Download Why Data Preprocessing?

Lecture 2: Preprocessing
Techniques for Data Mining
周水庚
2007年3月18日
2007-4-1
Data Mining: Tech. & Appl.
1
Outline
„
Introduction to Data
„
Why preprocess the data?
„
Data cleaning
„
Data integration and transformation
„
Data reduction
„
Discretization and concept hierarchy generation
„
Summary
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Outline
„
Introduction to Data
„
Why preprocess the data?
„
Data cleaning
„
Data integration and transformation
„
Data reduction
„
Discretization and concept hierarchy generation
„
Summary
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What is Data?
„
„
Collection of data objects and
their attributes
Attribute is a property or
characteristic of an object
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Examples: eye color of a person,
temperature, etc.
Attribute is also known as variable,
field, characteristic, feature, or
observation
A collection of attributes
describe an object
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Object is also known as record,
point, case, sample, entity, or
instance
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Attribute Values
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Attribute values are numbers or symbols assigned to
an attribute
Distinction between attributes and attribute values
„ Same attribute can be mapped to different
attribute values
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Example: height can be measured in feet or meters
Different attributes can be mapped to the same set
of values
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Example: Attribute values for ID and age are integers
But properties of attribute values can be different
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– ID has no limit but age has a maximum and minimum value
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Types of Attributes
„
There are different types of attributes
„ Nominal
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Ordinal
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Examples: calendar dates, temperatures in Celsius or
Fahrenheit.
Ratio
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Examples: rankings (e.g., taste of potato chips on a scale
from 1-10), grades, height in {tall, medium, short}
Interval
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Examples: ID numbers, eye color, zip codes
Examples: temperature in Kelvin, length, time, counts
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Properties of Attribute Values
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The type of an attribute depends on which of the
following properties it possess:
„ Distinctness: = ≠
„ Order: < >
„ Addition: + „ Multiplication: * /
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Nominal attribute: distinctness
Ordinal attribute: distinctness & order
Interval attribute: distinctness, order & addition
Ratio attribute: all 4 properties
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Categorical vs. Numerical
„
Collectively, we refer
„ Nominal attribute and ordinal attribute to
categorical or qualitative attribute
„ The other two types of attributes, interval
and ratio attributes to numerical or
quantitative attributes
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Discrete and Continuous Values
„
Discrete Attribute
„
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Has only a finite or countably infinite set of values
Examples: zip codes, counts, or the set of words in a
collection of documents
Often represented as integer variables.
Note: binary attributes are a special case of discrete
attributes
Continuous Attribute
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Has real numbers as attribute values
Examples: temperature, height, or weight.
Practically, real values can be measured and represented
using a finite number of digits.
Continuous attributes are typically represented as
floating-point variables
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Asymmetric Attributes
„
Only presence (a non-zero attribute value) is
regarded as important. Examples:
„ Words present in documents
„ Items present in customer transactions
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Types of Data Sets
„
Common Types
„ Record
„ Graph
„ Ordered
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Record Data
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Data that consists of a collection of records,
each of which consists of a fixed set of
attributes
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Data Matrix
„
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If data objects have the same fixed set of
numeric attributes, then the data objects can
be thought of as points in a multi-dimensional
space, where each dimension represents a
distinct attribute
Such data set can be represented by an m by n
matrix, where there are m rows, one for each
object, and n columns, one for each attribute
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Document Data
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Each document becomes a `term' vector,
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each term is a component (attribute) of the vector,
the value of each component is the number of times
the corresponding term occurs in the document
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Transaction Data
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A special type of record data, where
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each record (transaction) involves a set of items.
For example, consider a grocery store. The set of
products purchased by a customer during one
shopping trip constitute a transaction, while the
individual products that were purchased are the
items
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Graph Data
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Examples: Generic graph and HTML Links
<a href="papers/papers.html#bbbb">
Data Mining </a>
<li>
<a href="papers/papers.html#aaaa">
Graph Partitioning </a>
<li>
<a href="papers/papers.html#aaaa">
Parallel Solution of Sparse Linear System of Equations </a>
<li>
<a href="papers/papers.html#ffff">
N-Body Computation and Dense Linear System Solvers
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Chemical Data
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Benzene Molecule: C6H6
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Ordered Data
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Sequences of transactions
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Ordered Data
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Genomic sequence data
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Ordered Data
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Spatio-Temporal Data
Average monthly temperature of land and ocean
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Outline
„
Introduction to Data
„
Why preprocess the data?
„
Data cleaning
„
Data integration and transformation
„
Data reduction
„
Discretization and concept hierarchy generation
„
Summary
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Why Data Preprocessing?
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Data in the real world is dirty
„ 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
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Why is Data Dirty?
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Incomplete data comes from
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human’s negligence
different consideration between the time when the data was
collected and when it is analyzed
hardware/software problems
Noisy data comes from the process of data
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collection
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entry
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transmission
Inconsistent data comes from
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Different data sources
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Functional dependency violation
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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. —Bill Inmon
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Multi-Dimensional Measure of Data Quality
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A well-accepted multidimensional view:
„ Accuracy
„ Completeness
„ Consistency
„ Timeliness
„ Believability
„ Value added
„ Interpretability
„ Accessibility
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Major Tasks in Data Preprocessing
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Data cleaning (数据清洗)
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Data integration (数据整合)
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Obtains reduced representation in volume but produces the
same or similar analytical results
Data discretization (数据离散化)
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Normalization and aggregation
Data reduction (数据裁减)
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Integration of multiple databases, data cubes, or files
Data transformation (数据转换)
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Fill in missing values, smooth noisy data, identify or remove
outliers, and resolve inconsistencies
Part of data reduction but with particular importance,
especially for numerical data
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Forms of Data Preprocessing
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Outline
2007-4-1
„
Introduction to Data
„
Why preprocess the data?
„
Data cleaning
„
Data integration and transformation
„
Data reduction
„
Discretization and concept hierarchy generation
„
Summary
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Data Cleaning
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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
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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
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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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Incorrect Data
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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
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Duplicate Data
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Data set may include data objects that are
duplicates, or almost duplicates of one another
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Examples:
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Major issue when merging data from heterogeneous
sources
Same person with multiple email addresses
Deduplication
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Process of dealing with duplicate data issues
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Noisy Data
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Noise refers to modification of original values,
or random error or variance in a measured
variable
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Examples: distortion of a person’s voice when
talking on a poor phone and “snow” on television
screen
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Outliers
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Outliers are data objects with characteristics
that are considerably different than most of
the other data objects in the data set
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How to Deal with Outliers?
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Special algorithms are required to effectively
and efficiently detect outliers from large
datasets
Outliers are not noise, although sometime
noise may be regarded as outliers
Outliers are a kind of small patterns hidden in
data. It should be regarded as the counterpart
of clusters
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How to Handle Noisy Data?
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Binning method:
„ first sort data and partition into (equi-depth) bins
„ then one can smooth by bin means, smooth by bin
median, smooth by bin boundaries, etc.
Clustering
„ detect and remove outliers
Combined computer and human inspection
„ detect suspicious values and check by human (e.g.,
deal with possible outliers)
Regression
„ smooth by fitting the data into regression functions
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Simple Discretization Methods: Binning
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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.
„ This is the most straightforward way, 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
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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 (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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Cluster Analysis
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Regression
y
Y1
y=x+1
Y1’
X1
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x
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Outline
„
Introduction to Data
„
Why preprocess the data?
„
Data cleaning
„
Data integration and transformation
„
Data reduction
„
Discretization and concept hierarchy generation
„
Summary
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Data Integration
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Data integration:
„ combines data from multiple sources into a coherent
store
Schema integration
„ integrate metadata from different sources
„ Entity identification problem: identify real world
entities from multiple data sources, e.g., A.cust-id ≡
B.cust-#
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 in Data Integration
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Redundant data occur often when integration of
multiple databases
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The same attribute may have different names in
different databases
One attribute may be a “derived” attribute in
another table, e.g., annual revenue
Redundant data may be able to be detected by correlational 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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Data Transformation
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Smoothing: remove noise from data
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Aggregation: summarization, data cube construction
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Generalization: concept hierarchy climbing
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Normalization: scaled to fall within a small, specified
range
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min-max normalization
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z-score normalization
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normalization by decimal scaling
Attribute/feature construction
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New attributes constructed from the given ones
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Data Transformation: Normalization
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min-max normalization
v − minA
v' =
(new _ maxA − new _ minA) + new _ minA
maxA − minA
„
z-score normalization(Zero-mean normalization)
v − mean A
v'=
stand _ dev
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normalization by decimal scaling
v
v' = j
10
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A
Where j is the smallest integer such that Max(| v ' |)<1
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Outline
„
Introduction to Data
„
Why preprocess the data?
„
Data cleaning
„
Data integration and transformation
„
Data reduction
„
Discretization and concept hierarchy generation
„
Summary
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Data Reduction Strategies
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A 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—remove unimportant
attributes
„ Data Compression
„ Numerosity reduction—fit data into models
„ Discretization and concept hierarchy generation
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Data Aggregation
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Combining two or more attributes (or objects)
into a single attribute (or object)
Purpose
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Data reduction
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Change of scale
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cities aggregated into regions, states, countries,
etc
More “stable” data
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reduce the number of attributes or objects
aggregated data tends to have less variability
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Data Aggregation
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Variation of Precipitation in Australia
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Data Cube Aggregation
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The lowest level of a data cube -- base cuboid
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Further reduce the size of data to deal with
Reference appropriate levels
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e.g., a customer in a phone calling data warehouse.
Multiple levels of aggregation in data cubes
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the aggregated data for an individual entity of
interest
Use the smallest representation which is enough to
solve the task
Queries regarding aggregated information should be
answered using data cube, when possible
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Curse of Dimensionality
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When dimensionality
increases, data
becomes increasingly
sparse in the space
that it occupies
Definitions of density
and distance between
points, which is critical
for clustering and
outlier detection,
become less
meaningful
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Dimensionality Reduction
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Purpose
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Avoid curse of dimensionality
Reduce amount of time and memory required by
data mining algorithms
Allow data to be more easily visualized
May help to eliminate irrelevant features or reduce
noise
Techniques
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Principle Component Analysis
Singular Value Decomposition
Others: supervised and non-linear techniques
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Dimensionality Reduction
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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
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Example of Decision Tree Induction
Initial attribute set:
{A1, A2, A3, A4, A5, A6}
A4 ?
A6?
A1?
Class 1
>
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Class 2
Class 1
Class 2
Reduced attribute set: {A1, A4, A6}
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Data Compression
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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
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Data Compression
Compressed
Data
Original Data
lossless
Original Data
Approximated
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sy
s
lo
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Principal Component Analysis
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Given N data vectors from k-dimensions, find c <= k
orthogonal vectors that can be best used to represent
data
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The original data set is reduced to one consisting of
N data vectors on c principal components (reduced
dimensions)
Each data vector is a linear combination of the c
principal component vectors
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Works for numeric data only
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Used when the number of dimensions is large
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Principal Component Analysis
X2
Y1
Y2
X1
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Numerosity Reduction
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Parametric methods
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Assume the data fits some model, estimate model
parameters, store only the parameters, and
discard the data (except possible outliers)
Log-linear models: obtain value at a point in m-D
space as the product on appropriate marginal
subspaces
Non-parametric methods
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Do not assume models
„
Major families: histograms, clustering, sampling
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Regression and Log-Linear Models
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Linear regression: Data are modeled to fit a straight
line
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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
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Log-linear model: approximates discrete
multidimensional probability distributions
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Regress Analysis and Log-Linear Models
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Linear regression: Y = α + β X
„ Two parameters , α and β 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.
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Probability: p(a, b, c, d) = αab βacχad δbcd
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Histograms
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30
25
20
15
10
5
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100000
90000
80000
70000
60000
50000
0
40000
„
35
30000
„
40
20000
„
A popular data
reduction technique
Divide data into
buckets and store
average (sum) for each
bucket
Can be constructed
optimally in one
dimension using dynamic
programming
Related to quantization
problems.
10000
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Clustering
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Partition data set into clusters, and one can store
cluster representation 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
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There are many choices of clustering definitions and
clustering algorithms, further detailed in Chapter 8
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Sampling
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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
Sampling may not reduce database I/Os (page at a
time).
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Sampling
OR om
W
SRS le rand ut
p
m
i
tho
i
s
(
w
ple
t)
m
n
a
s
e
em
c
a
l
rep
SRSW
R
Raw Data
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Sampling
Raw Data
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Cluster/Stratified Sample
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Hierarchical Reduction
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„
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Use multi-resolution structure with different degrees
of reduction
Hierarchical clustering is often performed but tends to
define partitions of data sets rather than “clusters”
Parametric methods are usually not amenable to
hierarchical representation
Hierarchical aggregation
„ An index tree hierarchically divides a data set into
partitions by value range of some attributes
„ Each partition can be considered as a bucket
„ Thus an index tree with aggregates stored at each
node is a hierarchical histogram
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Outline
„
Introduction to Data
„
Why preprocess the data?
„
Data cleaning
„
Data integration and transformation
„
Data reduction
„
Discretization and concept hierarchy generation
„
Summary
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Discretization
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Three types of attributes:
„ Nominal — values from an unordered set
„ Ordinal — values from an ordered set
„ Continuous — 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
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Discretization and Concept Hierachy
„
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
Concept hierarchies
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reduce the data by collecting and replacing low
level concepts (such as numeric values for the
attribute age) by higher level concepts (such as
young, middle-aged, or senior)
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Discretization and Concept Hierarchy
Generation for Numeric Data
„
Binning (see sections before)
„
Histogram analysis (see sections before)
„
Clustering analysis (see sections before)
„
Entropy-based discretization
„
Segmentation by natural partitioning
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Entropy-Based Discretization
„
Given a set of samples S, if S is partitioned into two
intervals S1 and S2 using boundary T, the entropy
after partitioning is
E (S ,T ) =
„
„
| S 1|
|S|
Ent ( S 1) +
|S 2|
|S|
Ent ( S 2)
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, e.g.,
Ent ( S ) − E (T , S ) > δ
„
Experiments show that it may reduce data size and
improve classification accuracy
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Segmentation by Natural Partitioning
„
A simply 3-4-5 rule can be used to segment
numeric data into relatively uniform, “natural”
intervals
„
„
„
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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
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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
Low=-$1,000
(-$1,000 - 0)
(-$400 - 0)
(-$200 -$100)
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(-$100 0)
Max
High=$2,000
($1,000 - $2,000)
(0 -$ 1,000)
(-$4000 -$5,000)
Step 4:
(-$300 -$200)
High(i.e, 95%-0 tile)
$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: Tech. & Appl.
($2,000 - $5, 000)
($2,000 $3,000)
($3,000 $4,000)
($4,000 $5,000)
75
Concept Hierarchy Generation for
Categorical Data
„
„
„
Specification of a partial ordering of attributes
explicitly at the schema level by users or experts
„ street<city<state<country
Specification of a portion of a hierarchy by explicit
data grouping
„ {Urbana, Champaign, Chicago}<Illinois
Specification of a set of attributes.
„ System automatically generates partial ordering by
analysis of the number of distinct values
E.g., street < city <state < country
Specification of only a partial set of attributes
„ E.g., only street < city, not others
„
„
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Automatic Concept Hierarchy Generation
„
Some concept hierarchies can be automatically
generated based on the analysis of the number of
distinct values per attribute in the given data set
„ The attribute with the most distinct values is
placed at the lowest level of the hierarchy
„ Note: Exception—weekday, month, quarter, year
country
15 distinct values
province_or_ state
65 distinct values
city
3567 distinct values
street
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674,339 distinct values
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Outline
„
Introduction to Data
„
Why preprocess the data?
„
Data cleaning
„
Data integration and transformation
„
Data reduction
„
Discretization and concept hierarchy generation
„
Summary
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Summary
„
Data preparation is a big issue for both warehousing
and mining
„
„
Data preparation includes
„
Data cleaning and data integration
„
Data reduction and feature selection
„
Discretization
A lot a methods have been developed but still an
active area of research
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References
„
„
„
„
„
„
„
„
„
„
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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
D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments.
Communications of ACM, 42:73-78, 1999.
H.V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the
Technical Committee on Data Engineering, 20(4), December 1997.
A. Maydanchik, Challenges of Efficient Data Cleansing (DM Review - Data Quality
resource portal)
D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999.
D. Quass. A Framework for research in Data Cleaning. (Draft 1999)
V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data
Cleaning and Transformation, VLDB’2001.
T. Redman. Data Quality: Management and Technology. Bantam Books, New York, 1992.
Y. Wand and R. Wang. Anchoring data quality dimensions ontological foundations.
Communications of ACM, 39:86-95, 1996.
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.
http://www.cs.ucla.edu/classes/spring01/cs240b/notes/data-integration1.pdf
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Homework
„
„
Read Chapter 3
Finish Exercise 3.3, 3.5, and 3.7
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