Data processing

Data Preprocessing
Lecture 3
Data Mining: Concepts and Techniques 1

 Why preprocess the data?
 Data cleaning
 Data integration and transformation
 Data reduction
 Discretization and concept hierarchy generation

Why Data Preprocessing?
 Data in the real world is dirty
 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 may come from
 “Not applicable” data value when collected
 Different considerations between the time when the data was
collected and when it is analyzed.
 Human/hardware/software problems
 Noisy data (incorrect values) may come from
 Faulty data collection instruments
 Human or computer error at data entry
 Errors in data transmission
 Inconsistent data may come from
 Different data sources
 Functional dependency violation (e.g., modify some linked data)
 Duplicate records also need data cleaning

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 extraction, cleaning, and transformation comprises
the majority of the work of building a data warehouse

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

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

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
 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)

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

 Example:

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
- Bin 2: 21, 21, 25, 25
- Bin 3: 26, 26, 26, 34

 Suppose the data for analysis includes the
attribute Age. The age values for the data tuples
(instances) are (in increasing order):
13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25,
25,30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52,
70.
 Use binning (by bin means) to smooth the above
data using a bin data, depth of 3.

Regression
x
y
y = x + 1
X1
Y1
Y1’

Cluster Analysis

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,
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

Handling Redundancy in Data Integration
 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
 For nominal data, we use the chi-square test. For numeric attributes,
we can use the correlation coefficient and covariance.
 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
 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
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
=
−

Data Reduction Strategies
 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
 Dimensionality reduction — e.g., remove unimportant attributes
 Wavelet transforms and principal components analysis which transform
or project the original data onto a smaller space. Attribute subset
selection is a method of dimensionality reduction in which irrelevant,
weakly relevant, or redundant attributes or dimensions are detected and
removed .
 Numerosity reduction — e.g., fit data into models
 replace the original data volume by alternative, smaller forms of data
representation. These techniques may be parametric or nonparametric.
For parametric methods, a model is used to estimate the data, so that
typically only the data parameters need to be stored, instead of the actual
data. Regression and log-linear models are examples. Nonparametric
methods for storing reduced representations of the data include
histograms, clustering, sampling, and data cube aggregation
 Data compression
 Dimensionality reduction and numerosity reduction techniques
can also be considered forms of data compression.

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
 Step-wise backward elimination
 Combining forward selection and backward elimination
 Decision-tree induction

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

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}

Numerosity Reduction
 Parametric methods
 Assume the data fits some model, estimate model
parameters, store only the parameters, and discard
the data (except possible outliers)
 Example: Regression, Log-linear models
 Non-parametric methods
 Do not assume models
 Major families: histograms, clustering, sampling

Histograms
 A popular data reduction
technique
 Divide data into buckets
and store average (or
sum) for each bucket
0
5
10
15
20
25
30
35
40
10000 30000 50000 70000 90000

Histogram types
 Equal-width: In an equal-width histogram, the width of each
bucket range is uniform
 Equal-frequency (or equal-depth): In an equal-frequency
histogram, the buckets are created so that, roughly, the frequency of
each bucket is constant (i.e., each bucket contains roughly the
same number of contiguous data samples).
Example:
 not yet in school: 2
 in primary school: 5
 in high school: 9

Clustering
 Partitions data set into clusters, and models it by one
representative from each cluster
 Can be very effective if data is clustered but not if data
is “smeared”

Sampling
 Sampling can be used as a data reduction technique because it
allows a large data set to be represented by a much smaller random
data sample (or subset). Suppose that a large data set, D, contains N
tuples.
 Simple random sample without replacement (SRSWOR) of
size s: This is created by drawing s of the N tuples from D (s < N),
where the probability of drawing any tuple in D is 1=N, that is, all
tuples are equally likely to be sampled.
 Simple random sample with replacement (SRSWR) of size
s: This is similar to SRSWOR, except that each time a tuple is drawn
from D, it is recorded and then replaced. That is, after a tuple is
drawn, it is placed back in D so that it may be drawn again.

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

Sampling
Raw Data Cluster/Stratified Sample
•The number of samples drawn from each
cluster/stratum is analogous to its size
•Thus, the samples represent better the data and
outliers are avoided

Data Cube Aggregation
 Concept hierarchies may exist for each attribute, allowing the analysis
of data at multiple abstraction levels. For example, a hierarchy for
branch could allow branches to be grouped into regions, based on
their address. Data cubes provide fast access to precomputed,
summarized data, thereby benefiting online analytical processing as
well as data mining.
 The lowest level of a data cube (base cuboid)
 The aggregated data for an individual entity of interest
 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

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. (e.g. age are replaced by interval labels :0–
10, 11–20, etc.)
 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).

Data processing

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