1.6.data preprocessing
Transcript of 1.6.data preprocessing
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Data Preprocessing
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Introduction
Real World databases Huge size Noisy, Missing and Inconsistent
Data Preprocessing Data Cleaning Data Integration Data Transformation Data Reduction
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Need for Data Preprocessing
Incomplete Data Lacking certain attributes of interest May not have been considered important during data entry Equipment Malfunctioning Deleted due to clashes with other data Only aggregate data maybe present
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Need for Data Preprocessing
Noisy data Incorrect attribute values Errors or outliers e.g., Salary=“-10” Data collection instruments – faulty Data entry errors Transmission errors – limited buffer size
Inconsistent Containing discrepancies in codes or names e.g., Age=“42”
Birthdate=“03/07/1997” Different data sources Functional dependency violation (e.g., modify some linked
data) Duplicate records also need data cleaning
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Need for Data Preprocessing
Quality data 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
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Major Tasks in Data Preprocessing
Data cleaning Fill in missing values Smooth noisy data Identify or remove outliers Resolve inconsistencies
Data integration Integration of multiple databases, data cubes, or files Attributes may have different names Eliminating redundancies
Some attributes can be inferred from others
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Major Tasks in Data Preprocessing
Data transformation Normalization and aggregation
Data reduction Obtains reduced representation in volume but produces the same or
similar analytical results Data Aggregation Dimension Reduction Data Compression Numerosity Reduction Generalization
Data discretization Part of data reduction but with particular importance, especially for
numerical data
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Forms of Data Preprocessing
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Data Cleaning
Importance “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
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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 need to be inferred.
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Handling Missing Data
Ignore the tuple
Usually done when class label is missing (assuming the task is
classification)—not effective when the percentage of missing
values per attribute varies considerably.
Fill in the missing value manually
Tedious + infeasible
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Handling Missing Data
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
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Noisy Data Noise: random error or variance in a measured
variable Binning
first sort data and partition into 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)
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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 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
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Binning 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
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Regression
x
y
y = x + 1
X1
Y1
Y1’
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Cluster Analysis
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Human Inspection
Combined Computer and Human Inspection Outliers in Handwritten character recognition
Surprise value Garbage / Outliers Human identification
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Inconsistent Data
Data discrepancy detection Use metadata (e.g., domain, range, dependency)
Check Functional dependency relationships
Use commercial tools Data scrubbing: use simple domain knowledge 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) Discrepancy detection and transformation
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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
Other Issues Detecting redundancy (tuple level and attribute level) 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
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Handling Redundancy
Redundant data occur often during 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 detected by correlation analysis Careful integration - helps to reduce/avoid redundancies and
inconsistencies and improve mining speed and quality
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Correlation Analysis
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
If rA,B > 0, A and B are positively correlated (A’s values increase
as B’s). The higher the value, the stronger the correlation.
rA,B = 0: independent; rA,B < 0: negatively correlated
BAn
BBAAr BA σσ)1(
))((, −
−−= ∑
A B
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Correlation Analysis Chi-square test
χ2 = ∑ i=1
c ∑ j=1
r (oij – eij)2 / eij
c – Number of possibilities for attribute 1; r – for attribute 2
eij = Expected Frequency : count(A=ai) x count(B=bj) / N
o – Observed Frequency
e – Expected Frequency
Compare χ2 value with table and decide
(r-1) x (c-1) : degrees of freedom
Chi-square test
Male Female Total
Fiction 250 (90) 200 (360) 450
Non-fiction 50 (210) 1000 (840) 1050
Total 300 1200 1500
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χ2 = (250-90)2/90 + (200-360)2/360 + (50-210)2/210 + (1000-840)2/840 = 507.93
Hypothesis: Gender and preferred reading are independent507.83 > 10.83
So hypothesis is rejectedConclusion: Gender and preferred_reading are strongly correlated
Chi-square test
Degrees of freedom (df)
χ2 value
1 0.004 0.02 0.06 0.15 0.46 1.07 1.64 2.71 3.84 6.64 10.83
2 0.10 0.21 0.45 0.71 1.39 2.41 3.22 4.60 5.99 9.21 13.82
3 0.35 0.58 1.01 1.42 2.37 3.66 4.64 6.25 7.82 11.34 16.27
4 0.71 1.06 1.65 2.20 3.36 4.88 5.99 7.78 9.49 13.28 18.47
5 1.14 1.61 2.34 3.00 4.35 6.06 7.29 9.24 11.07 15.09 20.52
6 1.63 2.20 3.07 3.83 5.35 7.23 8.56 10.64 12.59 16.81 22.46
7 2.17 2.83 3.82 4.67 6.35 8.38 9.80 12.02 14.07 18.48 24.32
8 2.73 3.49 4.59 5.53 7.34 9.52 11.03 13.36 15.51 20.09 26.12
9 3.32 4.17 5.38 6.39 8.34 10.66 12.24 14.68 16.92 21.67 27.88
10 3.94 4.86 6.18 7.27 9.34 11.78 13.44 15.99 18.31 23.21 29.59
P value (Probability) 0.95 0.90 0.80 0.70 0.50 0.30 0.20 0.10 0.05 0.01 0.001
Non-significant Significant
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Data Transformation
1. Smoothing: remove noise from data – Binning, Clustering, Regression
2. Normalization: scaled to fall within a small, specified range min-max normalization z-score normalization normalization by decimal scaling
1. Attribute/feature construction New attributes constructed from the given ones
1. Aggregation: summarization, data cube construction
2. Generalization: concept hierarchy climbing
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1. Smoothing
Binning
Equal-width (distance) partitioning
Equal-depth (frequency) partitioning
Clustering
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1. SmoothingRegression 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 multidimensional probability
distributions
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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: Approximation of joint probabilities Estimate the probability of each point in a multi-dimensional space from a
smaller subset of dimensions
1. SmoothingRegression and Log-Linear Models
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2. 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 $73,600 is mapped to
Z-score normalization (μ: mean, σ: standard deviation)
Ex. Let μ = 54,000, σ = 16,000. Then for 73600
Normalization by decimal scaling
716.00)00.1(000,12000,98
000,12600,73 =+−−−
AAA
AA
A
minnewminnewmaxnewminmax
minvv _)__(' +−
−−=
A
Avv
σµ−='
j
vv
10'= Where j is the smallest integer such that Max(|ν’|) < 1
225.1000,16
000,54600,73 =−
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3. Attribute Construction
New attributes are constructed from given attributes To improve accuracy and understanding of structure Area from height and width Product operator and ‘and’
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4. Aggregation
Data Cubes Store Multi-dimensional aggregated information Each cell holds an aggregate data value Concept hierarchies – allow analysis at multiple
levels Provide fast access to pre-computed summarized
data
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A Sample 3D Data CubeTotal annual salesof TV in U.S.A.Date
Produ
ct
Cou
ntr
ysum
sum TV
VCRPC
1Qtr 2Qtr 3Qtr 4Qtr
U.S.A
Canada
Mexico
sum
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4. Aggregation Data Cube Aggregation
The lowest level of abstraction
Base Cuboid
Highest level of abstraction
Apex Cuboid
Multiple levels
Lattice of Cuboids
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Cube: A Lattice of Cuboids
time,item
time,item,location
time, item, location, supplier
all
time item location supplier
time,location
time,supplier
item,location
item,supplier
location,supplier
time,item,supplier
time,location,supplier
item,location,supplier
0-D(apex) cuboid
1-D cuboids
2-D cuboids
3-D cuboids
4-D(base) cuboid
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5. Generalization - Concept hierarchy
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) Detail lost but more meaningful Mining becomes easier Several concept hierarchies can be defined for the
same attribute