preprocessing
 Data transformation
 Normalization and aggregation
 Data reduction
 Obtains reduced representation in volume but produces the same or
similar analytical results
 Data Aggregation
 Dimension Reduction
 Data Compression
 Numerosity Reduction
 Generalization
 Data discretization
 Part of data reduction but with particular importance, especially for
numerical data

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Data Cleaning
 Importance
 “Data cleaning is the number one problem in data
warehousing”—DCI survey
 Data cleaning tasks
 Fill in missing values
 Identify outliers and smooth out noisy data
 Correct inconsistent data
 Resolve redundancy caused by data integration

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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 need to be inferred.

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Handling Missing Data
 Ignore the tuple
 Usually done when class label is missing (assuming the task is
classification)—not effective when the percentage of missing
values per attribute varies considerably.
 Fill in the missing value manually
 Tedious + infeasible

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Handling Missing Data
 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
 Binning
 first sort data and partition into 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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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
 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
 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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Regression
x
y
y = x + 1
X1
Y1
Y1’

18
Human Inspection
 Combined Computer and Human Inspection
 Outliers in Handwritten character recognition
 Surprise value
 Garbage / Outliers
 Human identification

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Inconsistent Data
 Data discrepancy detection
 Use metadata (e.g., domain, range, dependency)
 Check Functional dependency relationships
 Use commercial tools
 Data scrubbing: use simple domain knowledge 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)
 Discrepancy detection and transformation

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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
 Other Issues
 Detecting redundancy (tuple level and attribute level)
 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
 Redundant data occur often during 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 detected by correlation analysis
 Careful integration - helps to reduce/avoid redundancies and
inconsistencies and improve mining speed and quality

22
Correlation Analysis
 Correlation coefficient (also called Pearson’s product moment
coefficient)
where n is the number of tuples, and are the respective means
of A and B, σA and σB are the respective standard deviation of A and
B
 If rA,B > 0, A and B are positively correlated (A’s values increase
as B’s). The higher the value, the stronger the correlation.
 rA,B = 0: independent; rA,B < 0: negatively correlated
BAn
BBAA
r BA
σσ)1(
))((
,
−
−−
=
∑
A B

23
Correlation Analysis
 Chi-square test
χ2
= ∑ i=1
c
∑ j=1
r
(oij – eij)2
/ eij
c – Number of possibilities for attribute 1; r – for attribute 2
eij =Expected Frequency : count(A=ai) x count(B=bj) / N
o – Observed Frequency
e – Expected Frequency
Compare χ2
value with table and decide
(r-1) x (c-1) : degrees of freedom

Chi-square test
Male Female Total
Fiction 250 (90) 200 (360) 450
Non-fiction 50 (210) 1000 (840) 1050
Total 300 1200 1500
24
χ2
= (250-90)2
/90 + (200-360)2
/360 +
(50-210)2
/210 + (1000-840)2
/840 = 507.93
Hypothesis: Gender and preferred reading are independent
507.83 > 10.83
So hypothesis is rejected
Conclusion: Gender and preferred_reading are strongly correlated

Chi-square test
Degrees of
freedom (df)
χ2
value
1 0.004 0.02 0.06 0.15 0.46 1.07 1.64 2.71 3.84 6.64 10.83
2 0.10 0.21 0.45 0.71 1.39 2.41 3.22 4.60 5.99 9.21 13.82
3 0.35 0.58 1.01 1.42 2.37 3.66 4.64 6.25 7.82 11.34 16.27
4 0.71 1.06 1.65 2.20 3.36 4.88 5.99 7.78 9.49 13.28 18.47
5 1.14 1.61 2.34 3.00 4.35 6.06 7.29 9.24 11.07 15.09 20.52
6 1.63 2.20 3.07 3.83 5.35 7.23 8.56 10.64 12.59 16.81 22.46
7 2.17 2.83 3.82 4.67 6.35 8.38 9.80 12.02 14.07 18.48 24.32
8 2.73 3.49 4.59 5.53 7.34 9.52 11.03 13.36 15.51 20.09 26.12
9 3.32 4.17 5.38 6.39 8.34 10.66 12.24 14.68 16.92 21.67 27.88
10 3.94 4.86 6.18 7.27 9.34 11.78 13.44 15.99 18.31 23.21 29.59
P value (Probability) 0.95 0.90 0.80 0.70 0.50 0.30 0.20 0.10 0.05 0.01 0.001
Non-significant Significant
25

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Data Transformation
1. Smoothing: remove noise from data – Binning, Clustering,
Regression
2. Normalization: scaled to fall within a small, specified range
 min-max normalization
 z-score normalization
 normalization by decimal scaling
1. Attribute/feature construction
 New attributes constructed from the given ones
1. Aggregation: summarization, data cube construction
2. Generalization: concept hierarchy climbing

27
1. Smoothing
 Binning
 Equal-width (distance) partitioning
 Equal-depth (frequency) partitioning
 Clustering

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1. Smoothing
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 multidimensional probability
distributions

29
 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:
 Approximation of joint probabilities
 Estimate the probability of each point in a multi-dimensional space from a
smaller subset of dimensions
1. Smoothing
Regression and Log-Linear Models

30
2. Normalization
 Min-max normalization: to [new_minA, new_maxA]
 Ex. Let income range $12,000 to $98,000 normalized to [0.0,
1.0]. Then $73,600 is mapped to
 Z-score normalization (μ: mean, σ: standard deviation)
 Ex. Let μ = 54,000, σ = 16,000. Then for 73600
 Normalization by decimal scaling
716.00)00.1(
000,12000,98
000,12600,73
=+−
−
−
AAA
AA
A
minnewminnewmaxnew
minmax
minv
v _)__(' +−
−
−
=
A
Av
v
σ
µ−
='
j
v
v
10
'= Where j is the smallest integer such that Max(|ν’|) < 1
225.1
000,16
000,54600,73
=
−

31
3. Attribute Construction
 New attributes are constructed from given attributes
 To improve accuracy and understanding of structure
 Area from height and width
 Product operator and ‘and’

32
4. Aggregation
 Data Cubes
 Store Multi-dimensional aggregated information
 Each cell holds an aggregate data value
 Concept hierarchies – allow analysis at multiple
levels
 Provide fast access to pre-computed summarized
data

33
A Sample 3D Data Cube
Total annual sales
of TV in U.S.A.Date
Product
Country
sum
sum
TV
VCR
PC
1Qtr 2Qtr 3Qtr 4Qtr
U.S.A
Canada
Mexico
sum

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4. Aggregation
Data Cube Aggregation
 The lowest level of abstraction
 Base Cuboid
 Highest level of abstraction
 Apex Cuboid
 Multiple levels
 Lattice of Cuboids

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Cube: A Lattice of Cuboids
time,item
time,item,location
time, item, location, supplier
all
time item location supplier
time,location
time,supplier
item,location
item,supplier
location,supplier
time,item,supplier
time,location,supplier
item,location,supplier
0-D(apex) cuboid
1-D cuboids
2-D cuboids
3-D cuboids
4-D(base) cuboid

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5. Generalization - Concept hierarchy
 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)
 Detail lost but more meaningful
 Mining becomes easier
 Several concept hierarchies can be defined for the
same attribute

1.6.data preprocessing

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