UNIT 1_2.ppt

June 16, 2022 Data Mining: Concepts and Techniques 1
Data Preprocessing
 Why preprocess the data?
 Descriptive data summarization
 Data cleaning
 Data integration and transformation
 Data reduction
 Discretization and concept hierarchy generation
 Summary

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

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

Why Is Data Preprocessing Important?
 No quality data, no quality mining results!
 Quality decisions must be based on quality data
 e.g., duplicate or missing data may cause incorrect or even
misleading statistics.
 Data warehouse needs consistent integration of quality
data
 Data extraction, cleaning, and transformation comprises
the majority of the work of building a data warehouse

Multi-Dimensional Measure of Data Quality
 A well-accepted multidimensional view:
 Accuracy
 Completeness
 Consistency
 Timeliness
 Believability
 Value added
 Interpretability
 Accessibility
 Broad categories:
 Intrinsic, contextual, representational, and accessibility

Major Tasks in Data Preprocessing
 Data cleaning
 Fill in missing values, smooth noisy data, identify or remove
outliers, and resolve inconsistencies
 Data integration
 Integration of multiple databases, data cubes, or files
 Data transformation
 Normalization and aggregation
 Data reduction
 Obtains reduced representation in volume but produces the same
or similar analytical results
 Data discretization
 Part of data reduction but with particular importance, especially
for numerical data

Forms of Data Preprocessing

Chapter 2: Data Preprocessing
 Data cleaning
 Data reduction
 Summary

Mining Data Descriptive Characteristics
 Motivation
 To better understand the data: central tendency, variation and
spread
 Data dispersion characteristics
 median, max, min, quantiles, outliers, variance, etc.
 Numerical dimensions correspond to sorted intervals
 Data dispersion: analyzed with multiple granularities of
precision
 Boxplot or quantile analysis on sorted intervals
 Dispersion analysis on computed measures
 Folding measures into numerical dimensions
 Boxplot or quantile analysis on the transformed cube

Measuring the Central Tendency
 Mean (algebraic measure) (sample vs. population):
 Weighted arithmetic mean:
 Trimmed mean: chopping extreme values
 Median: A holistic measure
 Middle value if odd number of values, or average of the middle two
values otherwise
 Estimated by interpolation (for grouped data):
 Mode
 Value that occurs most frequently in the data
 Unimodal, bimodal, trimodal
 Empirical formula:
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Symmetric vs. Skewed Data
 Median, mean and mode of
symmetric, positively and
negatively skewed data

Measuring the Dispersion of Data
 Quartiles, outliers and boxplots
 Quartiles: Q1 (25th percentile), Q3 (75th percentile)
 Inter-quartile range: IQR = Q3 – Q1
 Five number summary: min, Q1, M, Q3, max
 Boxplot: ends of the box are the quartiles, median is marked, whiskers, and
plot outlier individually
 Outlier: usually, a value higher/lower than 1.5 x IQR
 Variance and standard deviation (sample: s, population: σ)
 Variance: (algebraic, scalable computation)
 Standard deviation s (or σ) is the square root of variance s2 (or σ2)
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Properties of Normal Distribution Curve
 The normal (distribution) curve
 From μ–σ to μ+σ: contains about 68% of the
measurements (μ: mean, σ: standard deviation)
 From μ–2σ to μ+2σ: contains about 95% of it
 From μ–3σ to μ+3σ: contains about 99.7% of it

Boxplot Analysis
 Five-number summary of a distribution:
Minimum, Q1, M, Q3, Maximum
 Boxplot
 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

Visualization of Data Dispersion: Boxplot Analysis

Histogram Analysis
 Graph displays of basic statistical class descriptions
 Frequency histograms
 A univariate graphical method
 Consists of a set of rectangles that reflect the counts or
frequencies of the classes present in the given data

Quantile Plot
 Displays all of the data (allowing the user to assess both
the overall behavior and unusual occurrences)
 Plots quantile information
 For 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

Quantile-Quantile (Q-Q) Plot
 Graphs the quantiles of one univariate distribution against
the corresponding quantiles of another
 Allows the user to view whether there is a shift in going
from one distribution to another

Scatter plot
 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

Loess Curve
 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

Positively and Negatively Correlated Data

Not Correlated Data

Graphic Displays of Basic Statistical Descriptions
 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

 Data cleaning
 Data reduction
 Summary

Data Cleaning
 Importance
 “Data cleaning is one of the three biggest problems
in data warehousing”—Ralph Kimball
 “Data cleaning is the number one problem in data
warehousing”—DCI survey
 Data cleaning tasks
 Fill in missing values
 Identify outliers and smooth out noisy data
 Correct inconsistent data
 Resolve redundancy caused by data integration

Missing Data
 Data is not always available
 E.g., many tuples have no recorded value for several
attributes, such as customer income in sales data
 Missing data may be due to
 equipment malfunction
 inconsistent with other recorded data and thus deleted
 data not entered due to misunderstanding
 certain data may not be considered important at the time of
entry
 not register history or changes of the data
 Missing data may need to be inferred.

How to Handle Missing Data?
 Ignore the tuple: usually done when class label is missing (assuming
the tasks in classification—not effective when the percentage of
missing values per attribute varies considerably.
 Fill in the missing value manually: tedious + infeasible?
 Fill in it automatically with
 a global constant : e.g., “unknown”, a new class?!
 the attribute mean
 the attribute mean for all samples belonging to the same class:
smarter
 the most probable value: inference-based such as Bayesian
formula or decision tree

Noisy Data
 Noise: random error or variance in a measured variable
 Incorrect attribute values may due to
 faulty data collection instruments
 data entry problems
 data transmission problems
 technology limitation
 inconsistency in naming convention
 Other data problems which requires data cleaning
 duplicate records
 incomplete data
 inconsistent data

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

Simple Discretization Methods: Binning
 Equal-width (distance) partitioning
 Divides the range into N intervals of equal size: uniform grid
 if A and B are the lowest and highest values of the attribute, the
width of intervals will be: W = (B –A)/N.
 The most straightforward, but outliers may dominate presentation
 Skewed data is not handled well
 Equal-depth (frequency) partitioning
 Divides the range into N intervals, each containing approximately
same number of samples
 Good data scaling
 Managing categorical attributes can be tricky

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

Regression
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Cluster Analysis

Data Cleaning as a Process
 Data discrepancy detection
 Use metadata (e.g., domain, range, dependency, distribution)
 Check field overloading
 Check uniqueness rule, consecutive rule and null rule
 Use commercial tools
 Data scrubbing: use simple domain knowledge (e.g., postal
code, spell-check) to detect errors and make corrections
 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
 Data migration tools: allow transformations to be specified
 ETL (Extraction/Transformation/Loading) tools: allow users to
specify transformations through a graphical user interface
 Integration of the two processes
 Iterative and interactive (e.g., Potter’s Wheels)

 Data cleaning
 Data reduction
 Summary

Data Integration
 Data integration:
 Combines data from multiple sources into a coherent
store
 Schema integration: e.g., A.cust-id  B.cust-#
 Integrate metadata from different sources
 Entity identification problem:
 Identify real world entities from multiple data sources,
e.g., Bill Clinton = William Clinton
 Detecting and resolving data value conflicts
 For the same real world entity, attribute values from
different sources are different
 Possible reasons: different representations, different
scales, e.g., metric vs. British units

Handling Redundancy in Data Integration
 Redundant data occur often when integration of multiple
databases
 Object identification: The same attribute or object
may have different names in different databases
 Derivable data: One attribute may be a “derived”
attribute in another table, e.g., annual revenue
 Redundant attributes may be able to be detected by
correlation analysis
 Careful integration of the data from multiple sources may
help reduce/avoid redundancies and inconsistencies and
improve mining speed and quality

Correlation Analysis (Numerical Data)
 Correlation coefficient (also called Pearson’s product
moment coefficient)
where n is the number of tuples, and are the respective
means of A and B, σA and σB are the respective standard deviation
of A and B, and Σ(AB) is the sum of the AB cross-product.
 If rA,B > 0, A and B are positively correlated (A’s values
increase as B’s). The higher, the stronger correlation.
 rA,B = 0: independent; rA,B < 0: negatively correlated
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Correlation Analysis (Categorical Data)
 Χ2 (chi-square) test
 The larger the Χ2 value, the more likely the variables are
related
 The cells that contribute the most to the Χ2 value are
those whose actual count is very different from the
expected count
 Correlation does not imply causality
 # of hospitals and # of car-theft in a city are correlated
 Both are causally linked to the third variable: population
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Chi-Square Calculation: An Example
 Χ2 (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
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Like science fiction 250(90) 200(360) 450
Not like science fiction 50(210) 1000(840) 1050
Sum(col.) 300 1200 1500

Data Transformation
 Smoothing: remove noise from data
 Aggregation: summarization, data cube construction
 Generalization: concept hierarchy climbing
 Normalization: scaled to fall within a small, specified
range
 min-max normalization
 z-score normalization
 normalization by decimal scaling
 Attribute/feature construction
 New attributes constructed from the given ones

Data Transformation: Normalization
 Min-max normalization: to [new_minA, new_maxA]
 Ex. Let income range $12,000 to $98,000 normalized to [0.0,
1.0]. Then $73,000 is mapped to
 Z-score normalization (μ: mean, σ: standard deviation):
 Ex. Let μ = 54,000, σ = 16,000. Then
 Normalization by decimal scaling
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 Data cleaning
 Data reduction
 Summary

Data Reduction Strategies
 Why data reduction?
 A database/data warehouse may store terabytes of data
 Complex data analysis/mining may take a very long time to run
on the complete data set
 Data reduction
 Obtain a reduced representation of the data set that is much
smaller in volume but yet produce the same (or almost the
same) analytical results
 Data reduction strategies
 Data cube aggregation:
 Dimensionality reduction — e.g., remove unimportant attributes
 Data Compression
 Numerosity reduction — e.g., fit data into models

Data Cube Aggregation
 The lowest level of a data cube (base cuboid)
 The aggregated data for an individual entity of interest
 E.g., a customer in a phone calling data warehouse
 Multiple levels of aggregation in data cubes
 Further reduce the size of data to deal with
 Reference appropriate levels
 Use the smallest representation which is enough to
solve the task
 Queries regarding aggregated information should be
answered using data cube, when possible

Attribute Subset Selection
 Feature selection (i.e., attribute subset selection):
 Select a minimum set of features such that the
probability distribution of different classes given the
values for those features is as close as possible to the
original distribution given the values of all features
 reduce # of patterns in the patterns, easier to
understand
 Heuristic methods (due to exponential # of choices):
 Step-wise forward selection
 Step-wise backward elimination
 Combining forward selection and backward elimination
 Decision-tree induction

Example of Decision Tree Induction
Initial attribute set:
{A1, A2, A3, A4, A5, A6}
A4 ?
A1? A6?
Class 1 Class 2 Class 1 Class 2
> Reduced attribute set: {A1, A4, A6}

Heuristic Feature Selection Methods
 There are 2d possible sub-features of d features
 Several heuristic feature selection methods:
 Best single features under the feature independence
assumption: choose by significance tests
 Best step-wise feature selection:
 The best single-feature is picked first
 Then next best feature condition to the first, ...
 Step-wise feature elimination:
 Repeatedly eliminate the worst feature
 Best combined feature selection and elimination
 Optimal branch and bound:
 Use feature elimination and backtracking

Data Compression
 String compression
 There are extensive theories and well-tuned algorithms
 Typically lossless
 But only limited manipulation is possible without
expansion
 Audio/video compression
 Typically lossy compression, with progressive refinement
 Sometimes small fragments of signal can be
reconstructed without reconstructing the whole
 Time sequence is not audio
 Typically short and vary slowly with time

Data Compression
Original Data Compressed
Data
lossless
Original Data
Approximated

Dimensionality Reduction:
Wavelet Transformation
 Discrete wavelet transform (DWT): linear signal
processing, multi-resolutional analysis
 Compressed approximation: store only a small fraction of
the strongest of the wavelet coefficients
 Similar to discrete Fourier transform (DFT), but better
lossy compression, localized in space
 Method:
 Length, L, must be an integer power of 2 (padding with 0’s, when
necessary)
 Each transform has 2 functions: smoothing, difference
 Applies to pairs of data, resulting in two set of data of length L/2
 Applies two functions recursively, until reaches the desired length
Haar2 Daubechie4

DWT for Image Compression
 Image
Low Pass High Pass
Low Pass High Pass
Low Pass High Pass

 Given N data vectors from n-dimensions, find k ≤ n orthogonal
vectors (principal components) that can be best used to represent data
 Steps
 Normalize input data: Each attribute falls within the same range
 Compute k orthonormal (unit) vectors, i.e., principal components
 Each input data (vector) is a linear combination of the k principal
component vectors
 The principal components are sorted in order of decreasing
“significance” or strength
 Since 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 data
 Works for numeric data only
 Used when the number of dimensions is large
Dimensionality Reduction: Principal
Component Analysis (PCA)

X1
X2
Y1
Y2
Principal Component Analysis

Numerosity Reduction
 Reduce data volume by choosing alternative, smaller
forms of data representation
 Parametric methods
 Assume the data fits some model, estimate model
parameters, store only the parameters, and discard
the data (except possible outliers)
 Example: Log-linear models—obtain value at a point
in m-D space as the product on appropriate marginal
subspaces
 Non-parametric methods
 Do not assume models
 Major families: histograms, clustering, sampling

Data Reduction Method (1):
Regression and Log-Linear Models
 Linear regression: Data are modeled to fit a straight line
 Often uses the least-square method to fit the line
 Multiple regression: allows a response variable Y to be
modeled as a linear function of multidimensional feature
vector
 Log-linear model: approximates discrete
multidimensional probability distributions

 Linear regression: Y = w X + b
 Two regression coefficients, w and b, specify the line
and are to be estimated by using the data at hand
 Using the least squares criterion to the known values
of Y1, Y2, …, X1, X2, ….
 Multiple regression: Y = b0 + b1 X1 + b2 X2.
 Many nonlinear functions can be transformed into the
above
 Log-linear models:
 The multi-way table of joint probabilities is
approximated by a product of lower-order tables
 Probability: p(a, b, c, d) = ab acad bcd
Regress Analysis and Log-Linear Models

Data Reduction Method (2): Histograms
 Divide data into buckets and store
average (sum) for each bucket
 Partitioning rules:
 Equal-width: equal bucket range
 Equal-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 β–1 largest differences
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Data Reduction Method (3): Clustering
 Partition data set into clusters based on similarity, and store cluster
representation (e.g., centroid and diameter) only
 Can be very effective if data is clustered but not if data is “smeared”
 Can have hierarchical clustering and be stored in multi-dimensional
index tree structures
 There are many choices of clustering definitions and clustering
algorithms
 Cluster analysis will be studied in depth in Chapter 7

Data Reduction Method (4): Sampling
 Sampling: obtaining a small sample s to represent the
whole data set N
 Allow a mining algorithm to run in complexity that is
potentially sub-linear to the size of the data
 Choose a representative subset of the data
 Simple random sampling may have very poor
performance in the presence of skew
 Develop adaptive sampling methods
 Stratified sampling:
 Approximate the percentage of each class (or
subpopulation of interest) in the overall database
 Used in conjunction with skewed data
 Note: Sampling may not reduce database I/Os (page at a
time)

Sampling: with or without Replacement
Raw Data

Sampling: Cluster or Stratified Sampling
Raw Data Cluster/Stratified Sample

 Data cleaning
 Data reduction
 Summary

Discretization
 Three types of attributes:
 Nominal — values from an unordered set, e.g., color, profession
 Ordinal — values from an ordered set, e.g., military or academic
rank
 Continuous — real numbers, e.g., integer or real numbers
 Discretization:
 Divide the range of a continuous attribute into intervals
 Some classification algorithms only accept categorical attributes.
 Reduce data size by discretization
 Prepare for further analysis

Discretization and Concept Hierarchy
 Discretization
 Reduce the number of values for a given continuous attribute by
dividing the range of the attribute into intervals
 Interval labels can then be used to replace actual data values
 Supervised vs. unsupervised
 Split (top-down) vs. merge (bottom-up)
 Discretization can be performed recursively on an attribute
 Concept hierarchy formation
 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)

Discretization and Concept Hierarchy
Generation for Numeric Data
 Typical methods: All the methods can be applied recursively
 Binning (covered above)
 Top-down split, unsupervised,
 Histogram analysis (covered above)
 Top-down split, unsupervised
 Clustering analysis (covered above)
 Either top-down split or bottom-up merge, unsupervised
 Entropy-based discretization: supervised, top-down split
 Interval merging by 2 Analysis: unsupervised, bottom-up merge
 Segmentation by natural partitioning: top-down split, unsupervised

Entropy-Based Discretization
 Given 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 S1
 The boundary that minimizes the entropy function over all possible
boundaries is selected as a binary discretization
 The process is recursively applied to partitions obtained until some
stopping criterion is met
 Such a boundary may reduce data size and improve classification
accuracy
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Entropy
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Interval Merge by 2 Analysis
 Merging-based (bottom-up) vs. splitting-based methods
 Merge: Find the best neighboring intervals and merge them to form
larger intervals recursively
 ChiMerge [Kerber AAAI 1992, See also Liu et al. DMKD 2002]
 Initially, each distinct value of a numerical attr. A is considered to be
one interval
 2 tests are performed for every pair of adjacent intervals
 Adjacent intervals with the least 2 values are merged together, since
low 2 values for a pair indicate similar class distributions
 This merge process proceeds recursively until a predefined stopping
criterion is met (such as significance level, max-interval, max
inconsistency, etc.)

Segmentation by Natural Partitioning
 A simply 3-4-5 rule can be used to segment numeric data
into relatively uniform, “natural” intervals.
 If an interval covers 3, 6, 7 or 9 distinct values at the
most significant digit, partition the range into 3 equi-
width intervals
 If it covers 2, 4, or 8 distinct values at the most
significant digit, partition the range into 4 intervals
 If it covers 1, 5, or 10 distinct values at the most
significant digit, partition the range into 5 intervals

Example of 3-4-5 Rule
(-$400 -$5,000)
(-$400 - 0)
(-$400 -
-$300)
(-$300 -
-$200)
(-$200 -
-$100)
(-$100 -
0)
(0 - $1,000)
(0 -
$200)
($200 -
$400)
($400 -
$600)
($600 -
$800) ($800 -
$1,000)
($2,000 - $5, 000)
($2,000 -
$3,000)
($3,000 -
$4,000)
($4,000 -
$5,000)
($1,000 - $2, 000)
($1,000 -
$1,200)
($1,200 -
$1,400)
($1,400 -
$1,600)
($1,600 -
$1,800)
($1,800 -
$2,000)
msd=1,000 Low=-$1,000 High=$2,000
Step 2:
Step 4:
Step 1: -$351 -$159 profit $1,838 $4,700
Min Low (i.e, 5%-tile) High(i.e, 95%-0 tile) Max
count
(-$1,000 - $2,000)
(-$1,000 - 0) (0 -$ 1,000)
Step 3:
($1,000 - $2,000)

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}

Automatic Concept Hierarchy Generation
 Some 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 hierarchy
 Exceptions, e.g., weekday, month, quarter, year
country
province_or_ state
city
street
15 distinct values
365 distinct values
3567 distinct values
674,339 distinct values

UNIT 1_2.ppt

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UNIT 1_2.ppt