DM Lecture 3

Data Preprocessing
— Chapter 2 —
©Jiawei Han and Micheline Kamber
Modified by Donghui Zhang
September 6, 2014 Data Mining: Concepts and Techniques 1

Chapter 3: Data Preprocessing
 Why preprocess the data?
 Data cleaning
 Data integration and transformation
 Data reduction
 Discretization and concept hierarchy generation
 Summary

Data Mining: A KDD Process
 Data mining: the core of
knowledge discovery
process.
Data
Warehouse
Pattern Evaluation
Data Mining
© Copyright 2006, Natasha Balac 3
Data Cleaning
Data Integration
Databases
Task-relevant Data
Selection and Transformation

Why Data Preprocessing?
 Data in the real world is dirty (huge size, multiple heterogeneous sources)
 incomplete: lacking attribute values, lacking certain
attributes of interest, or containing only aggregate data
 e.g., occupation=“”
 noisy: containing errors or outliers
 e.g., Salary=“-10”
 inconsistent: containing discrepancies in codes or
names
 e.g., Age=“42” Birthday=“03/07/1997”
 e.g., Was rating “1,2,3”, now rating “A, B, C”
 e.g., discrepancy between duplicate records

Why Is Data Dirty?
 Incomplete data comes from
 n/a data value when collected
 different consideration between the time when the data was
collected and when it is analyzed.
 human/hardware/software problems
 Noisy data comes from the process of data
 collection
 entry
 transmission
 Inconsistent data comes from
 Different data sources
 Functional dependency violation

Why Is Data Preprocessing 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 Processing helps improve efficiency and ease of
mining process
 Data extraction, cleaning, and transformation comprises
the majority of the work of building a data warehouse. —
Bill Inmon

Multi-Dimensional Measure of Data Quality
 A well-accepted multidimensional view:
 Accuracy
 Completeness
 Consistency
 Believability
 Timeliness
 Value added
 Interpretability
 Accessibility
 Broad categories:
 intrinsic, contextual, representational, and accessibility.
http://www.dataquality.com/998mathieu.htm

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

Forms of data preprocessing

 Detecting data anomalies, rectifying them early
and reducing the data to be analysed can lead to
huge payoffs for decision making.
 Improves efficiency and ease of the mining
process

 Data cleaning
 Data reduction
 Summary

Data Cleaning
 Importance
 “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
 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.

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?
 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

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

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

Simple Discretization Methods: 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.

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

Cluster Analysis

Regression
x
y
y = x + 1
X1
Y1
Y1’

 Data cleaning
 Data reduction
 Summary

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 º 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

Handling Redundancy 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
 Redundant data may be able to be detected by
correlational analysis
 Careful integration of the data from multiple sources may
help reduce/avoid redundancies and inconsistencies and
improve mining speed and quality

Data Transformation
 Smoothing: remove noise from data
 Aggregation: summarization, data cube construction
 Generalization: concept hierarchy climbing
Low level raw data -> higher level concepts eg. Age -> youth, middle_age, senior
 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 (v - value of attribute A)
v' v min ( _ - _ ) + _
A new max new min new min
A A A
= -
max -
min
A A
 z-score normalisation (zero-mean normalisation) use when min and max
values unknown, outliers dominate min max normalisation
v v mean
A
'= -
stand _
dev
 normalisation by decimal scaling
A
'= Where j is the smallest integer such that Max(| v ' |)<1
j
v v
10
Exercise: normalize {0, 6, 8, 14} and {6, 6, 8, 8}

 Data cleaning
 Data reduction
 Summary

Data Reduction Strategies
 A 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 (aggregation operations to construct data cube)
 Dimensionality reduction— remove unimportant attributes, encoding mechanism to
reduce data size
 Data Compression
 Numerosity reduction—fit data into models (parametric: store model parameters.
Non-parametric: clustering, sampling, histogram)
 Discretization and concept hierarchy generation – raw data values replaced by
ranges or higher conceptual levels
Computational time on data reduction not to outweigh time saved in mining reduced data
set

Data Cube Aggregation
 The lowest level of a data cube (called the base cuboid)
 the aggregated data for an individual entity of interest
 e.g., sales, customer in a phone calling data warehouse.
 Multiple levels of aggregation in data cubes (cuboids, lattice)
 Higher levels of abstraction 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

Dimensionality Reduction
 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 attributes in the discovered patterns makes it
easier to understand the pattern
 How to find ‘good’ subset of original attributes?
Heuristic methods (due to exponential # of choices, n attr -> 2n subsets):
 step-wise forward selection
 step-wise backward elimination
 combining forward selection and backward elimination
 decision-tree induction

Example of Decision Tree Induction
Initial attribute set:
{A1, A2, A3, A4, A5, A6}
A4 ?
Y
N
internal non-leaf node - test on that
attribute
Branch – test outcome
Leaf node - decision
A1? A6?
At each node choose best
attribute to partition data into
individual classes (from
given data). Attributes not in
tree are irrelevant
Y N Y
N
Class 1 Class 2 Class 1 Class 2
> Reduced attribute set: {A1, A4, A6}

Data Compression (compressed representation of
original data)
 String compression
 There are extensive theories and well-tuned algorithms
 Typically lossless (original can be reconstructed without loss of
data)
 But only limited manipulation is possible without
expansion
 Audio/video compression
 Typically lossy compression, with progressive
refinement (approximate reconstruction of original)
 Sometimes small fragments of signal can be
reconstructed without reconstructing the whole
 Time sequence
 Typically short and vary slowly with time

Data Compression
Original Data Compressed
Data
lossless
Original Data
Approximated
lossy

Wavelet Transformation
Haar2 Daubechie4
 Discrete wavelet transform (DWT): linear signal
processing, multiresolutional 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 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

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

Numerosity Reduction
Can we reduce data volume by choosing alternative smaller forms of
data representation?
 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

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

Regress Analysis and Log-Linear
Models
 Linear regression: Y = a + b X
 Two parameters , a 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:
 The multi-way table of joint probabilities is
approximated by a product of lower-order tables.
 Probability: p(a, b, c, d) = aab baccad dbcd

Histograms (buckets :- attribute-value/frequency)
 A popular data reduction
technique
 Divide data into buckets
and store average (sum)
for each bucket
 Can be constructed
optimally in one
dimension using dynamic
programming
 Related to quantization
problems.
40
35
30
25
20
15
10
5
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
Eg: List of prices of items sold 1,1,5,5,5,5,5,8,8,10,10,10,10,10,12,14,14,14,15,15,15,15,15,15,18,18,18,18,18,18,18,18,,20,20,20,20,20,20,20,21,21,21,21,25,25,25,25,25,28,28,30,30,30

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

Sampling (a large data set represented by much smaller random sample)
 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
 Sampling may not reduce database I/Os (page at a time).

Sampling
SRSWOR
(simple random
sample without
replacement)
SRSWR
Raw Data

Sampling
Raw Data Cluster/Stratified Sample

Hierarchical Reduction
 Use multi-resolution structure with different degrees of
reduction
 Hierarchical clustering is often performed but tends to
define partitions of data sets rather than “clusters”
 Parametric methods are usually not amenable to
hierarchical representation
 Hierarchical aggregation
 An index tree hierarchically divides a data set into
partitions by value range of some attributes
 Each partition can be considered as a bucket
 Thus an index tree with aggregates stored at each
node is a hierarchical histogram

 Data cleaning
 Data reduction
 Summary

Discretization (divide range of attributes into intervals)
 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

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)

Discretization and Concept Hierarchy
Generation for Numeric Data
 Binning (see sections before)
 Histogram analysis (see sections before)
 Clustering analysis (see sections before)
 Entropy-based discretization
 Segmentation by natural partitioning

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 S S Ent S
E S T
| |
| |
= 1 + ( )
S
Ent
| 2
|
| S
|
( )
1
2
 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.,
Ent(S) - E(T,S) >d
 Experiments show that it may reduce data size and
improve classification accuracy

Segmentation by Natural Partitioning
 A simply 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
 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

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
msd=Step 2: 1,000 Low=-$1,000 High=$2,000
(-$1,000 - $2,000)
(-$1,000 - 0) (0 -$ 1,000)
(-$400 -$5,000)
(-$400 - 0)
Step 3:
Step 4:
(-$400 -
-$300)
(-$300 -
-$200)
(-$200 -
-$100)
(-$100 -
0)
(0 - $1,000)
(0 -
$200)
($200 -
$400)
($400 -
$600)
($600 -
$800) ($800 -
$1,000)
($2,000 - $5, 000)
($2,000 -
$3,000)
($3,000 -
$4,000)
($4,000 -
$5,000)
($1,000 - $2,000)
($1,000 - $2, 000)
($1,000 -
$1,200)
($1,200 -
$1,400)
($1,400 -
$1,600)
($1,600 -
$1,800) ($1,800 -
$2,000)

Concept Hierarchy Generation for
Categorical Data
Discrete data. Categorical attributes have finite (but possibly large) number of distinct vales. No
ordering among values, eg. geographic location, job category, item type
 Specification of a partial ordering of attributes explicitly at the
schema level by users or experts
 street<city<state<country
 Specification of a portion of a hierarchy by explicit data
grouping
 {Urbana, Champaign, Chicago}<Illinois
 Specification of a set of attributes.
 System automatically generates partial ordering by
analysis of the number of distinct values (a higher levell attribute has
less distinct values than lower level attribute)
 E.g., street < city <state < country
 Specification of only a partial set of attributes
 E.g., only street < city, not others

Automatic Concept Hierarchy
Generation
 Some concept hierarchies can be automatically
generated based on the analysis of the number of
distinct values per attribute in the given data set
 The attribute with the most distinct values is placed
at the lowest level of the hierarchy
 Note: Exception—weekday, month, quarter, year
country
province_or_ state
city
street
15 distinct values
65 distinct
values
3567 distinct values
674,339 distinct values

 Data cleaning
 Data reduction
 Discretization and concept hierarchy
generation
 Summary

Summary
 Data preparation is a big issue for both warehousing
and mining
 Data preparation includes
 Data cleaning and data integration
 Data reduction and feature selection
 Discretization
 A lot a methods have been developed but still an active
area of research

References
 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
 D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments.
Communications of ACM, 42:73-78, 1999.
 H.V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the
Technical Committee on Data Engineering, 20(4), December 1997.
 A. Maydanchik, Challenges of Efficient Data Cleansing (DM Review - Data Quality
resource portal)
 D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999.
 D. Quass. A Framework for research in Data Cleaning. (Draft 1999)
 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, New York, 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.
 http://www.cs.ucla.edu/classes/spring01/cs240b/notes/data-integration1.pdf

www.cs.uiuc.edu/~hanj
TThhaannkk yyoouu !!!!!!

DM Lecture 3

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