Data preprocessing

Data Preprocessing
Adapted from:
Data Mining Concepts and Techniques by
Jiawei Han, Micheline Kamber and Jian Pei
Gajanand Sharma
M E Scholar,
UVCE Bangalore

Why preprocess the data?
Measuring the Central Tendency
Data cleaning
Data integration and transformation
Data reduction
Discretization and concept hierarchy generation
Content…

Data in the real world is Dirty…
 Incomplete Data: Lacking attribute values, Lacking certain attributes of
interest, or containing only aggregate data
e.g. Occupation=“ ”, year_salary = “13.000”, …
 Inconsistent Data: Containing discrepancies in codes or names
e.g. Age=“42” Birthday=“03/07/1997”
Previous rating “1,2,3”, Present rating “A, B, C”
Discrepancy between duplicate records
 Noisy Data: Containing errors or outliers
e.g. Salary=“-10”, Family=“Unknown”, …
Why preprocess the data?

Why data is dirty?
Incomplete data may come from-
 “Not applicable” data value when collected:
 Different considerations between the time when the data was collected and
when it is analyzed: Modern life insurance questionnaires would now be: Do
you smoke?, Weight?, Do you drink?, …
 Human/hardware/software problems: forgotten fields…/limited space…/year
2000 problem … etc.
Noisy data (Incorrect values) may come from-
 Faulty data collection instruments
 Human or computer error at data entry
 Errors in data transmission etc.

Why data is dirty?
Inconsistent data may come from-
 Integration of different data sources
e.g. Different customer data, like addresses, telephone numbers; spelling
conventions (oe, o”, o), etc.
 Functional dependency violation
e.g. Modify some linked data: Salary changed, while derived values like tax or tax
deductions, were not updated
Duplicate records also need data cleaning-
 Which one is correct?
 Is it really a duplicate record?
 Which data to maintain?
Jan Jansen, Utrecht, 1-1 2008, 10.000, 1, 2, …
Jan Jansen, Utrecht, 1-1 2008, 11.000, 1, 2, …

Why Data Preprocessing is Important?
No quality data, no quality mining results!
 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
 A very laborious task
 Legacy data specialist needed
 Tools and data quality tests to support these tasks

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 (restriction to useful values, and/or attributes only, etc.)
 Data discretization
Part of data reduction but with particular importance, especially for numerical data

Measuring the Central Tendency
 Mean (algebraic measure) (sample vs. population):
 Weighted arithmetic mean:
 Trimmed mean: chopping extreme values
 Median : A holistic measure
 Middle value if odd number of values; average of the middle two values otherwise
 Estimated by interpolation (for grouped data) if an interval containing the median
frequency is known.
 Mode : Value that occurs most frequently in the data.
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Data Cleaning
 Why Data Cleaning?
 “Data cleaning is one of the three biggest problems in data warehousing”—Ralph
Kimball
 “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

Missing Data
 Data is not always available- 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 (left blank)
 Certain data may not be considered important at the time of entry (left blank)
 Not registered history or changes of the data
 Missing data may need to be inferred (blanks can prohibit application of statistical or other
functions)

How to Handle Missing Data?
 Ignore the tuple: usually done when class label is missing (assuming the tasks in
classification—not effective when the percentage of missing values per attribute varies
considerably.
 Fill in the missing value manually: tedious + infeasible?
 Use a global constant to fill in the missing value: e.g., “unknown”, a new class?!
 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: smarter
 Use the most probable value to fill in the missing value: inference-based such as
Bayesian formula or decision tree

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 (H. Shree, HShree, H.Shree, H Shree etc.)
 Other data problems which requires data cleaning
 Duplicate records (omit duplicates)
 Incomplete data (interpolate, estimate, etc.)
 Inconsistent data (decide which one is correct …)

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)

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(boundaries 4 and 15, report closest boundary)
- Bin 2: 21, 21, 25, 25
- Bin 3: 26, 26, 26, 34

How to handle noisy data: Regression
y = x + 1
x
y
Y1
Y1’
X1

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 (Talend Data Quality Tool, Sept. 2008)
 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)

Handle Noisy Data: Cluster Analysis

 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 and use 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
Data integration and transformation

 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
Handling Redundancy in Data Integration

 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, 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
Correlation Analysis (Numerical Data)
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Correlation Analysis (Categorial Data)
 Χ2 (chi-square) test
 The larger the Χ2 value, the more likely the variables A, B are related (Observed is
actual count of event (Ai,Bj))
 The cells that contribute the most to the Χ2 value are those whose actual count is very
different from the expected count (based on totals)
 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)
 It shows that like_science_fiction and play_chess are correlated in the group (as 507 >
significance level ~10)
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Play Chess Don’t play chess Sum (Row)
Like science fiction 250(90) 200(360) 450
Don’t Like science fiction 50(210) 1000(840) 1050
Sum (Column) 300 1200 1500

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
 New attributes constructed from the given ones

Data Transformation: 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 $73,000 is mapped to
 Z-score normalization (μ: mean, σ: standard deviation):
 Ex. Let μ = 54,000, σ = 16,000. Then
 Normalization by decimal scaling
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Data Reduction
 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

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 (in size) representation which is enough to solve the task
 Queries regarding aggregated information should be answered using the data cube, when
possible

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 (start with empty selection and add best attributes)
 Step-wise backward elimination (start with all attributes, and reduce with the least
informative attribute)
 Combining forward selection and backward elimination
 Decision-tree induction (ID3, C4.5, CART)

Example of Decision Tree Induction
Initial attribute set:
{A1, A2, A3, A4, A5, A6}
Class 2Class 1Class 1 Class 2
A4 ?
A6 ?A1 ?
Reduced attribute set: {A1, A4, A6}

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

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

Data Compression
Original Data
Original Data
Approximated
Compressed
Data
lossless

Regression
Predict a value of a given continuous valued variable based on the
values of other variables, assuming a linear or nonlinear model of
dependency.
Greatly studied in statistics, neural network fields.
Examples:
Predicting sales amounts of new product based on advertising
expenditure.
Predicting wind velocities as a function of temperature, humidity, air
pressure, etc.
Time series prediction of stock market indices.

Data Reduction Method (1): Regression
 Linear regression: Data are modeled to fit a straight line
 Often uses the least-square method to fit the line
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: Allows a response variable Y to be modeled as a linear function of a
multidimensional feature vector
Y = b0 + b1 X1 + b2 X2.
 Many nonlinear functions can be transformed into the above

Data Reduction Method (2): Histograms
 Divide data into buckets and store
average (sum) for each bucket
 Partitioning rules:
 Equal-width: equal bucket range
 Equal-frequency (or equal-depth)
 V-optimal: with the least histogram variance
(weighted sum of the original values that
each bucket represents)
 MaxDiff: set bucket boundary between each
pair for pairs have the β–1 largest differences
0
5
10
15
20
25
30
35
40
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000

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)

Sampling: with or without Replacement
Raw Data

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

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

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)

Discretization and Concept Hierarchy Generation for
Numeric Data
 Typical methods: All the methods can be applied recursively
 Binning (covered above)
 Top-down split, unsupervised,
 Histogram analysis (covered above)
 Top-down split, unsupervised
 Clustering analysis (covered above)
 Either top-down split or bottom-up merge, unsupervised
 Entropy-based discretization: supervised, top-down split
 Segmentation by natural partitioning: top-down split, unsupervised

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
 Entropy is calculated based on class distribution of the samples in the set. Given m classes,
the entropy of S1 is
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
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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 lowest 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.)

Segmentation by Natural Partitioning
 A simple 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 equi-width intervals (e.g. [12030, 81254] =>
[10000,80000] and 8-1 = 7 => 7 distinct values at the most significant digit)
 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

Concept Hierarchy Generation for Categorical 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}

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

References
 Data preprocessing ppt by Prof. Deepak Moud, Poornima Group of Colleges.
 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

Data preprocessing

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Data preprocessing