UNIT-2 Data Preprocessing
Lecture Topic
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Lecture-13 Why preprocess the data?
Lecture-14 Data cleaning
Lecture-15 Data integration and transformation
Lecture-16 Data reduction
Lecture-17 Discretization and concept
hierarchgeneration
Lecture-13
Why preprocess the data?
Lecture-13 Why Data Preprocessing?
Data in the real world is:
incomplete: lacking attribute values, lacking certain
attributes of interest, or containing only aggregate
data
noisy: containing errors or outliers
inconsistent: containing discrepancies in codes or
names
No quality data, no quality mining results!
Quality decisions must be based on quality data
Data warehouse needs consistent integration of
quality data
Lecture-13 Why Data Preprocessing?
Multi-Dimensional Measure of Data Quality
A well-accepted multidimensional view:
Accuracy
Completeness
Consistency
Timeliness
Believability
Value added
Interpretability
Accessibility
Broad categories:
intrinsic, contextual, representational, and
accessibility.
Lecture-13 Why Data Preprocessing?
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 transformation
Normalization and aggregation
Data reduction
Obtains reduced representation in volume but produces the
same or similar analytical results
Data discretization
Part of data reduction but with particular importance, especially
for numerical data
Lecture-13 Why Data Preprocessing?
Forms of data preprocessing
Lecture-13 Why Data Preprocessing?
Lecture-14
Data cleaning
Data Cleaning
Data cleaning tasks
Fill in missing values
Identify outliers and smooth out noisy data
Correct inconsistent data
Lecture-14 - Data cleaning
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.
Lecture-14 - Data cleaning
How to Handle Missing Data?
Ignore the tuple: usually done when class label
is missing
Fill in the missing value manually
Use a global constant to fill in the missing value:
ex. “unknown”
Lecture-14 - Data cleaning
How to Handle Missing Data?
Use the attribute mean to fill in the missing value
Use the attribute mean for all samples belonging to the
same class to fill in the missing value
Use the most probable value to fill in the missing value:
inference-based such as Bayesian formula or decision
tree
Lecture-14 - Data cleaning
Noisy Data
Noise: random error or variance in a measured
variable
Incorrect attribute values may due to
faulty data collection instruments
data entry problems
data transmission problems
technology limitation
inconsistency in naming convention
Other data problems which requires data cleaning
duplicate records
incomplete data
inconsistent data
Lecture-14 - Data cleaning
How to Handle Noisy Data?
Binning method:
first sort data and partition into (equal-
frequency) bins
then one can smooth by bin means, smooth
by bin median, smooth by bin boundaries
Clustering
detect and remove outliers
Regression
smooth by fitting the data to a regression
functions – linear regression
Lecture-14 - Data cleaning
Simple Discretization Methods: Binning
Equal-width (distance) partitioning:
It 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:
It divides the range into N intervals, each containing
approximately same number of samples
Good data scaling
Managing categorical attributes can be tricky.
Lecture-14 - Data cleaning
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 (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
Lecture-14 - Data cleaning
Cluster Analysis
Lecture-14 - Data cleaning
Regression
y
Y1
Y1’ y=x+1
X1 x
Lecture-14 - Data cleaning
Lecture-15
Data integration and
transformation
Data Integration
Data integration:
combines data from multiple sources into a coherent
store
Schema integration
integrate metadata from different sources
Entity identification problem: identify real world entities
from multiple data sources, e.g., A.cust-id B.cust-#
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
Lecture-15 - Data integration and transformation
Handling Redundant Data in Data
Integration
Redundant data occur often when
integration of multiple databases
The same attribute may have different names
in different databases
One attribute may be a “derived” attribute in
another table, e.g., annual revenue
Lecture-15 - Data integration and transformation
Handling Redundant Data in Data
Integration
Redundant data 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
Lecture-15 - Data integration and transformation
Data Transformation
Smoothing: remove noise from data
Aggregation: summarization, data cube
construction
Generalization: concept hierarchy climbing
Lecture-15 - Data integration and transformation
Data Transformation
Normalization: scaled to fall within a small,
specified range
min-max normalization
z-score normalization
normalization by decimal scaling
Attribute/feature construction
New attributes constructed from the given ones
Lecture-15 - Data integration and transformation
Data Transformation: Normalization
min-max normalization
v minA
v' (new _ maxA new _ minA) new _ minA
maxA minA
z-score normalization
v mean A
v'
stand _ dev A
normalization by decimal scaling
v
v' j Where j is the smallest integer such that Max(| v ' |)<1
10
Lecture-15 - Data integration and transformation
Lecture-16
Data reduction
Data Reduction
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
Obtains a reduced representation of the data set
that is much smaller in volume but yet produces
the same (or almost the same) analytical results
Lecture-16 - Data reduction
Data Reduction Strategies
Data reduction strategies
Data cube aggregation
Attribute subset selection
Dimensionality reduction
Numerosity reduction
Discretization and concept hierarchy
generation
Lecture-16 - Data reduction
Data Cube Aggregation
The lowest level of a data cube
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
Lecture-16 - Data reduction
Dimensionality Reduction
Feature selection (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
step-wise forward selection
step-wise backward elimination
combining forward selection and backward elimination
decision-tree induction
Lecture-16 - Data reduction
Wavelet Transforms
Haar2 Daubechie4
Discrete wavelet transform (DWT): linear signal
processing
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 0s, 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
Lecture-16 - Data reduction
Principal Component Analysis
Given N data vectors from k-dimensions, find c
<= k orthogonal vectors that can be best used
to represent data
The original data set is reduced to one consisting of N
data vectors on c principal components (reduced
dimensions)
Each data vector is a linear combination of the c
principal component vectors
Works for numeric data only
Used when the number of dimensions is large
Lecture-16 - Data reduction
Principal Component Analysis
X2
Y1
Y2
X1
Lecture-16 - Data reduction
Attribute subset selection
Attribute subset selection reduces the data
set size by removing irrelevent or
redundant attributes.
Goal is find min set of attributes
Uses basic heuristic methods of attribute
selection
Lecture-16 - Data reduction
Example of Decision Tree Induction
Initial attribute set:
{A1, A2, A3, A4, A5, A6}
A4 ?
A1? A6?
Class 1 Class 2 Class 1 Class 2
> Reduced attribute set: {A1, A4, A6}
Lecture-16 - Data reduction
Numerosity Reduction
Parametric methods
Assume the data fits some model, estimate model
parameters, store only the parameters, and discard
the data (except possible outliers)
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
Lecture-16 - Data reduction
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
Lecture-16 - Data reduction
Regress Analysis and Log-Linear
Models
Linear regression: Y = + X
Two parameters , and 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 acad bcd
Lecture-16 - Data reduction
Histograms
A popular data
reduction technique 40
Divide data into 35
buckets and store 30
average (sum) for
25
each bucket
20
Can be constructed
optimally in one 15
dimension using 10
dynamic programming
5
Related to
0
quantization problems. 10000 30000 50000 70000 90000
Lecture-16 - Data reduction
Clustering
Partition data set into clusters, and one can store cluster
representation 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.
Lecture-16 - Data reduction
Sampling
Allows a large data set to be represented
by a much smaller of the data.
Let a large data set D, contains N tuples.
Methods to reduce data set D:
Simple random sample without replacement
(SRSWOR)
Simple random sample with replacement
(SRSWR)
Cluster sample
Stright sample
Lecture-16 - Data reduction
Sampling
W O R
SRS le random
i m p ho ut
( s e wi t
l
samp ment)
p l a ce
re
SRSW
R
Raw Data
Lecture-16 - Data reduction
Sampling
Raw Data Cluster/Stratified Sample
Lecture-16 - Data reduction
Lecture-17
Discretization and concept
hierarchy generation
Discretization
Three types of attributes:
Nominal — values from an unordered set
Ordinal — values from an ordered set
Continuous — 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
Lecture-17 - Discretization and concept hierarchy generation
Discretization and Concept hierachy
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.
Concept hierarchies
reduce the data by collecting and replacing low level
concepts (such as numeric values for the attribute
age) by higher level concepts (such as young,
middle-aged, or senior).
Lecture-17 - Discretization and concept hierarchy generation
Discretization and concept hierarchy
generation for numeric data
Binning
Histogram analysis
Clustering analysis
Entropy-based discretization
Discretization by intuitive partitioning
Lecture-17 - Discretization and concept hierarchy generation
Entropy-Based Discretization
Given a set of samples S, if S is partitioned into
two intervals S1 and S2 using boundary T, the
entropy after partitioning is
| S 1| |S 2|
E (S ,T ) Ent ( S 1) Ent ( S 2)
|S| |S|
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, e.g.,
Experiments showEnt ( Sthat
) Eit(may
T , S ) reduce
data size
and improve classification accuracy
Lecture-17 - Discretization and concept hierarchy generation
Discretization by intuitive partitioning
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 equal-width
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
Lecture-17 - Discretization and concept hierarchy generation
Example of 3-4-5 rule
count
Step 1: -$351 -$159 profit $1,838 $4,700
Min Low (i.e, 5%-tile) High(i.e, 95%-0 tile) Max
Step 2: msd=1,000 Low=-$1,000 High=$2,000
(-$1,000 - $2,000)
Step 3:
(-$1,000 - 0) (0 -$ 1,000) ($1,000 - $2,000)
(-$4000 -$5,000)
Step 4:
($2,000 - $5, 000)
(-$400 - 0) (0 - $1,000) ($1,000 - $2, 000)
(0 -
($1,000 -
(-$400 - $200)
$1,200) ($2,000 -
-$300) $3,000)
($200 -
($1,200 -
$400)
(-$300 - $1,400)
($3,000 -
-$200)
($400 - ($1,400 - $4,000)
(-$200 - $600) $1,600) ($4,000 -
-$100) ($600 - ($1,600 - $5,000)
$800) ($800 - ($1,800 -
$1,800)
(-$100 - $1,000) $2,000)
0)
Lecture-17 - Discretization and concept hierarchy generation
Concept hierarchy generation for categorical
data
Specification of a partial ordering of attributes
explicitly at the schema level by users or experts
Specification of a portion of a hierarchy by
explicit data grouping
Specification of a set of attributes, but not of
their partial ordering
Specification of only a partial set of attributes
Lecture-17 - Discretization and concept hierarchy generation
Specification of a set of attributes
Concept hierarchy can be automatically
generated based on the number of distinct
values per attribute in the given attribute set.
The attribute with the most distinct values is
placed at the lowest level of the hierarchy.
country 15 distinct values
province_or_ state 65 distinct
values
city 3567 distinct values
street 674,339 distinct values
Lecture-17 - Discretization and concept hierarchy generation
