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DLZNK464L9 Data Preprocessing

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 Learning Objectives
Upon completion, you will be able to:

● Explain data pre-processing tasks.

● Illustrate methods to handle missing values and noisy data.
● Explain the importance of outlier removal and redundant data removal from datasets.
● List the methods for dimensionality reduction and numerosity reduction .
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● Define data discretization and its methods.
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● Explain data transformation and the importance of normalization.

● Demonstrate typical data pre-processing tasks in Python.

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 Data Quality and Data Format
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 Agenda
In this session, we will discuss:
● Concepts of Data Pre-processing:
○ Data Quality
○ Data Formats
○ Major Tasks in Data Pre-processing
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 Data Quality: Why Preprocess the Data ?
Measures for data quality: A multidimensional view

● Accuracy: proper or incorrect, accurate or not.

● Completeness: not recorded, un-available, missing values, important variables not included

● Consistency: dangling and some features are modified but some features not
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● Interpretability: how easily the data can be understood, codes as variable names, or coded values,

nominal values – semantic ambiguity in the data

● Timeliness: is timely updated?

● Believability: how much data is trustable are as perceived by the end user

● Evaluate all of the above to assess data’s fitness for the task
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 Data Formats: Tidy Data
1. Each variable forms a column.

2. Each observation forms a row.

3. Each type of observational unit forms a table.

Var 1 Var 2 … … Var n
Obs 1
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DLZNK464L9 2.3 34 Yes 123.45 0.3
Obs 2 3.6 23 No 567.34 0.7
Obs n 5.6 56 No 112.7 0.56

● Provides a standard way of structuring a dataset.

● Make it easier to extract needed variables for analysis.

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 Data Formats: Wide Format vs Long Format
● “wide” format: consider variable “Math/English”

Name Math English

Anna 86 90
John 43 75
Cath 80 82
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● “long” format: considered variable “Subject”

Name Subject Grade
Anna Math 86
Anna English 90
John Math 43
John English 75
Cath Math 80
Cath English 82
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 Data Pre-processing: Major Tasks
● Data cleaning
○ Handling missing values, noisy data, resolve inconsistencies and identify or remove the outliers
● Data integration
○ Integration of multiple databases, data cubes, or files
● Data reduction
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○ Dimensionality reduction (PCA)

○ Numerosity reduction
● Data transformation
○ Normalization
○ Data discretization
○ Concept of hierarchy generation
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 Data Pre-processing: Major Tasks

Tasks Methods
Binning, Histogram analysis
Missing values
Regression
Noisy data
Clustering, Classification
Outliers Correlation/covariance
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Redundancy
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PCA, Feature selection
Box plots
Dimensionality reduction
Sampling
Numerosity reduction
Data compression
Data discretization Data Normalization
Scale differences Concept hierarchy

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 Summary
In this session, we discussed:

● Data quality: format, accuracy, completeness, consistency, timeliness, believability, interpretability.

● Tidy data provides a standard way of structuring a dataset.
● Major pre-processing tasks - Data cleaning, data integration, data reduction, and data
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transformation.
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 Tasks and Methods:
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Missing Values and Noisy Data

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 Agenda
In this session, we will discuss:
● Different Tasks and Methods
○ Missing values
○ How to handle missing data?
○ Simple Linear Regression
○ Multiple Linear Regression
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○ Noisy data

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 Missing Values
● Empty cells or cells filled with “NA”-like tokens.
● Semantics of missing data
○ An empty data cell could mean:
■ Value exists
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● Value is available but not recorded due to human error, for example
○ Negative findings are left empty (e.g., negative for asymmetric binary variables)
● Value is not available (e.g., I don’t know my grandpa’s birthday)
■ Value does not exist:
● Absence of a value (I don’t have a middle name)
● Not applicable (I don’t have a tail)
○ Different semantics should be encoded as different values,
NA-not applicable, Missing Sharing –applicable
or but
publishing the contents Rightsnot available,
inReserved.
part or Unauthorized use or etc.
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 How to Handle Missing Data ?
● Ignore the tuples with missing value
○ when the class label is missing (when doing classification)
○ not effective when the percentage of missing information varies greatly per attribute - resulting
in a large number of tuples not being included in analyses.
● Fill in the missing value manually: major feasibility issue
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● Replace empty cells with ‘NA’, “Missing”, etc. More see https://support.datacite.org/docs/schema-
values-unknown-information-v42

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 How to Handle Missing Data ?
● Fill in automatically with (imputation)
○ A global constant: e.g., NA. Not ideal but often done
○ The attribute mean/median/mode
○ The mean/median/mode for all data objects in the same class (smarter)
○ The most probable value: regression or inference-based such as Bayesian inference or decision
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tree: best, but is this problem-free?

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 Simple Linear Regression
● A statistical method that summarizes and studies the relationships between two continuous
(quantitative) variables
○ Independent (predictor) variable: x = height
○ Dependent (response) variable: y = weight
● Goal: find the best straight line that fits the data
○ y = bx +a
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● Method: find a and b that minimize the objective function

● How good is the fit?: coefficient of determination (R Squared,=1 is the best)

Adjusted R Squared
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 Simple Linear Regression
y y = bx + a
250
Residual
200
r = 100 - 150 = -50
Weight (lbs)

150
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r
100 (55, 100)

50

x
10 20 30 40 50 60

Height (inches)

‘r’ here shows a residual, the difference between the true value and the predicted value.
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 Multiple Linear Regression
● Multiple linear regression (more than 1 independent variables, X and beta are vectors).
● Tips on choosing the best model.
○ http://blog.minitab.com/blog/adventures-in-statistics-2/how-to-choose-the-best-regression-
model
● Use for:
○ missing values: use predicted values to replace missing values.
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○ data smoothing: use predicted values to replace original data.

○ data reduction: save only the function, parameters, and outliers (not the original data for the
predicated dimensions).
○ outlier detection: identify (visualize) data that are far away from the predicted values.

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 Noisy Data: Noise
● Noise has two main sources:
○ Implicit inaccuracies caused by measuring devices
○ Random errors caused by human errors or other issues
● Noise can occur in attribute names and attribute values, including class labels

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 Noisy Data: How to Handle Noisy Data ?
● Binning/Histogram analysis
○ First, sort data and partition it into (e.g., equal-frequency) bins.
○ Then smooth by bin means, smooth by bin median, or smooth by bin borders.
● Regression
○ Smooth by fitting data into the regression functions
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● Clustering
○ Smooth data by cluster centres
○ detect and remove outliers/errors

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 Noisy Data: How to Handle Noisy Data ?
● Truncation
○ Truncate the least significant digits in a real number
● Human inspection and Combined computer
○ Detect suspicious values and check by humans
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 Noisy Data: Smooth by Binning
● Divide sorted data into bins.
● Partitioning rules:
○ Equal-width: equal bin range
○ Equal-frequency (or equal-depth): equal # of
data points in the bins
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● For data smoothing/discretization, replace data

with bin mean, median, etc/bin label.
● In effect, it also reduced the number of different
data values (cardinality of the variable)

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 Noisy Data: Equal-width binning
● Equal-width (interval) partitioning
○ Divides the range into N bins of equal intervals.
○ if A is lowest and B is highest values of the attribute,
The width of intervals will be:
W = (B –A)/N.
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○ In practice: Freedman-Diaconis rule works well (more rules)

■ W=2×IQR×n−1/3 . N = (B−A)/W

○ The most straightforward, but outliers may dominate the presentation.

○ Data can’t be handled well if it is skewed

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 Noisy Data: Equal-Depth Binning
● Equal-depth (count, frequency) partitioning
○ Divides the entire range into N bins of equal number of data points.
○ Good data scaling with varied bin width

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 Noisy Data: Example Equal-Depth Binning for Data Smoothing
● Sorted data for the 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
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○ Smoothing by bin boundaries:
■ Bin 1: 4, 4, 4, 15
■ Bin 2: 21, 21, 25, 25
■ Bin 3: 26, 26, 26, 34
○ Smoothing by bin means:
■ Bin 1: 9, 9, 9, 9
■ Bin 2: 23, 23, 23, 23
■ Bin 3: 29, 29, 29, 29
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 Noisy Data: Clustering
● Partition continuous, discrete, or mixed datasets into clusters
based on similarity [distance].
○ There are many choices of distance functions, clustering
definitions, and clustering algorithms
● Can be used to smooth noisy data, detect outliers, numerosity
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reduction, and data discretization.

○ Data smoothing/discretization: take cluster means,
median, etc.
○ Data reduction: store cluster representation only
○ Outlier detection: visualize data points far away

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 Noisy Data: Clustering
● Can be very useful if the data is clustered, but it
cannot be effective if the data is "splattered."
● Can have hierarchical clustering and be stored in
multi-dimensional index tree structures.
● A non-parametric method: no assumption. Let the
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data tell the story.

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 Summary
In this session, we discussed,

● Empty cells or cells filled with “NA”-like tokens are referred to as missing data.
● Noisy Data can be implicit errors introduced by measurement tools, such as different types of
sensors, or random errors.
● There are different ways to handle missing data and noisy data, including various imputation
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methods and data smoothing methods.

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 Tasks and Methods:
Outliers and Data Redundancy
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 Agenda
In this session, we will discuss:
● Tasks and Methods
○ Outliers
○ Data Redundancy

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 Outliers: Outlier Detection
● Exploratory data analysis:
○ Data summary plots – boxplots
○ Histogram analysis
● Regression
○ Data that doesn’t fit the known distribution model are outliers.
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● Clustering
○ Outliers form small and distant clusters or not be included in any cluster.

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 Data Redundancy: Data Integration
● Data integration:
○ Data from multiple sources is combined into a coherent storage.
● Database schema integration
○ Challenging; examining metadata carefully originates from various
sources.
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● Data redundancy, e.g., entity identification problem:

○ Identify real-world entities from a variety of data sources
● Detecting and resolving data value conflicts and scale differences.
○ Attribute values from different sources differ for the same real-world
item.
○ Possible reasons: different representations (e.g., date, GPA), different
scales, e.g., metric vs.Proprietary
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 Data Redundancy: Handling Redundancy in Data Integration
● Redundant attributes may be detected by correlation analysis or covariance analysis.

● Redundant attributes should be removed

● Attributes that are correlated but not redundant should often be kept.

● Careful integration of data from various sources may aid in the reduction/avoidance of redundancies
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and inconsistencies, as well as the improvement of mining speed and quality.

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 Data Redundancy: Correlation Analysis (Nominal Data)
Play chess Not play chess Sum (row)
[c1] [c2]
Like science fiction[r1] 250(90) 200(360) 450 [R=r1]
Not like science fiction 50(210) 1000(840) 1050 [R=r2]
[r2]
Sum(col.)
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300 [C=c1] 1200 [C=c2] 1500 [n]

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 Data Redundancy: Chi-Square Calculation
Play chess Not play chess Sum (row)
Like science fiction 250(90) 200(360) 450

Not like science fiction 50(210) 1000(840) 1050

Sum(col.) 300 1200 1500

● H0: A and B are not correlated. alpha = 0.001

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● Χ2 (chi-square) value calculation

● Using the Χ2 table (next slide), we find the critical value=10.828 for the alpha and d.f.=1
● Χ2 > 10.828, reject H0, so A and B are correlated.
● Most tests will give you a p-value; if p-value < alpha, reject H0.

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 Data Redundancy: Critical Value Table
Critical values of the Chi-square distribution with d
degrees of freedom

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 Data Redundancy: Correlation Analysis (Numeric Data)
● Correlation coefficient (also called Pearson’s product moment coefficient) [-1, 1]

○ Where n is the number of tuples, and are the respective means of A and B,
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○ σA and σB are the respective standard deviation of A and B

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○ Σ(aibi) is the sum of the AB cross-product.

● If rA,B > 0, A and B are positively linearly correlated (A’s values increase as B’s). The higher the value of
rA,B, the stronger the correlation.
● rA,B = 0: not linearly correlated; may still be associated in other ways.
● rAB < 0: negatively linearly correlated

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 Data Redundancy: Visually Evaluating Correlation

Scatter plots showing Pearson

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coefficient from –1 to 1.

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 Data Redundancy: Covariance (Numeric Data)
● Covariance is similar to the correlation.

Contrast: Correlation coefficient:

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○ where n is the number of tuples, are the respective mean or expected values (E) of A
and B, σA and σB are the respective standard deviation of A and B.

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 Data Redundancy: Covariance (Numeric Data)
● Positive covariance: Cov A and B> 0, indicating A and B both tend to be larger than their expected
values.

● Negative covariance: CovA and B < 0, indicating two variables change in different directions: one is
larger and the other one is smaller than their expected values.
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● Independence: CovA and B= 0, but the reverse is not true:
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○ Some random variable pairings may have a covariance of zero but they are not independent. A
covariance of 0 implies independence only under certain additional conditions (for example,
the data have multivariate normal distributions).

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 Data Redundancy: Co-Variance: An Example

● Suppose two stocks A and B have the following values in one week: (2,5), (3, 8), (5, 10), (4,
11), (6, 14).
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● Question: Are the prices of A and B rise or fall together?

● E(A) = (2 + 3 + 5 + 4 + 6)/5 = 20/5 = 4
● E(B) = (5 + 8 + 10 + 11 + 14)/5 = 48/5 = 9.6
● Cov(A,B) = (2x5+3x8+5x10+4x11+6x14)/5 - 4 x 9.6 = 4
Thus, A and B rise together since Cov(A, B) > 0.

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 Summary
In this session, we discussed,

● Outliers can be detected.

● Data redundancy occurs mostly because of data integration, and redundant attributes may be
detected by correlation or covariance analysis.
● Redundant attributes should be removed.
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● Correlated attributes are often useful in mining tasks.

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 Tasks and Methods:
sainathgunda99@gmail.com Dimensionality Reduction and
Numerosity Reduction
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 Agenda
In this session, we will discuss:
● Tasks and Methods
○ Dimensionality reduction
○ Curse of Dimensionality and data sparseness
○ PCA – Principal Component Analysis
○ Numerosity reduction and random sampling methods
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 Data Reduction Strategies
● Data reduction: Obtain a reduced representation of the data set that is much smaller in volume but
yet produces the same (or almost the same) analytical results.

● Why data reduction? — A database/data warehouse may store terabytes of data. Complex data
analysis may take a long time on the complete data set.
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 Data Reduction Strategies
● Data reduction strategies
○ Dimensionality reduction, e.g., removing or merging attributes
■ Principal Components Analysis (PCA).
■ Feature subset selection, feature creation
○ Numerosity reduction (reduce data volume, use smaller forms of data representation)
■ Regression
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■ Histograms/binning, clustering, sampling

■ Data cube aggregation
○ Data compression

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 Dimensionality Reduction: Curse of Dimensionality
● Curse of dimensionality
○ When dimensionality of features in the dataset increases, data becomes increasingly sparse in
feature space.
○ Density and distance between points, which are important for grouping and outlier analysis,
become less relevant.
○ The number of possible subspace combinations will expand exponentially.
● Dimensionality reduction
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○ Avoid the curse of dimensionality by reducing features

○ Dimensionality reduction help in eliminate irrelevant features and reduce noise.
○ Reduces time and space required in data mining.
○ Ease to visualize
● Dimensionality reduction techniques
○ Principal Component Analysis
○ Supervised techniques
○ Nonlinear techniques (e.g., feature selection)
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 Curse of Dimensionality: sparseness

A single feature does not

result in a perfect separation
of our training data
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Adding a third feature

results in a linearly
separable classification
problem in our training data

Adding a second feature still does

not result in a linearly separable
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 Sparseness: More Training Data Needed

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 Sparseness -> Everything is Equal-Distanced

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● With increased dimensionality, the hypersphere occupies only a very small

portion of the search space; all training examples are essentially located in
the corners.
● When dim -> infinity, all training examples are at the same distance from all
other examples.
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 Principal Component Analysis (PCA): Numeric Data
● Finds the projection that captures the most variety in the data.
● The original data can be reflected into a much smaller space, which reduces dimensionality while
keeping variability. We find the eigenvectors (“characteristic” vectors) of the covariance matrix, and
these eigenvectors define the new space.
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 Principal Component Analysis (PCA): Numeric Data

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 Principal Component Analysis (PCA)
• First three PCs capture 75% of original
variance based on loadings.
• Component values are weighted sum of
the original dimensions.
• Comp1 = 0.361*Sepal.Length +
0.867*Petal.Length + 0.358*Petal.Width
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• Subsequent analysis will use reduced

presentation/dimensions

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 Numerosity Reduction
● Reduce the size of data volume by choosing alternative smaller forms of data representation.
● Parametric methods (Example: regression)
○ Consider the data fits some model, estimate model parameters, store only the parameters, and
discard the data (except possible outliers).
● Non-parametric methods
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○ Do not assume parameterized probability distributions.

○ Major families: histograms/binning, clustering, sampling, …

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 Sampling
● Obtaining a small sample “s” to represent the whole data set “N”.

● Also used in sampling training and test examples.

● Allow mining algorithms to run at a complexity that is possibly sub-linear to data size.

● Key principle: choose a representative subset of the data.

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○ In skewed datasets, simple random sampling may perform poorly.

○ Develop adaptive sampling methods, e.g., stratified sampling.

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 Summary
In this session, we discussed,

● Data reduction obtains a reduced representation of the data set that is much smaller in volume but
yet produces the same (or almost the same) analytical results.
● Data reduction can be done by:
○ Dimensionality reduction - It is the process of removing unimportant attributes.
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○ Numerosity reduction - It reduces data volume; uses smaller forms of data representation.
○ Data compression
● Sampling is about obtaining a small sample s to represent the whole data set N.

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 Tasks and Methods:
Data Transformation
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 Agenda
In this session, we will discuss:
● Tasks and Methods
○ Data transformation: Normalization
○ Data discretization methods
○ Concept Hierarchy generation
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 Data Transformation
● Data are transformed or consolidated into forms appropriate for mining.
● Methods
○ Smoothing: Remove noise from data
○ Attribute / feature construction
■ New attributes constructed from the given ones
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○ Aggregation: Data cube construction, summarization

○ Normalization: Scaled to fall within a smaller, specified range for more meaningful comparison
■ min-max normalization
■ z-score normalization
■ normalization by decimal scaling
○ Discretization: Concept hierarchy climbing
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 Normalization
● Min-max normalization: to [new_minA, new_maxA]

○ Ex. Let income range from $12,000 to $98,000 normalized to [0.0,

1.0]. Then $73,600 is mapped to
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● Z-score normalization (μ: mean, σ: standard deviation):

○ Ex. Let μ = 54,000, σ = 16,000. Then

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 Normalization
● Normalization by decimal scaling

○ Ex. (50, 20) -> (0.5, 0.2) with j=2

Where j is the smallest integer such

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 Data Discretization
Discretization: Divide the range of a continuous attribute into intervals.

● Actual data values are replaced with interval labels..

● Reduce attribute cardinality
● Handles outliers and skewed data
● Supervised vs. unsupervised
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● Prepare data for further analysis, e.g., classification.

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 Data Discretization Methods
Typical methods:

All the methods mentioned below can be applied recursively.

● Histogram and Binning analysis

○ Top-down split
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○ Unsupervised

● Clustering analysis (unsupervised, top-down split, or bottom-up merge)

● Classification analysis, e.g., decision-tree (supervised, top-down split)

● Correlation (e.g., χ2) analysis, e.g., ChiMerge (supervised, bottom-up merge)

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 Discretization by Correlation Analysis
Correlation analysis (e.g., Chi-merge: χ2-based discretization)

● Exploit the correlation between intervals and class labels.

● "Interval – Class” contingency tables

● If two adjacent intervals have low χ2 values (less correlated to the class labels), merge them to form
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a larger interval (keeping them separate does not offer more information on how to classify objects).

● Merge performed recursively until a predefined stopping condition is met.

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 Chi-Merge Discretization Example
ChiMerge Discretization
Sample F K

● Statistical approach to Data 1 1 1

Discretization. 2 3 2
3 7 1
● Discretizing the data based on class 4 8 1
labels, using the Chi-square
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5 9 1
approach.
6 11 2
● F:attribute 7 23 1
8 37 1
● K:class label 9 39 2
10 45 1
11 46 2
12 59 1
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 Chi-Merge Discretization Example
ChiMerge Discretization Example Sample F K Intervals
● Sort and arrange the
1 1 1 {0,2}
attributes you want to 2 3 2 {2,5}
group (Example: 3 7 1 {5,7.5}
attribute F). 4 8 1
● Begin by having each {7.5,8.5}
unique value in the
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DLZNK464L9 5 9 1 {8.5,10}
attribute in its own 6 11 2 {10,17}
interval. 7 23 2 {17,30}
8 37 1 {30,38}
9 39 2 {38,42}
10 45 1 {42,45.5}
11 46 1 {45.5,52}
12 59 1 {52,60}
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 Chi-Merge Discretization Example
ChiMerge Discretization Example Sample F K

● Begin calculating the Chi- 1 1 1

square test on every pair 2 3 2
of adjacent intervals 3 7 1

● Interval/class contingency 4 8 1
tables:
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5 9 1
Sample K=1 K=2 6 11 2
2 0 1 1 7 23 2
3 1 0 1
8 37 1
total 1 1 2
9 39 2
Sample K=1 K=2
10 45 1
3 1 0 1
11 46 1
4 1 0 1
total 2 0 2 12 59
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 Chi-Merge Discretization Example
Sampl K=1 K=2 E11 = (1/2)*1 = .05
e E12 = (1/2)*1 = .05
E21 = (1/2)*1 = .05
2 0 1 1
E22 = (1/2)*1 = .05
3 1 0 1
total 1 1 2
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DLZNK464L9 X2 = (0-.5)2/.5 + (0-.5)2/.5 + (0-.5)2/.5 + (0-.5)2/.5 = 2
Sampl K=1 K=2
E11 = (1/2)*2 = 1
e
E12 = (0/2)*2 = 0
3 1 0 1 E21 = (1/2)*2 = 1
4 1 0 1 E22 = (0/2)*2 = 0

total 2 0 2
X2 = (1-1)2/1+(0-0)2/0+ (1-1)2/1+(0-0)2/0 = 0
Sig Level 0.1 with df=1 from Chi square distribution X2 critical value = 2.7024. Not
correlated, can be merged. ProprietarySharing
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 Chi-Merge Discretization Example

Sample F K Intervals Chi2 ● Calculate all the Chi-square

1 1 1 {0,2} values for all intervals.
2
● Merge the intervals with the
2 3 2 {2,5}
2 smallest Chi values.
3 7 1 {5,7.5}
0
4 8 1 {7.5,8}
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5 9 1 {8.5,10}
2
6 11 2 {10,17}
0
7 23 2 {17,30}
2
8 37 1 {30,38}
2
9 39 2 {38,42}
2
10 45 1 {42,45.5}
0
11 46 1 {45.5,52}
0
12 59 1 {52,60}
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 Chi-Merge Discretization Example
Intervals Chi2
Samp F K
1 1 1 {0,2} 2
2 3 2 {2,5}
Repeat.
3 7 1 4
Keep merging intervals with small X2
4 8 1 {5,10} until all X2 > 2.7024
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DLZNK464L9 5 9 1 5
6 11 2
7 23 2 {10,30}
3
8 37 1 {30,38}
2
9 39 2 {38,42}
10 45 1 4
11 46 1 {42,60}
12 59 1
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 Chi-Merge Discretization Example
Sample F K Intervals Chi2
1 1 1
2 3 2 {0,10}
3 7 1
4 8 1 ● End: There are no
more intervals with
5 9 1 2.72
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6 11 2 ● These intervals are

7 23 2 {10,30} correlated with class
8 37 1 labels.
9 39 2
3.93

10 45 1
11 46 1 {42,60}
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 Concept Hierarchy Generation
● Concept hierarchy organises concepts (attribute values) hierarchically and is typically associated with
each dimension in a data warehouse.
● In data warehouses, concept hierarchies enable drilling and rolling to see data at various
granularities.
● Concept hierarchy generation
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○ Specified by domain experts, taxonomies/thesaurus/ ontologies

○ Generated from data sets (for some simple, specific cases)
■ Discretization for numerical or ordinal data
■ Frequency counts for categorical data (limited cases)
○ Concept hierarchy learning
■ Natural language processing and ML approaches.
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 Concept Hierarchy Generation for Nominal 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, Canada} < Illinois
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● 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
● Some hierarchies can be built automatically based on a study of the number of distinct values for
each attribute in the data collection.
○ The attribute with the most distinct values is at the bottom of the hierarchy.
○ Exceptions,
Example: weekday, month, quarter, year
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country 15 distinct values

province_or_ state 365 distinct values

city 3567 distinct values

street 674,339 distinct values

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 Summary
In this session, we discussed:

● Normalization – The data is scaled to fall within a smaller, specified range for more meaningful
comparison.
● Discretization divides the range of a continuous attribute into the interval.
● Chi-Merge Discretization example
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● Concept hierarchy organizes concepts (i.e., attribute values) hierarchically and is usually associated
with each dimension in a data warehouse.
● Concept hierarchy generation for nominal data

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 Learning Outcomes
You should now be able to:

● Apply data pre-processing tasks and methods to prepare data for a data mining task.
● Summarize the importance of outlier removal and redundant data removal from data sets.
● Explain the methods for dimensionality reduction and numerosity reduction.
● Implement data transformation strategies, such as normalization, discretization, and concept
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hierarchy generation.
● Perform typical data pre-processing tasks in Python.

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sainathgunda99@gmail.com
DLZNK464L9 Thank you !

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