Data
Pre

processing
Lecture 3
Gonca
Gulser
What is it?
Ideas????
Definition: Series of actions to improve the quality of data for
making it ready to any kind of analysis
Possible Problems...
Identifying INCOMPLETE data
Missing attribute
Lack
of Attribute Values
Contain only aggregate
data
Eliminate NOISE
Errors
Outliers (should we always get rid of them? Any special case
?)
Identify INCONSISTANCY
A value can be code differently across whole
DB
Too DISPERSE to analyse
Too many attributes for any algorithm.
Forms of Data Prepossessing
Forms of Data
Pre

process
Data
Cleaning
Data Integration
Data Transformation
Data Reduction
Data Cleaning
Missing Value
Handling
Smooth out
Noise
Correct inconsistencies
Missing Value Handling
(Data Cleaning)
Any ideas???
Missing Value Handling
(Data Cleaning)
1)
Ignore
Tuple
not
very effective especially if the tuple contains several missing.
It
is poor when the percentage of missing values per attribute varies considerably
2)
Fill the missing Manually
•
Time consuming especially in huge
datasets
3)
Use global constant to fill in the missing
•
Replace with “unknown” or “missing”
•
Not useful because may lead Data mining tool to produce interesting results for
them
4)
Use attribute mean/mode/median to fill the missing value
•
What about categorical data?
•
Why is mean dangerous?
•
Skewed data
5)
Use the attribute mean for all sample belonging to the same class
•
Categorize the attributes & Use mean of each category to fill the missing
6)
Use the most probable value to fill in the missing value
•
Regression/inference

based tools/ decision tree
Methods from 3 to 6 are
biased.

The
generated values might not be correct so it increase the algorithm's
error rate
6
th
method is the most popular one because it uses more past data to predict the current situation... You
must be sure that your past data is reliable...
Smooth out Noise
(Data Cleaning)
What is
Noise?

Random
error or variance in the measured
data
Methods
1) Binning
Sort the data
Divide into equal chunks (bins)
Get the mean of each bin and replace Smoothing with
boundaries
Sorted data for price
= 4,8,15,21,21,24,25,28,34
Partition into Bins:
Bin1: 4,8,15
Bin2: 21,21,24
Bin3: 25,28,34
Smoothing By means
Bin1: 9,9,9
Bin2: 22,22,22
Bin3: 29,29,29
Smoothing By boundaries
Bin1: 4,5,15
Bin2: 21,21,24
Bin3: 25,25,34
Smooth out Noise
(Data Cleaning) cont...
2) Combined
Human and Computer Power
By any given algorithm let computer produce an outlier or noise list called “surprise”
Then go over the list and remove the irrelevant data by hand...
It is easier and time saving than go through all data
set
3) Regression
Linear
MultiLinear
Logarithmic
4) Other
methods
Data reduction involving discretization (divide data into sub

categories like low
\
medium
\
high) such as
decision tree reduce the data step by step
Concept
Hierarchies

a form of discretization also used for noise
Forms of Data
Pre

process
Data
Cleaning
Data Integration
Data Transformation
Data Reduction
Data Integration and Transformation
What is it?
INTEGRATION
: Merge
Data from multiple data
sources
TRANSFORMATION:
Transform
data into an appropriate format for any given data
mining algorithm.
Data Integration
Schema Integration
Meta Data can solve the problem... ex:
Cut_id
and
cust_number
are same
thing
Redundancy
An attribute is redundant if it can be derived from any given attribute in the
database ex: annual revenue
Can be detected by correlation
analysis
Remove one of the duplicate attributes
Detection and Resolution of Data Conflicts
Because of different metrics and different perceptions on data, multiple sources
have same data in totally different formats and logic.
Examples:
•
A unit may be hold in European metric system (kg) in one data source and
in
British
metric system (pounds) in another data
source
•
A
price of a room may be in different currencies and also may contain different
attributes (such as Hilton's room price may include breakfast but Sheraton’s may
not)
If result > 0, then A and B are positively correlated
If result < 0, then A and B are negatively correlated
If result = 0, then A and B are not correlated
Data Transformation
Transform or consolidate data into appropriate forms for Data
Mining
Methods
Smoothing
–
Get rid of noise
Aggregation
–
Summary or aggregation operation. To use data to calculate new
measure. (calculated measure in OLAP cubes)
e.x
. Using daily sales to calculate
quarterly or annual sales.
Generalization
–
Transform into higher level concept
e.x
. Concept hierarchies or
divide age into
young
\
medium
\
old
Normalization
–
fall the data into specific range usually

1 to 1
Useful for classification and clustering algorithms.
The classification algorithms like neural networks, needs data into the range between

1 to 1
Distance based clustering algorithms like k

means does not require data into range. However, we
usually need to normalize values in order not give over emphasize on naturally higher value
attributes.
e.x
. If we put age and salary as attribute we need to normalize both in order to get rid
of the effects of higher values of salary.
Data Transformation cont...
Normalization Algorithms
Min

Max normalization
–
performs linear transformation on the original
data
𝑂 𝑖𝑔𝑖𝑎
𝑉𝑎
−
min
(
𝑎𝑖
)
max
𝑎𝑖
−
min
(
𝑎𝑖
)
e.x
Suppose that the min and max values for the attribute income are
$12,000 and $98,000 we would like to map the income to the range
0.0, 1.0. By min

max normalization a value of $73,600 for income is
transformed
to
(73,600

12,000)/(98,000

12,000)= 0.716
Data Transformation cont...
Z

score normalization
–
the values of an attribute is
normalized based on mean and the standard deviation of the
attribute.
𝑂 𝑖𝑔𝑖𝑎
𝑉𝑎
−
𝑎
(
𝑎𝑖
)
(
𝑎𝑖
)
e.x
Suppose that the mean and the standard deviation of income are $54.000
and $16,000 respectively. With z

score normalization, a value for $73,600 is
transformed
to
(73,600

54,000)/16,000 = 1.225
Data Transformation cont...
Normalization by decimal scaling
–
normalizes by moving the
decimal points moved depends on the maximum absolute
value of the attribute
V
normalize
=
10
𝑗
where, j is the smallest integer that max(
v
normalize
)=1
e.x. Suppose that the value range for A is

986
–
917. The maximum absolute
value for A is 986. To normalize based on decimal scaling we need to divide
each value by 1000 (j=3) so that

986 normalizes to

0.986
Data Transformation cont...
Attribute Construction (feature construction)
–
new attributes
are constructed and added from the given set of attributes to
help the mining process
e.x
adding attribute area to data set by using height and width
Forms of Data
Pre

process
Data
Cleaning
Data Integration
Data Transformation
Data Reduction
Data Reduction
Make the amount of data
smaller
Be Careful!!!!
Reduced dataset should represent the original data set
Results of reduces dataset should be reflect the original sets data
Reduction should ease and fasten the data mining process
Data Reduction Strategies
Data Cube Aggregation
–
aggregation should be applied to construct data cubes
Dimension Reduction
–
irrelevant, weakly relevant or redundant attributes or dimensions
may be detected and removed
Data Compression
–
encoding mechanisms are used to reduce the data set size
Numerosity
Reduction
–
data is replaced or estimated by using a smaller data
representation
Discretization and concept hierarchy generation
–
data values for attributes are replaced
by ranges or higher conceptual levels.
Golden Rule
–
Reduction Time > Saved Time
No Reduction
Data Reduction
Data Cube
Aggregation
Climbing
up the upper level of concept
hierarchy...
OLAP
facility to summarize data
2008
2009
2010
Quarter
Sales
Sales
Sales
Q1
$224,000
$250,000
&249,000
Q2
$408,000
Q3
$350,000
Q4
$586,000
Year
Sales
2008
$1,586,000
2009
$2,345,677
2010
$3,594,000
Data Reduction
Dimension
Reduction
Reduce the irrelevant or redundant
attributes
Select the attribute subsets
–
attribute subset selection: find the minimum subset
of attributes to perform data mining action by not effecting the reliability and
robustness
.
AWARE
!!!
All methods can only find local optimum... we just hope the local one is
also global optimum
METHODS:
Stepwise Forward Selection
–
start with empty set. Add one by one attributes. Stop if no more
information gained ...
Stepwise Backward Selection
–
start with full set of attribute. Eliminate one by one until
information gain changed significantly
Combination of Forward and Backward Selection
–
in each step algorithm selects the best attribute
and eliminates the worst attribute
Decision Tree Induction
–
When constructing a tree, algorithm starts with the best attribute and get
the second best and so on... Algorithm stops when there is not any significant information gain.
Data Reduction
Data
Compression
Data
encoding and transformations are applied to obtain a
reduced or compressed representation of the original data.
If the original data can be reconstructed from the compressed
version, the technique is called “lossless”
If only the approximation is gained after reconstructing, the
technique is called “
lossy
”
Two main techniques
Wavelet Transformation
Principal Component Analysis (PCA)
METHODS:
Principal Component Analysis
–
It searches the c (components) in the k

dimensional orthogonal vectors that can be best represent the data where
c<=k
PCA can also be used as dimension reduction also
I
t can not eliminate the attributes to form new attribute set. PCA construct totally
new attributes (components) that can explain the min %70 of all attributes.
Data Reduction
Numerosity
Reduction
Gathering a smaller representation of original data. A way of
getting samples from original data.
AWARE!!! not to loose essence of data... Best representative
should be chosen.
Techniques
Regression & Log linear model
–
they can handle skewed data. They both are
sensitive to high dimensions (We will deal with them in clustering in
detail)
Histograms
: Use binning to approximate data distributions and are a popular
form of data reduction. A histogram for an attribute A partition the data
distribution of A into disjoint subsets or buckets
The
buckets are displayed on
horizontal axis, while the height (area) of a bucket typically reflects the average
frequency of the values represented by the bucket.
Data Reduction
Numerosity
Reduction

Histograms
How are the buckets determined and the attribute values partitioned?
Partition
Rules:
Equiwidth
–
the width of the bucket range is uniform.
Equidepth
–
the buckets are created so that, roughly, the frequency of
each bucket is constant (each bucket contains the sane number of
contiguous data samples)
V

optimal
–
Histogram with the least variance Histogram variance is a
weighted some of the original values that each bucket represents,
where bucket weight is equal to the number of values in the bucket. (if
data is one dimensional, V

optimal is K

means)
MaxDiff
–
The difference between each pair of adjacent values. A
bucket boundary is established between each pair for pairs having the
K

1 largest difference, where K is specified by user
Properties of Histograms
Highly effective at approximating both sparse and dense data
Effective at approximating skewed and uniform data
Histograms can be multidimensional
Multidimensional histograms can capture dependencies between attributes
Multidimensional histograms are good at handling data sets that have up to 5
dimensions.
They also are good to store outliers as well.
Data Reduction
Numerosity
Reduction

Histograms
Data Reduction
Numerosity
Reduction cont...
Other than histograms also the following used for
numerosity
reduction
Clustering
Sampling
Simple Random Sampling
Simple Random Sampling with replacement
Cluster Sample
Stratified Sample
Data Reduction
Discretization and Concept Hierarchy Generation
Reduce the number of values for a given continues attribute
by dividing the range of the attribute into intervals.
Discretization and concept hierarchy generation for Numeric
Data
Binning
Histogram Analysis
Cluster Analysis
Entropy

Based Discretization
–
An info based measure called “entropy” can be
used to recursively partition the values of numeric attribute A, resulting in a
hierarchical discretization (we come back at decision trees)
Segmentation by natural partitioning
–
user defined partitioning
Data Reduction
Discretization and Concept Hierarchy Generation
Reduce the number of values for a given continues attribute
by dividing the range of the attribute into intervals.
Discretization and concept hierarchy generation for Numeric
Data
Binning
Histogram Analysis
Cluster Analysis
Entropy

Based Discretization
–
An info based measure called “entropy” can be
used to recursively partition the values of numeric attribute A, resulting in a
hierarchical discretization (we come back at decision trees)
Segmentation by natural partitioning
–
user defined partitioning
For
categorical
data
Basically
user defined concept hierarchies and
discretization
e.x
. Geographical location, job category, colours and
etc
Data Reduction
Discretization and Concept Hierarchy Generation cont...
For categorical data
Basically user defined concept hierarchies and discretization
e.x
. Geographical location, job category, colours and
etc
Thank You !!!
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