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*Data Mining: Concepts and Techniques*Data Mining: Concepts and
Techniques Chapter 2 Jiawei HanDepartment of Computer Science
University of Illinois at Urbana-Champaignwww.cs.uiuc.edu/~hanj2006
Jiawei Han and Micheline Kamber, All rights reserved
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Chapter 2: Data
PreprocessingWhy preprocess the data?Descriptive data
summarizationData cleaning Data integration and transformationData
reductionDiscretization and concept hierarchy generationSummary
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Why Data
Preprocessing?Data in the real world is dirtyincomplete: lacking
attribute values, lacking certain attributes of interest, or
containing only aggregate datae.g., occupation= noisy: containing
errors or outlierse.g., Salary=-10inconsistent: containing
discrepancies in codes or namese.g., Age=42
Birthday=03/07/1997e.g., Was rating 1,2,3, now rating A, B, Ce.g.,
discrepancy between duplicate records
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Why Is Data
Dirty?Incomplete data may come fromNot applicable data value when
collectedDifferent considerations between the time when the data
was collected and when it is analyzed.Human/hardware/software
problemsNoisy data (incorrect values) may come fromFaulty data
collection instrumentsHuman or computer error at data entryErrors
in data transmissionInconsistent data may come fromDifferent data
sourcesFunctional dependency violation (e.g., modify some linked
data)Duplicate records also need data cleaning
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Why Is Data Preprocessing
Important?No quality data, no quality mining results!Quality
decisions must be based on quality datae.g., duplicate or missing
data may cause incorrect or even misleading statistics.Data
warehouse needs consistent integration of quality dataData
extraction, cleaning, and transformation comprises the majority of
the work of building a data warehouse
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Multi-Dimensional Measure
of Data QualityA well-accepted multidimensional
view:AccuracyCompletenessConsistencyTimelinessBelievabilityValue
addedInterpretabilityAccessibilityBroad categories:Intrinsic,
contextual, representational, and accessibility
Data Mining: Concepts and Techniques*
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*Data Mining: Concepts and Techniques*Major Tasks in Data
PreprocessingData cleaningFill in missing values, smooth noisy
data, identify or remove outliers, and resolve inconsistenciesData
integrationIntegration of multiple databases, data cubes, or
filesData transformationNormalization and aggregationData
reductionObtains reduced representation in volume but produces the
same or similar analytical resultsData discretizationPart of data
reduction but with particular importance, especially for numerical
data
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Forms of Data
Preprocessing
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Chapter 2: Data
PreprocessingWhy preprocess the data?Descriptive data
summarizationData cleaning Data integration and transformationData
reductionDiscretization and concept hierarchy generationSummary
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Mining Data Descriptive
CharacteristicsMotivationTo better understand the data: central
tendency, variation and spreadData dispersion characteristics
median, max, min, quantiles, outliers, variance, etc.Numerical
dimensions correspond to sorted intervalsData dispersion: analyzed
with multiple granularities of precisionBoxplot or quantile
analysis on sorted intervalsDispersion analysis on computed
measuresFolding measures into numerical dimensionsBoxplot or
quantile analysis on the transformed cube
Data Mining: Concepts and Techniques*
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*Data Mining: Concepts and Techniques*Measuring the Central
TendencyMean (algebraic measure) (sample vs. population):Weighted
arithmetic mean:Trimmed mean: chopping extreme valuesMedian: A
holistic measureMiddle value if odd number of values, or average of
the middle two values otherwiseEstimated by interpolation (for
grouped data):ModeValue that occurs most frequently in the
dataUnimodal, bimodal, trimodalEmpirical formula:
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques* Symmetric vs. Skewed
DataMedian, mean and mode of symmetric, positively and negatively
skewed data
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Measuring the Dispersion
of DataQuartiles, outliers and boxplotsQuartiles: Q1 (25th
percentile), Q3 (75th percentile)Inter-quartile range: IQR = Q3 Q1
Five number summary: min, Q1, M, Q3, maxBoxplot: ends of the box
are the quartiles, median is marked, whiskers, and plot outlier
individuallyOutlier: usually, a value higher/lower than 1.5 x
IQRVariance and standard deviation (sample: s, population:
)Variance: (algebraic, scalable computation)
Standard deviation s (or ) is the square root of variance s2 (or
2)
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Properties of Normal
Distribution CurveThe normal (distribution) curveFrom to +:
contains about 68% of the measurements (: mean, : standard
deviation) From 2 to +2: contains about 95% of itFrom 3 to +3:
contains about 99.7% of it
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques* Boxplot
AnalysisFive-number summary of a distribution:
Minimum, Q1, M, Q3, MaximumBoxplotData is represented with a
boxThe ends of the box are at the first and third quartiles, i.e.,
the height of the box is IRQThe median is marked by a line within
the boxWhiskers: two lines outside the box extend to Minimum and
Maximum
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Visualization of Data
Dispersion: Boxplot Analysis
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Histogram AnalysisGraph
displays of basic statistical class descriptionsFrequency
histograms A univariate graphical methodConsists of a set of
rectangles that reflect the counts or frequencies of the classes
present in the given data
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Quantile PlotDisplays all
of the data (allowing the user to assess both the overall behavior
and unusual occurrences)Plots quantile informationFor a data xi
data sorted in increasing order, fi indicates that approximately
100 fi% of the data are below or equal to the value xi
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Quantile-Quantile (Q-Q)
PlotGraphs the quantiles of one univariate distribution against the
corresponding quantiles of anotherAllows the user to view whether
there is a shift in going from one distribution to another
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Scatter plotProvides a
first look at bivariate data to see clusters of points, outliers,
etcEach pair of values is treated as a pair of coordinates and
plotted as points in the plane
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Loess CurveAdds a smooth
curve to a scatter plot in order to provide better perception of
the pattern of dependenceLoess curve is fitted by setting two
parameters: a smoothing parameter, and the degree of the
polynomials that are fitted by the regression
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Positively and Negatively
Correlated Data
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques* Not Correlated Data
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Graphic Displays of Basic
Statistical DescriptionsHistogram: (shown before)Boxplot: (covered
before)Quantile plot: each value xi is paired with fi indicating
that approximately 100 fi % of data are xi Quantile-quantile (q-q)
plot: graphs the quantiles of one univariant distribution against
the corresponding quantiles of anotherScatter plot: each pair of
values is a pair of coordinates and plotted as points in the
planeLoess (local regression) curve: add a smooth curve to a
scatter plot to provide better perception of the pattern of
dependence
Data Mining: Concepts and Techniques*
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*Data Mining: Concepts and Techniques*Chapter 2: Data
PreprocessingWhy preprocess the data?Descriptive data
summarizationData cleaning Data integration and transformationData
reductionDiscretization and concept hierarchy generationSummary
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data
CleaningImportanceData cleaning is one of the three biggest
problems in data warehousingRalph KimballData cleaning is the
number one problem in data warehousingDCI surveyData cleaning
tasksFill in missing valuesIdentify outliers and smooth out noisy
data Correct inconsistent dataResolve redundancy caused by data
integration
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Missing DataData is not
always availableE.g., many tuples have no recorded value for
several attributes, such as customer income in sales dataMissing
data may be due to equipment malfunctioninconsistent with other
recorded data and thus deleteddata not entered due to
misunderstandingcertain data may not be considered important at the
time of entrynot register history or changes of the dataMissing
data may need to be inferred.
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*How to Handle Missing
Data?Ignore the tuple: usually done when class label is missing
(assuming the tasks in classificationnot effective when the
percentage of missing values per attribute varies considerably.Fill
in the missing value manually: tedious + infeasible?Fill in it
automatically witha global constant : e.g., unknown, a new class?!
the attribute meanthe attribute mean for all samples belonging to
the same class: smarterthe most probable value: inference-based
such as Bayesian formula or decision tree
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Noisy DataNoise: random
error or variance in a measured variableIncorrect attribute values
may due tofaulty data collection instrumentsdata entry problemsdata
transmission problemstechnology limitationinconsistency in naming
convention Other data problems which requires data
cleaningduplicate recordsincomplete datainconsistent data
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*How to Handle Noisy
Data?Binningfirst sort data and partition into (equal-frequency)
binsthen one can smooth by bin means, smooth by bin median, smooth
by bin boundaries, etc.Regressionsmooth by fitting the data into
regression functionsClusteringdetect and remove outliersCombined
computer and human inspectiondetect suspicious values and check by
human (e.g., deal with possible outliers)
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Simple Discretization
Methods: BinningEqual-width (distance) partitioningDivides the
range into N intervals of equal size: uniform gridif 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 presentationSkewed data is not handled
wellEqual-depth (frequency) partitioningDivides the range into N
intervals, each containing approximately same number of samplesGood
data scalingManaging categorical attributes can be tricky
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Binning Methods for Data
SmoothingSorted 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
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Regression
xyy = x + 1X1Y1Y1
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Cluster Analysis
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data Cleaning as a
ProcessData discrepancy detectionUse metadata (e.g., domain, range,
dependency, distribution)Check field overloading Check uniqueness
rule, consecutive rule and null ruleUse commercial toolsData
scrubbing: use simple domain knowledge (e.g., postal code,
spell-check) to detect errors and make correctionsData auditing: by
analyzing data to discover rules and relationship to detect
violators (e.g., correlation and clustering to find outliers)Data
migration and integrationData migration tools: allow
transformations to be specifiedETL
(Extraction/Transformation/Loading) tools: allow users to specify
transformations through a graphical user interfaceIntegration of
the two processesIterative and interactive (e.g., Potters
Wheels)
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Chapter 2: Data
PreprocessingWhy preprocess the data?Data cleaning Data integration
and transformationData reductionDiscretization and concept
hierarchy generationSummary
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data IntegrationData
integration: Combines data from multiple sources into a coherent
storeSchema integration: e.g., A.cust-id B.cust-#Integrate metadata
from different sourcesEntity identification problem: Identify real
world entities from multiple data sources, e.g., Bill Clinton =
William ClintonDetecting and resolving data value conflictsFor the
same real world entity, attribute values from different sources are
differentPossible reasons: different representations, different
scales, e.g., metric vs. British units
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Handling Redundancy in
Data IntegrationRedundant data occur often when integration of
multiple databasesObject identification: The same attribute or
object may have different names in different databasesDerivable
data: One attribute may be a derived attribute in another table,
e.g., annual revenueRedundant attributes may be able to be detected
by correlation analysisCareful integration of the data from
multiple sources may help reduce/avoid redundancies and
inconsistencies and improve mining speed and quality
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Correlation Analysis
(Numerical Data)Correlation coefficient (also called Pearsons
product moment coefficient)
where n is the number of tuples, and are the respective means of
A and B, A and B are the respective standard deviation of A and B,
and (AB) is the sum of the AB cross-product.If rA,B > 0, A and B
are positively correlated (As values increase as Bs). The higher,
the stronger correlation.rA,B = 0: independent; rA,B < 0:
negatively correlated
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Correlation Analysis
(Categorical Data)2 (chi-square) test
The larger the 2 value, the more likely the variables are
relatedThe cells that contribute the most to the 2 value are those
whose actual count is very different from the expected
countCorrelation does not imply causality# of hospitals and # of
car-theft in a city are correlatedBoth are causally linked to the
third variable: population
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Chi-Square Calculation: An
Example
2 (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
Play chessNot play chessSum (row)Like science
fiction250(90)200(360)450Not like science
fiction50(210)1000(840)1050Sum(col.)30012001500
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data
TransformationSmoothing: remove noise from dataAggregation:
summarization, data cube constructionGeneralization: concept
hierarchy climbingNormalization: scaled to fall within a small,
specified rangemin-max normalizationz-score
normalizationnormalization by decimal scalingAttribute/feature
constructionNew attributes constructed from the given ones
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data Transformation:
NormalizationMin-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 (: mean, :
standard deviation):
Ex. Let = 54,000, = 16,000. ThenNormalization by decimal
scaling
Where j is the smallest integer such that Max(||) < 1
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Chapter 2: Data
PreprocessingWhy preprocess the data?Data cleaning Data integration
and transformationData reductionDiscretization and concept
hierarchy generationSummary
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data Reduction
StrategiesWhy data reduction?A database/data warehouse may store
terabytes of dataComplex data analysis/mining may take a very long
time to run on the complete data setData 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 resultsData
reduction TechniquesData cube aggregation:Dimensionality reduction
e.g., remove unimportant attributesData CompressionNumerosity
reduction e.g., fit data into modelsDiscretization and concept
hierarchy generation
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data Cube
AggregationAggregation operations are applied to the data in
construction of a data cube.Data cubes store multidimensional
aggregated information.The lowest level of a data cube (base
cuboid)The aggregated data for an individual entity of
interestE.g., a customer in a phone calling data warehouseMultiple
levels of aggregation in data cubesFurther reduce the size of data
to deal with
Data Mining: Concepts and Techniques
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Reference appropriate levelsUse the smallest representation
which is enough to solve the taskQueries regarding aggregated
information should be answered using data cube, when possible
*Data Mining: Concepts and Techniques*
Data Mining: Concepts and Techniques
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*DW/DM: Data cube Computation*A Data Cube
Cor1Cor2Cam1Cam2Lex1Lex2DammamJeddahRiyadhAllAllBranchProductAggregate
cellBase cellApex CuboidProduct cuboidBranch cuboidBase cuboid
101112310111969671298573
474844
332926172311
139
DW/DM: Data cube Computation
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*Data Mining: Concepts and Techniques*Attribute Subset
Selectionattribute 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 featuresreduce
# of patterns in the patterns, easier to understandHeuristic
methods (due to exponential # of choices):Step-wise forward
selectionStep-wise backward eliminationCombining forward selection
and backward eliminationDecision-tree induction
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Example of Decision Tree
InductionInitial attribute set:{A1, A2, A3, A4, A5, A6}
A4 ?
A1?A6?
Class 1Class 2Class 1Class 2
Reduced attribute set: {A1, A4, A6}
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Heuristic Feature
Selection MethodsThere are 2d possible sub-features of d
featuresSeveral heuristic feature selection methods:Best single
features under the feature independence assumption: choose by
significance testsBest step-wise feature selection: The best
single-feature is picked firstThen next best feature condition to
the first, ...Step-wise feature elimination:Repeatedly eliminate
the worst featureBest combined feature selection and
eliminationOptimal branch and bound:Use feature elimination and
backtracking
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data CompressionString
compressionThere are extensive theories and well-tuned
algorithmsTypically losslessBut only limited manipulation is
possible without expansionAudio/video compressionTypically lossy
compression, with progressive refinementSometimes small fragments
of signal can be reconstructed without reconstructing the wholeTime
sequence is not audioTypically short and vary slowly with time
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data CompressionOriginal
DataCompressed DatalosslessOriginal DataApproximated lossy
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Dimensionality
Reduction:Wavelet Transformation Discrete wavelet transform (DWT):
linear signal processing, multi-resolutional analysisCompressed
approximation: store only a small fraction of the strongest of the
wavelet coefficientsSimilar to discrete Fourier transform (DFT),
but better lossy compression, localized in spaceMethod:Length, L,
must be an integer power of 2 (padding with 0s, when necessary)Each
transform has 2 functions: smoothing, differenceApplies to pairs of
data, resulting in two set of data of length L/2Applies two
functions recursively, until reaches the desired length
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*DWT for Image
CompressionImage
Low Pass High Pass
Low Pass High Pass
Low Pass High Pass
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Given N data vectors from
n-dimensions, find k n principal components that can be best used
to represent data StepsNormalize input data: Each attribute falls
within the same rangeCompute k orthonormal (unit) vectors, i.e.,
principal componentsEach input data (vector) is a linear
combination of the k principal component vectorsThe principal
components are sorted in order of decreasing significance or
strengthSince the components are sorted, the size of the data can
be reduced by eliminating the weak components, i.e., those with low
variance. (i.e., using the strongest principal components, it is
possible to reconstruct a good approximation of the original
dataWorks for numeric data onlyUsed when the number of dimensions
is large
Dimensionality Reduction: Principal Component Analysis (PCA)
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*
X1X2Y1Y2Principal Component Analysis
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Numerosity ReductionReduce
data volume by choosing alternative, smaller forms of data
representationParametric methodsAssume the data fits some model,
estimate model parameters, store only the parameters, and discard
the data (except possible outliers)Example: Log-linear modelsobtain
value at a point in m-D space as the product on appropriate
marginal subspaces Non-parametric methods Do not assume modelsMajor
families: histograms, clustering, sampling
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data Reduction Method (1):
Regression and Log-Linear ModelsLinear regression: Data are modeled
to fit a straight lineOften uses the least-square method to fit the
lineMultiple regression: allows a response variable Y to be modeled
as a linear function of multidimensional feature vectorLog-linear
model: approximates discrete multidimensional probability
distributions
Data Mining: Concepts and Techniques
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Linear regression: Y = w X + bTwo regression coefficients, w and
b, specify the line and are to be estimated by using the data at
handUsing 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 aboveLog-linear
models:The multi-way table of joint probabilities is approximated
by a product of lower-order tablesProbability: p(a, b, c, d) = ab
acad bcd
Regress Analysis and Log-Linear Models
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*Data Mining: Concepts and Techniques*Data Reduction Method (2):
HistogramsDivide data into buckets and store average (sum) for each
bucketPartitioning rules:Equal-width: equal bucket
rangeEqual-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 1 largest differences
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data Reduction Method (3):
ClusteringPartition data set into clusters based on similarity, and
store cluster representation (e.g., centroid and diameter) onlyCan
be very effective if data is clustered but not if data is
smearedCan have hierarchical clustering and be stored in
multi-dimensional index tree structuresThere are many choices of
clustering definitions and clustering algorithmsCluster analysis
will be studied in depth in Chapter 7
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Data Reduction Method (4):
SamplingSampling: obtaining a small sample s to represent the whole
data set NAllow a mining algorithm to run in complexity that is
potentially sub-linear to the size of the dataChoose a
representative subset of the dataSimple random sampling may have
very poor performance in the presence of skewDevelop adaptive
sampling methodsStratified sampling: Approximate the percentage of
each class (or subpopulation of interest) in the overall database
Used in conjunction with skewed dataNote: Sampling may not reduce
database I/Os (page at a time)
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Sampling: with or without
ReplacementSRSWOR(simple random sample without
replacement)SRSWR
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Sampling: Cluster or
Stratified Sampling
Raw Data Cluster/Stratified Sample
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Chapter 2: Data
PreprocessingWhy preprocess the data?Data cleaning Data integration
and transformationData reductionDiscretization and concept
hierarchy generationSummary
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*DiscretizationThree types
of attributes:Nominal values from an unordered set, e.g., color,
professionOrdinal values from an ordered set, e.g., military or
academic rank Continuous real numbers, e.g., integer or real
numbersDiscretization: Divide the range of a continuous attribute
into intervalsSome classification algorithms only accept
categorical attributes.Reduce data size by discretizationPrepare
for further analysis
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Discretization and Concept
HierarchyDiscretization Reduce the number of values for a given
continuous attribute by dividing the range of the attribute into
intervalsInterval labels can then be used to replace actual data
valuesSupervised vs. unsupervisedSplit (top-down) vs. merge
(bottom-up)Discretization can be performed recursively on an
attributeConcept hierarchy formationRecursively 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)
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Discretization and Concept
Hierarchy Generation for Numeric DataTypical methods: All the
methods can be applied recursivelyBinning (covered above)Top-down
split, unsupervised, Histogram analysis (covered above)Top-down
split, unsupervisedClustering analysis (covered above)Either
top-down split or bottom-up merge, unsupervisedEntropy-based
discretization: supervised, top-down splitInterval merging by 2
Analysis: unsupervised, bottom-up mergeSegmentation by natural
partitioning: top-down split, unsupervised
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Entropy-Based
DiscretizationGiven 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 S1The boundary that
minimizes the entropy function over all possible boundaries is
selected as a binary discretizationThe process is recursively
applied to partitions obtained until some stopping criterion is
metSuch a boundary may reduce data size and improve classification
accuracy
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Interval Merge by 2
AnalysisMerging-based (bottom-up) vs. splitting-based methodsMerge:
Find the best neighboring intervals and merge them to form larger
intervals recursivelyChiMerge [Kerber AAAI 1992, See also Liu et
al. DMKD 2002]Initially, each distinct value of a numerical attr. A
is considered to be one interval2 tests are performed for every
pair of adjacent intervalsAdjacent intervals with the least 2
values are merged together, since low 2 values for a pair indicate
similar class distributionsThis merge process proceeds recursively
until a predefined stopping criterion is met (such as significance
level, max-interval, max inconsistency, etc.)
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Segmentation by Natural
PartitioningA 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 intervalsIf it covers 2, 4, or 8
distinct values at the most significant digit, partition the range
into 4 intervalsIf it covers 1, 5, or 10 distinct values at the
most significant digit, partition the range into 5 intervals
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Example of 3-4-5 Rule
(-$400 -$5,000)Step 4:
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Concept Hierarchy
Generation for Categorical DataSpecification of a partial/total
ordering of attributes explicitly at the schema level by users or
expertsstreet < city < state < countrySpecification of a
hierarchy for a set of values by explicit data grouping{Urbana,
Champaign, Chicago} < IllinoisSpecification of only a partial
set of attributesE.g., only street < city, not othersAutomatic
generation of hierarchies (or attribute levels) by the analysis of
the number of distinct valuesE.g., for a set of attributes:
{street, city, state, country}
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Automatic Concept
Hierarchy GenerationSome 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 hierarchyExceptions,
e.g., weekday, month, quarter, year
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*Chapter 2: Data
PreprocessingWhy preprocess the data?Data cleaning Data integration
and transformationData reductionDiscretization and concept
hierarchy generationSummary
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*SummaryData preparation or
preprocessing is a big issue for both data warehousing and data
miningDiscriptive data summarization is need for quality data
preprocessingData preparation includesData cleaning and data
integrationData reduction and feature selectionDiscretizationA lot
a methods have been developed but data preprocessing still an
active area of research
Data Mining: Concepts and Techniques
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*Data Mining: Concepts and Techniques*ReferencesD. P. Ballou and
G. K. Tayi. Enhancing data quality in data warehouse environments.
Communications of ACM, 42:73-78, 1999T. Dasu and T. Johnson.
Exploratory Data Mining and Data Cleaning. John Wiley & Sons,
2003T. Dasu, T. Johnson, S. Muthukrishnan, V. Shkapenyuk. Mining
Database Structure; Or, How to Build a Data Quality Browser.
SIGMOD02. H.V. Jagadish et al., Special Issue on Data Reduction
Techniques. Bulletin of the Technical Committee on Data
Engineering, 20(4), December 1997D. Pyle. Data Preparation for Data
Mining. Morgan Kaufmann, 1999E. Rahm and H. H. Do. Data Cleaning:
Problems and Current Approaches. IEEE Bulletin of the Technical
Committee on Data Engineering. Vol.23, No.4V. Raman and J.
Hellerstein. Potters Wheel: An Interactive Framework for Data
Cleaning and Transformation, VLDB2001T. Redman. Data Quality:
Management and Technology. Bantam Books, 1992Y. Wand and R. Wang.
Anchoring data quality dimensions ontological foundations.
Communications of ACM, 39:86-95, 1996R. Wang, V. Storey, and C.
Firth. A framework for analysis of data quality research. IEEE
Trans. Knowledge and Data Engineering, 7:623-640, 1995
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