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Data Mining MTAT.03.183 Descrip5ve analysis, preprocessing, visualisa5on... Jaak Vilo 2015 Spring Why Data Preprocessing?
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Data in the real world is dirty
n  incomplete: lacking attribute values, lacking
certain attributes of interest, or containing
only aggregate data
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noisy: containing errors or outliers
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e.g., Salary=“-10”
inconsistent: containing discrepancies in codes
or names
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e.g., occupation=“ ”
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
Data Mining: Concepts and Techniques
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Why Is Data Dirty?
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Incomplete data may come from
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Noisy data (incorrect values) may come from
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Faulty data collection instruments
Human or computer error at data entry
Errors in data transmission
Inconsistent data may come from
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“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
Different data sources
Functional dependency violation (e.g., modify some linked data)
Duplicate records also need data cleaning
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Why Is Data Preprocessing Important?
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No quality data, no quality mining results!
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Quality decisions must be based on quality data
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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
Garbage in, garbage out
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High quality data requirements
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High-quality data needs to pass a set of quality criteria. Those
include:
Accuracy: an aggregated value over the criteria of integrity,
consistency, and density
Integrity: an aggregated value over the criteria of completeness and
validity
Completeness: achieved by correcting data containing anomalies
Validity: approximated by the amount of data satisfying integrity
constraints
Consistency: concerns contradictions and syntactical anomalies
Uniformity: directly related to irregularities and in compliance with
the set 'unit of measure'
Density: the quotient of missing values in the data and the number
of total values ought to be known
http://en.wikipedia.org/wiki/Data_cleansing
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Multi-Dimensional Measure of Data Quality
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A well-accepted multidimensional view:
n  Accuracy
n  Completeness
n  Consistency
n  Timeliness
n  Believability
n  Value added
n  Interpretability
n  Accessibility
Broad categories:
n  Intrinsic, contextual, representational, and accessibility
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Major Tasks in Data Preprocessing
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Data cleaning
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Data integration
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Normalization and aggregation
Data reduction
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Integration of multiple databases, data cubes, or files
Data transformation
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Fill in missing values, smooth noisy data, identify or remove
outliers, and resolve inconsistencies
Obtains reduced representation in volume but produces the same
or similar analytical results
Data discretization
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Part of data reduction but with particular importance, especially
for numerical data
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Forms of Data Preprocessing
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Chapter 2: Data Preprocessing
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Why preprocess the data?
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Descriptive data summarization
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Data cleaning
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Data integration and transformation
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Data reduction
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Discretization and concept hierarchy generation
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Summary
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•  0.48 0.03 0.06 0.05 0.43 0.19 0.16 0.35 0.25 0.07 0.29 0.14 0.96 0.02 0.11 0.22 0.80 0.05 0.54 0.36 0.23 0.28 0.02 0.10 0.48 0.31 0.36 0.21 0.33 0.45 0.64 0.04 0.48 0.56 0.16 0.58 0.33 0.11 0.42 0.06 0.00 0.23 0.24 0.00 0.54 0.02 0.26 0.20 0.18 0.01 0.17 0.17 0.04 0.97 0.25 0.04 0.34 0.01 0.50 0.15 0.43 0.05 0.50 0.16 0.52 0.82 0.23 0.09 0.02 0.21 0.13 0.17 0.33 0.26 0.00 0.33 0.57 0.43 0.09 0.43 0.24 0.08 0.08 0.54 0.08 0.02 0.02 0.01 0.35 0.62 0.10 0.03 0.14 0.78 0.30 0.07 0.08 0.48 0.57 0.30 Jaak Vilo and other authors UT: Data Mining 2009 11 1,20#
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Jaak Vilo and other authors UT: Data Mining 2009 15 Characterise data use Big_University_DB mine characteris5cs as "Science_Students" in relevance to name,gender,major,birth_date,residence,pho
ne#,gpa from student where status in graduate Jaak Vilo and other authors UT: Data Mining 2009 16 Mining Data Descriptive Characteristics
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Motivation
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Data dispersion characteristics
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To better understand the data: central tendency, variation
and spread
median, max, min, quantiles, outliers, variance, etc.
Numerical dimensions correspond to sorted intervals
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Data dispersion: analyzed with multiple granularities of
precision
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Boxplot or quantile analysis on sorted intervals
Dispersion analysis on computed measures
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Folding measures into numerical dimensions
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Boxplot or quantile analysis on the transformed cube
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Measuring the Central Tendency
1 n
∑ xi
n  Mean (algebraic measure) (sample vs. population): x =
n i =1
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Weighted arithmetic mean:
x
N
n
∑w x
i
Trimmed mean: chopping extreme values
x=
i
i =1
n
∑w
i
Median: A holistic measure
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µ=∑
i =1
Middle value if odd number of values, or average of the middle two
values otherwise
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Estimated by interpolation (for grouped data):
median = L1 + (
Mode
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Value that occurs most frequently in the data
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Unimodal, bimodal, trimodal
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Empirical formula:
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n / 2 − (∑ f )l
f median
)c
mean − mode = 3 × (mean − median )
Data Mining: Concepts and Techniques
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• 
• 
Histograms and Probability Density FuncSons Probability Density FuncSons – 
• 
Frequency Histograms – 
– 
– 
• 
Total area under curve integrates to 1 Y-­‐axis is counts Simple interpretaSon Can't be directly related to probabiliSes or density funcSons RelaSve Frequency Histograms – 
– 
– 
– 
Divide counts by total number of observaSons Y-­‐axis is relaSve frequency Can be interpreted as probabiliSes for each range Can't be directly related to density funcSon • 
• 
Bar heights sum to 1 but won't integrate to 1 unless bar width = 1 Density Histograms – 
– 
– 
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Divide counts by (total number of observaSons X bar width) Y-­‐axis is density values Bar height X bar width gives probability for each range Can be directly related to density funcSon • 
Bar areas sum to 1 http://www.geog.ucsb.edu/~joel/g210_w07/lecture_notes/lect04/oh07_04_1.html
Jaak Vilo and other authors UT: Data Mining 2009 19 Jaak Vilo and other authors UT: Data Mining 2009 20 Jaak Vilo and other authors UT: Data Mining 2009 21 Jaak Vilo and other authors UT: Data Mining 2009 22 histograms •  equal sub-­‐intervals, known as `bins‘ •  break points •  bin width Jaak Vilo and other authors UT: Data Mining 2009 23 The data are (the log of) wing spans of aircraft built in from 1956 - 1984.
Jaak Vilo and other authors UT: Data Mining 2009 24 Jaak Vilo and other authors UT: Data Mining 2009 25 Jaak Vilo and other authors UT: Data Mining 2009 26 Histogram vs kernel density •  properSes of histograms with these two examples: –  they are not smooth –  depend on end points of bins –  depend on width of bins •  We can alleviate the first two problems by using kernel density es5mators. •  To remove the dependence on the end points of the bins, we centre each of the blocks at each data point rather than fixing the end points of the blocks. Jaak Vilo and other authors UT: Data Mining 2009 27 block of width 1 and height 1/12 (the dotted boxes) as they
are 12 data points, and then add them up
Jaak Vilo and other authors UT: Data Mining 2009 28 •  Blocks -­‐ it is sSll disconSnuous as we have used a disconSnuous kernel as our building block •  If we use a smooth kernel for our building block, then we will have a smooth density esSmate. Jaak Vilo and other authors UT: Data Mining 2009 29 •  It's important to choose the most appropriate bandwidth as a value that is too small or too large is not useful. •  If we use a normal (Gaussian) kernel with bandwidth or standard deviaSon of 0.1 (which has area 1/12 under the each curve) then the kernel density esSmate is said to undersmoothed as the bandwidth is too small in the figure below. •  It appears that there are 4 modes in this density -­‐ some of these are surely arSfices of the data. Jaak Vilo and other authors UT: Data Mining 2009 30 Jaak Vilo and other authors UT: Data Mining 2009 31 Jaak Vilo and other authors UT: Data Mining 2009 32 • Choose opSmal bandwith – Methods to esSmate it •  AMISE = AsymptoSc Mean Integrated Squared Error •  opSmal bandwidth = arg min AMISE Jaak Vilo and other authors UT: Data Mining 2009 33 •  The opSmal value of the bandwidth for our dataset is about 0.25. •  From the opSmally smoothed kernel density esSmate, there are two modes. As these are the log of aircrai wing span, it means that there were a group of smaller, lighter planes built, and these are clustered around 2.5 (which is about 12 m). •  Whereas the larger planes, maybe using jet engines as these used on a commercial scale from about the 1960s, are grouped around 3.5 (about 33 m). Jaak Vilo and other authors UT: Data Mining 2009 34 Jaak Vilo and other authors UT: Data Mining 2009 35 •  The properSes of kernel density esSmators are, as compared to histograms: –  smooth –  no end points –  depend on bandwidth Jaak Vilo and other authors UT: Data Mining 2009 36 Kernel Density esSmaSon -­‐ links •  Wikipedia: hkp://en.wikipedia.org/wiki/Kernel_density_esSmaSon •  Ricardo GuSerrez-­‐Osuna hkp://research.cs.tamu.edu/prism/lectures/pr/pr_l7.pdf •  Tutorial and Java applet for tesSng: –  hkp://parallel.vub.ac.be/research/causalModels/tutorial/kde.html •  Simple interacSve web demo at U. Tartu: –  hkps://courses.cs.ut.ee/demos/kernel-­‐density-­‐esSmaSon/ –  hkp://kde.tume-­‐maailm.pri.ee/ –  Jaak Vilo and other authors UT: Data Mining 2009 37 Jaak Vilo and other authors UT: Data Mining 2009 38 R – example (due K. Tretjakov) d = c(1,2,2,2,2,1,2,2,2,3,2,3,4,5,4,3,2,3,4,4,5,6,7); kernelsmooth <-­‐ funcSon(data, sigma, x) { result = 0; for (d in data) { result = result + exp(-­‐(x-­‐d)^2/2/sigma^2); } result/sqrt(2*pi)/sigma; } x = seq(min(d), max(d), by=0.1); y = sapply(x, funcSon(x) { kernelsmooth(d, 1, x) }); hist(d); lines(x,y); Jaak Vilo and other authors UT: Data Mining 2009 39 hkp://parallel.vub.ac.be/research/causalModels/tutorial/kde.html Jaak Vilo and other authors UT: Data Mining 2009 40 Jaak Vilo and other authors UT: Data Mining 2009 41 Jaak Vilo and other authors UT: Data Mining 2009 42 http://kde.tume-maailm.pri.ee/
Jaak Vilo and other authors UT: Data Mining 2009 43 http://kde.tume-maailm.pri.ee/
Jaak Vilo and other authors UT: Data Mining 2009 44 http://kde.tume-maailm.pri.ee/
Jaak Vilo and other authors UT: Data Mining 2009 45 AggregaSon, analysis and visualizaSon of geodata •  hkp://sightsmap.com •  Several large crowd-­‐sourced datasets: –  The whole Panoramio photobank used by Google maps –  The whole Wikipedia, geotags and wikipedia arScle logs –  Foursquare –  ... More •  Aggregate data, calculate popularites of places, calculate type tags •  Translate and categorize Stles and descripSons to get types •  Improve aggregaSon algorithms by learning •  Visualize heatmaps, type tags, aggregated sources By: Tanel Tammet
By: Tanel Tammet
By: Tanel Tammet
By: Tanel Tammet
By: Tanel Tammet
By: Tanel Tammet
Jaak Vilo and other authors UT: Data Mining 2009 52 •  hkp://176.32.89.45/~hideaki/res/kernel.html Jaak Vilo and other authors UT: Data Mining 2009 53 hkp://jmlr.csail.mit.edu/proceedings/papers/v2/kontkanen07a/kontkanen07a.pdf Jaak Vilo and other authors UT: Data Mining 2009 54 Jaak Vilo and other authors UT: Data Mining 2009 55 Jaak Vilo and other authors UT: Data Mining 2009 56 •  R tutorial –  hkp://cran.r-­‐project.org/doc/manuals/R-­‐
intro.html –  hkp://www.google.com/search?q=R+tutorial Jaak Vilo and other authors UT: Data Mining 2009 57 More links on R and kernel density •  hkp://en.wikipedia.org/wiki/Kernel_density_esSmaSon •  hkp://sekhon.berkeley.edu/stats/html/density.html •  hkp://stat.ethz.ch/R-­‐manual/R-­‐patched/library/stats/html/
density.html •  hkp://www.google.com/search?q=kernel+density+esSmaSon+R Jaak Vilo and other authors UT: Data Mining 2009 58 Jaak Vilo and other authors UT: Data Mining 2009 59 Jaak Vilo and other authors UT: Data Mining 2009 60 Jaak Vilo and other authors UT: Data Mining 2009 61 Jaak Vilo and other authors UT: Data Mining 2009 62 Symmetric vs. Skewed Data
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Median, mean and mode of
symmetric, positively and
negatively skewed data
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Measuring the Dispersion of Data
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Quartiles, outliers and boxplots
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Quartiles: Q1 (25th percentile), Q3 (75th percentile)
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Inter-quartile range: IQR = Q3 – Q1
n  Five
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number summary: min, Q1, M, Q3, max
Boxplot: ends of the box are the quartiles, median is marked, whiskers, and
plot outlier individually
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Outlier: usually, a value higher/lower than 1.5 x IQR
Variance and standard deviation (sample: s, population: σ)
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Variance: (algebraic, scalable computation)
1 n
1 n 2 1 n 2
2
s =
( xi − x ) =
[∑ xi − (∑ xi ) ]
∑
n − 1 i =1
n − 1 i =1
n i =1
2
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1
σ =
N
2
n
1
(
x
−
µ
)
=
∑
i
N
i =1
2
n
2
∑ xi − µ 2
i =1
Standard deviation s (or σ) is the square root of variance s2 (or σ2)
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Boxplot Analysis
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Five-number summary of a distribution:
Minimum, Q1, M, Q3, Maximum
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Boxplot
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Data is represented with a box
The ends of the box are at the first and third
quartiles, i.e., the height of the box is IRQ
The median is marked by a line within the box
Whiskers: two lines outside the box extend to
Minimum and Maximum
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Box Plots •  Tukey77: John W. Tukey, "Exploratory Data Analysis". Addison-­‐Wesley, Reading, MA. 1977. •  hkp://informaSonandvisualizaSon.de/blog/box-­‐plot •  Jaak Vilo and other authors UT: Data Mining 2009 66 Jaak Vilo and other authors UT: Data Mining 2009 67 Jaak Vilo and other authors UT: Data Mining 2009 68 1.5 x IQR – Inter Quartile range
Jaak Vilo and other authors UT: Data Mining 2009 69 Jaak Vilo and other authors UT: Data Mining 2009 70 Visualization of Data Dispersion: Boxplot Analysis
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Violin plot
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Violin plot – R
vertical kernel density
http://gallery.r-enthusiasts.com/graph/Violin_plot,43
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Combining plots…
Properties of Normal Distribution Curve
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The normal (distribution) curve
n  From µ–σ to µ+σ: contains about 68% of the
measurements (µ: mean, σ: standard deviation)
n  From µ–2σ to µ+2σ: contains about 95% of it
n  From µ–3σ to µ+3σ: contains about 99.7% of it
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n 
Example of plots-containing article:
n  http://www.kgs.ku.edu/Magellan/WaterLevels/
CD/Reports/OFR04_57/rep00.htm
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Quantile-Quantile (q-q) Plots
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http://onlinestatbook.com/2/advanced_graphs/q-q_plots.html
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Cumulative Distribution Function (CDF)
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A Q–Q plot comparing the distributions of standardizeddaily maximum
temperatures at 25 stations in the US state of Ohio in March and in July. The
curved pattern suggests that the central quantiles are more closely spaced in
July than in March, and that the March distribution is skewed to the right
compared to the July distribution. The data cover the period 1893–2001.
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Parametric modeling usually involves making
assumptions about the shape of data, or the
shape of residuals from a regression fit. Verifying
such assumptions can take many forms, but an
exploration of the shape using histograms and qq plots is very effective. The q-q plot does not
have any design parameters such as the number
of bins for a histogram.
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Kemmeren et.al. (Mol. Cell, 2002)
Randomized expression data
Yeast 2-hybrid studies
Known (literature) PPI
MPK1 YLR350w
SNF4 YCL046W"
SNF7 YGR122W.
Scatter plot
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Provides a first look at bivariate data to see clusters of
points, outliers, etc
Each pair of values is treated as a pair of coordinates and
plotted as points in the plane
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Not Correlated Data
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Numerical summary?
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Anscombe’s quartet
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Loess Curve
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Adds a smooth curve to a scatter plot in order to
provide better perception of the pattern of dependence
Loess curve is fitted by setting two parameters: a
smoothing parameter, and the degree of the
polynomials that are fitted by the regression
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Graphic Displays of Basic Statistical Descriptions
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Histogram: (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 another
Scatter plot: each pair of values is a pair of coordinates
and plotted as points in the plane
Loess (local regression) curve: add a smooth curve to a
scatter plot to provide better perception of the pattern of
dependence
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Chapter 2: Data Preprocessing
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Why preprocess the data?
n 
Descriptive data summarization
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Data cleaning
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Data integration and transformation
n 
Data reduction
n 
Discretization and concept hierarchy generation
n 
Summary
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Data Cleaning
n 
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Importance
n  “Data cleaning is one of the three biggest problems
in data warehousing”—Ralph Kimball
n  “Data cleaning is the number one problem in data
warehousing”—DCI survey
Data cleaning tasks
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Fill in missing values
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Identify outliers and smooth out noisy data
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Correct inconsistent data
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Resolve redundancy caused by data integration
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Missing Data
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Data is not always available
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Missing data may be due to
n 
equipment malfunction
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inconsistent with other recorded data and thus deleted
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data not entered due to misunderstanding
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E.g., many tuples have no recorded value for several
attributes, such as customer income in sales data
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.
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How to Handle Missing Data?
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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.
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Fill in the missing value manually: tedious + infeasible?
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Fill in it automatically with
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a global constant : e.g., “unknown”, a new class?!
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the attribute mean
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the attribute mean for all samples belonging to the same class:
smarter
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the most probable value: inference-based such
as Bayesian formula or decision tree
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K-NN impute
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K nearest neighbours imputation
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Find K neighbours on available data points
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Estimate the missing value
n 
(Hastie, Tibshirani, Troyanskaya, … Stanford
1999-2001)
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Noisy Data
n 
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Noise: random error or variance in a measured variable
Incorrect attribute values may due to
n  faulty data collection instruments
n  data entry problems
n  data transmission problems
n  technology limitation
n  inconsistency in naming convention
Other data problems which requires data cleaning
n  duplicate records
n  incomplete data
n  inconsistent data
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How to Handle Noisy Data?
n 
n 
n 
n 
Binning
n  first sort data and partition into (equal-frequency) bins
n  then one can smooth by bin means, smooth by bin
median, smooth by bin boundaries, etc.
Regression
n  smooth by fitting the data into regression functions
Clustering
n  detect and remove outliers
Combined computer and human inspection
n  detect suspicious values and check by human (e.g.,
deal with possible outliers)
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Simple Discretization Methods: Binning
n 
Equal-width (distance) partitioning
n 
Divides the range into N intervals of equal size: uniform grid
n 
if A and B are the lowest and highest values of the attribute, the
width of intervals will be: W = (B –A)/N.
n 
n 
The most straightforward, but outliers may dominate presentation
n 
Skewed data is not handled well
Equal-depth (frequency) partitioning
n 
Divides the range into N intervals, each containing approximately
same number of samples
n 
Good data scaling
n 
Managing categorical attributes can be tricky
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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
q 
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Regression
y
Y1
y=x+1
Y1’
X1
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x
106
Cluster Analysis
G1
G3
G2
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Data Cleaning as a Process
n 
n 
n 
Data discrepancy detection
n  Use metadata (e.g., domain, range, dependency, distribution)
n  Check field overloading
n  Check uniqueness rule, consecutive rule and null rule
n  Use commercial tools
n  Data scrubbing: use simple domain knowledge (e.g., postal
code, spell-check) to detect errors and make corrections
n  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
n  Data migration tools: allow transformations to be specified
n  ETL (Extraction/Transformation/Loading) tools: allow users to
specify transformations through a graphical user interface
Integration of the two processes
n  Iterative and interactive (e.g., Potter’s Wheels)
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Chapter 2: Data Preprocessing
n 
Why preprocess the data?
n 
Data cleaning
n 
Data integration and transformation
n 
Data reduction
n 
Discretization and concept hierarchy generation
n 
Summary
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Data Integration
n 
n 
n 
n 
Data integration:
n  Combines data from multiple sources into a coherent
store
Schema integration: e.g., A.cust-id ≡ B.cust-#
n  Integrate metadata from different sources
Entity identification problem:
n  Identify real world entities from multiple data sources,
e.g., Bill Clinton = William Clinton
Detecting and resolving data value conflicts
n  For the same real world entity, attribute values from
different sources are different
n  Possible reasons: different representations, different
scales, e.g., metric vs. British units
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Handling Redundancy in Data Integration
n 
Redundant data occur often when integration of multiple
databases
n 
n 
n 
n 
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
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Normalisation
n 
Making data comparable…
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0,8%
0,6%
0,4%
0,2%
Series1%
Series2%
Series3%
Series4%
0%
0%
20%
40%
60%
80%
100%
120%
!0,2%
!0,4%
!0,6% 9, 2015
March
Data Mining: Concepts and Techniques
114
Elements of microarray statistics
Reference
Test
M
= log2R – log2G
= log2(R/G)
A
= 1/2 (log2R + log2G)
Jaak Vilo and other authors UT: Data Mining 2009 116 Normalisation
can be used to
transform data
Expression Profiler
117
Chapter 2: Data Preprocessing
n 
Why preprocess the data?
n 
Data cleaning
n 
Data integration and transformation
n 
Data reduction
n 
Discretization and concept hierarchy generation
n 
Summary
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Data Reduction Strategies
n 
n 
n 
Why data reduction?
n  A database/data warehouse may store terabytes of data
n  Complex data analysis/mining may take a very long time to run
on the complete data set
Data reduction
n  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
n  Data cube aggregation:
n  Dimensionality reduction — e.g., remove unimportant attributes
n  Data Compression
n  Numerosity reduction — e.g., fit data into models
n  Discretization and concept hierarchy generation
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Chapter 2: Data Preprocessing
n 
Why preprocess the data?
n 
Data cleaning
n 
Data integration and transformation
n 
Data reduction
n 
Discretization and concept hierarchy generation
n 
Summary
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Discretization
n 
Three types of attributes:
n 
Nominal — values from an unordered set, e.g., color, profession
n 
Ordinal — values from an ordered set, e.g., military or academic
rank
n 
n 
Continuous — real numbers, e.g., integer or real numbers
Discretization:
n 
Divide the range of a continuous attribute into intervals
n 
Some classification algorithms only accept categorical attributes.
n 
Reduce data size by discretization
n 
Prepare for further analysis
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Discretization and Concept Hierarchy
n 
Discretization
n 
Reduce the number of values for a given continuous attribute by
dividing the range of the attribute into intervals
n 
n 
Interval labels can then be used to replace actual data values
n 
Supervised vs. unsupervised
n 
Split (top-down) vs. merge (bottom-up)
n 
Discretization can be performed recursively on an attribute
Concept hierarchy formation
n 
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)
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E.g.
n 
n 
n 
n 
0-18 y
19-65 y
66-105
1580
8394
2700
0-20
21-40
41-60
61-105
1780
4200
4767
2900
Vs
n 
n 
n 
n 
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Segmentation by Natural Partitioning
n 
A simply 3-4-5 rule can be used to segment numeric data
into relatively uniform, “natural” intervals.
n 
If an interval covers 3, 6, 7 or 9 distinct values at the
most significant digit, partition the range into 3 equiwidth intervals
n 
If it covers 2, 4, or 8 distinct values at the most
significant digit, partition the range into 4 intervals
n 
If it covers 1, 5, or 10 distinct values at the most
significant digit, partition the range into 5 intervals
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Example of 3-4-5 Rule
count
Step 1:
Step 2:
-$351
-$159
Min
Low (i.e, 5%-tile)
msd=1,000
profit
High(i.e, 95%-0 tile)
Low=-$1,000
(-$1,000 - 0)
(-$400 - 0)
(-$200 -$100)
(-$100 0)
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Max
High=$2,000
($1,000 - $2,000)
(0 -$ 1,000)
(-$400 -$5,000)
Step 4:
(-$300 -$200)
$4,700
(-$1,000 - $2,000)
Step 3:
(-$400 -$300)
$1,838
($1,000 - $2, 000)
(0 - $1,000)
(0 $200)
($1,000 $1,200)
($200 $400)
($1,200 $1,400)
($1,400 $1,600)
($400 $600)
($600 $800)
($800 $1,000)
($1,600 ($1,800 $1,800)
$2,000)
Data Mining: Concepts and Techniques
($2,000 - $5, 000)
($2,000 $3,000)
($3,000 $4,000)
($4,000 $5,000)
125
-351,976.00 .. 4,700,896.50
Example MIN= -351,976.00
MAX=4,700,896.50
LOW = 5th percentile -159,876
HIGH = 95th percentile 1,838,761
msd = 1,000,000 (most significant digit)
LOW = -1,000,000 (round down) HIGH = 2,000,000 (round up)
3 value ranges
1. (-1,000,000 .. 0]
2. (0 .. 1,000,000]
3. (1,000,000 .. 2,000,000]
Adjust with real MIN and MAX
1.
2.
3.
4.
(-400,000 .. 0]
(0 .. 1,000,000]
(1,000,000 .. 2,000,000]
(2,000,000 .. 5,000,000]
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Recursive …
1.1. (-400,000 .. -300,000 ]
1.2. (-300,000 .. -200,000 ]
1.3. (-200,000 .. -100,000 ]
1.4. (-100,000 .. 0 ]
2.1. (0 .. 200,000 ]
2.2. (200,000 .. 400,000 ]
2.3. (400,000 .. 600,000 ]
2.4. (600,000 .. 800,000 ]
2.5. (800,000 .. 1,000,000 ]
3.1. (1,000,000 .. 1,200,000 ]
3.2. (1,200,000 .. 1,400,000 ]
3.3. (1,400,000 .. 1,600,000 ]
3.4. (1,600,000 .. 1,800,000 ]
3.5. (1,800,000 .. 2,000,000 ]
4.1. (2,000,000 .. 3,000,000 ]
4.2. (3,000,000 .. 4,000,000 ]
4.3. (4,000,000 .. 5,000,000 ]
Jaak Vilo and other authors UT: Data Mining 2009 127 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}
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Automatic Concept Hierarchy Generation
n 
Some hierarchies can be automatically generated based
on the analysis of the number of distinct values per
attribute in the data set
n  The attribute with the most distinct values is placed
at the lowest level of the hierarchy
n  Exceptions, e.g., weekday, month, quarter, year
15 distinct values
country
province_or_ state
365 distinct values
city
3567 distinct values
street
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674,339 distinct values
Data Mining: Concepts and Techniques
129
Chapter 2: Data Preprocessing
n 
Why preprocess the data?
n 
Data cleaning
n 
Data integration and transformation
n 
Data reduction
n 
Discretization and concept hierarchy
generation
n 
Summary
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Summary
n 
n 
n 
n 
Data preparation or preprocessing is a big issue for both
data warehousing and data mining
Discriptive data summarization is need for quality data
preprocessing
Data preparation includes
n 
Data cleaning and data integration
n 
Data reduction and feature selection
n 
Discretization
A lot a methods have been developed but data
preprocessing still an active area of research
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References
n 
D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments. Communications
of ACM, 42:73-78, 1999
n 
T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley & Sons, 2003
n 
T. Dasu, T. Johnson, S. Muthukrishnan, V. Shkapenyuk.
Mining Database Structure; Or, How to Build a Data Quality Browser. SIGMOD’02.
n 
H.V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the Technical
Committee on Data Engineering, 20(4), December 1997
n 
D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999
n 
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
n 
V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data Cleaning and
Transformation, VLDB’2001
n 
T. Redman. Data Quality: Management and Technology. Bantam Books, 1992
n 
Y. Wand and R. Wang. Anchoring data quality dimensions ontological foundations. Communications of
ACM, 39:86-95, 1996
n 
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
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