Data mining Basics and complete description

What is Data?
• Collection of data objects and their
attributes
• An attribute is a property or
characteristic of an object
– Examples: eye color of a person,
temperature, etc.
– Attribute is also known as variable,
field, characteristic, or feature
• A collection of attributes describe an
object
– Object is also known as record, point,
case, sample, entity, or instance
Tid Refund Marital
Status
Taxable
Income Cheat
1 Yes Single 125K No
2 No Married 100K No
3 No Single 70K No
4 Yes Married 120K No
5 No Divorced 95K Yes
6 No Married 60K No
7 Yes Divorced 220K No
8 No Single 85K Yes
9 No Married 75K No
10 No Single 90K Yes
10
Attributes
Objects

Attribute Values
• 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
• Example: height can be measured in feet or meters
– Different attributes can be mapped to the same set of
values
• Example: Attribute values for ID and age are integers
• But properties of attribute values can be different
– ID has no limit but age has a maximum and minimum value

Measurement of Length
• The way you measure an attribute is somewhat may not match the attributes
properties.
1
2
3
5
5
7
8
15
10 4
A
B
C
D
E

Types of Attributes
• There are different types of attributes
– Nominal
• Examples: ID numbers, eye color, zip codes
– Ordinal
• Examples: rankings (e.g., taste of potato chips on a scale from 1-
10), grades, height in {tall, medium, short}
– Interval
• Examples: calendar dates, temperatures in Celsius or Fahrenheit.
– Ratio
• Examples: temperature in Kelvin, length, time, counts

Properties of Attribute Values
• The type of an attribute depends on which of the
following properties it possesses:
– Distinctness: = 
– Order: < >
– Addition: + -
– Multiplication: * /
– Nominal attribute: distinctness
– Ordinal attribute: distinctness & order
– Interval attribute: distinctness, order & addition
– Ratio attribute: all 4 properties

Attribute Type Description Examples Operations
Nominal The values of a nominal attribute
are just different names, i.e.,
nominal attributes provide only
enough information to distinguish
one object from another. (=, )
zip codes, employee
ID numbers, eye
color, gender: {male,
female}
mode, entropy,
contingency
correlation, 2 test
Ordinal The values of an ordinal attribute
provide enough information to order
objects. (<, >)
hardness of minerals,
{good, better, best},
grades, street
numbers
median,
percentiles, rank
correlation, run
tests, sign tests
Interval For interval attributes, the
differences between values are
meaningful, i.e., a unit of
measurement exists.
(+, - )
calendar dates,
temperature in Celsius
or Fahrenheit
mean, standard
deviation,
Pearson's
correlation, t and F
tests
Ratio For ratio variables, both differences
and ratios are meaningful. (*, /)
temperature in Kelvin,
monetary quantities,
counts, age, mass,
length, electrical
current
geometric mean,
harmonic mean,
percent variation

Attribute
Level
Transformation Comments
Nominal Any permutation of values If all employee ID numbers
were reassigned, would it
make any difference?
Ordinal An order preserving change of values,
i.e.,
new_value = f(old_value)
where f is a monotonic function.
An attribute encompassing the
notion of good, better best can
be represented equally well by
the values {1, 2, 3} or by { 0.5,
1, 10}.
Interval new_value =a * old_value + b where a
and b are constants
Thus, the Fahrenheit and
Celsius temperature scales
differ in terms of where their
zero value is and the size of a
unit (degree).
Ratio new_value = a * old_value Length can be measured in
meters or feet.

Discrete and Continuous Attributes
• Discrete Attribute
– 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
– Has real numbers as attribute values
– Examples: temperature, height, or weight.
– Practically, real values can only be measured and represented using a finite number
of digits.
– Continuous attributes are typically represented as floating-point variables.

• Dimensionality
– The dimensionality of a data set is the number of
attributes that the objects in the data set possess.
– Data with a small number of dimensions tends to be
qualitatively different than moderate or high-
dimensional data.
– The difficulties associated with analyzing high-
dimensional data are sometimes referred to as the
curse of dimensionality.
– Because of this, an important motivation in
preprocessing the data is dimensionality reduction.
Important Characteristics of Structured Data

• Sparsity
– For some data sets, such as those with asymmetric
features, most attributes of an object have values of 0; in
many cases, fewer than 1% of the entries are non-zero.
– In a database, sparsity and density describe the number
of cells in a table that are empty (sparsity) and that
contain information (density), though sparse cells are not
always technically empty—they often contain a “0” digit.
– Sparsity is an advantage because usually only the non-
zero values need to be stored and manipulated.

• Resolution
– It is frequently possible to obtain data at different levels of resolution;
and often the properties of the data are different at different resolution.
– For instance, the surface of the Earth seems very uneven at a
resolution of a few meters, but is relatively smooth at a resolution of
tens of kilometers.
– The patterns in the data also depend on the level of resolution,
• if the resolution is too fine, a pattern may not be visible or may be buried in noise;
• if the resolution is too coarse, the pattern may disappear.
– For example, variations in atmospheric pressure on a scale of hours
reflect the movement of storms and other weather systems, whereas,
on a scale of months, such phenomena are not detectable.

• Record
– Data Matrix
– Document Data
– Transaction Data
• Graph
– World Wide Web
– Molecular Structures
• Ordered
– Spatial Data
– Temporal Data
– Sequential Data
– Genetic Sequence Data
Types of Data Sets

Record Data
• Data that consists of a collection of records, each of
which consists of a fixed set of attributes
Tid Refund Marital
Status
Taxable
Income Cheat
1 Yes Single 125K No
2 No Married 100K No
3 No Single 70K No
4 Yes Married 120K No
5 No Divorced 95K Yes
6 No Married 60K No
7 Yes Divorced 220K No
8 No Single 85K Yes
9 No Married 75K No
10 No Single 90K Yes
10

Data Matrix
• 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
• A variation of record data, but because it consists of numeric attributes,
standard matrix operation can be applied to transform and manipulate the
data.
• Therefore, it is the standard format for most statistical data.
1.12.216.226.2512.65
1.22.715.225.2710.23
ThicknessLoadDistanceProjection
of y load
Projection
of x Load
1.12.216.226.2512.65
1.22.715.225.2710.23
ThicknessLoadDistanceProjection
of y load
Projection
of x Load

Document Data
• Each document becomes a `term' vector,
– 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.
Document 1
season
timeout
lost
wi
n
game
score
ball
pla
y
coach
team
Document 2
Document 3
3 0 5 0 2 6 0 2 0 2
0
0
7 0 2 1 0 0 3 0 0
1 0 0 1 2 2 0 3 0

Transaction Data
• A special type of record data, where
– 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.
TID Items
1 Bread, Coke, Milk
2 Beer, Bread
3 Beer, Coke, Diaper, Milk
4 Beer, Bread, Diaper, Milk
5 Coke, Diaper, Milk

Graph Data
• Examples: Generic graph and HTML Links
5
2
1
2
5
<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

Chemical Data
• Benzene Molecule: C6H6

Ordered Data
• Sequences of transactions
An element of the
sequence
Items/Events

Ordered Data
• Genomic sequence data
GGTTCCGCCTTCAGCCCCGCGCC
CGCAGGGCCCGCCCCGCGCCGTC
GAGAAGGGCCCGCCTGGCGGGCG
GGGGGAGGCGGGGCCGCCCGAGC
CCAACCGAGTCCGACCAGGTGCC
CCCTCTGCTCGGCCTAGACCTGA
GCTCATTAGGCGGCAGCGGACAG
GCCAAGTAGAACACGCGAAGCGC
TGGGCTGCCTGCTGCGACCAGGG

• Spatio-Temporal Data
Average Monthly
Temperature of land
and ocean
Ordered Data

Data Quality
• What kinds of data quality problems?
• How can we detect problems with the data?
• What can we do about these problems?
• Examples of data quality problems:
– Noise and outliers
– missing values
– duplicate data

Noise
• Noise refers to modification of original values
– Examples: distortion of a person’s voice when talking on a poor phone and “snow” on television
screen
• Techniques from signal/image processing are used to reduce noise.
Two Sine Waves Two Sine Waves + Noise

Outliers
• Outliers are data objects with characteristics that are
considerably different than most of the other data
objects in the data set; or
• Values of an attribute that are unusual with respect to
the typical values for that attribute

Missing Values
• Reasons for missing values
– Information is not collected
(e.g., people decline to give their age and weight)
– Attributes may not be applicable to all cases
(e.g., annual income is not applicable to children)
• Handling missing values
– Eliminate Data Objects
– Estimate Missing Values
– Ignore the Missing Value During Analysis
– Replace with all possible values (weighted by their
probabilities)

Duplicate Data
• Data set may include data objects that are duplicates, or
almost duplicates of one another
– Major issue when merging data from heterogeous sources
• Examples:
– Same person with multiple email addresses
• Data cleaning
– Process of dealing with duplicate data issues

Data Preprocessing
• Aggregation
• Sampling
• Dimensionality Reduction
• Feature subset selection
• Feature creation
• Discretization and Binarization
• Attribute Transformation

Aggregation
• Combining two or more attributes (or objects) into a
single attribute (or object)
• Purpose
– Data reduction
• Reduce the number of attributes or objects
– Change of scale
• Cities aggregated into regions, states, countries, etc
– More “stable” data
• Aggregated data tends to have less variability

Aggregation
Standard Deviation of
Average Monthly
Precipitation
Standard Deviation of
Average Yearly Precipitation
Variation of Precipitation in Australia from 1982 to 1993

Sampling
• Sampling is the main technique employed for data
selection.
• It is often used for both the preliminary investigation of the
data and the final data analysis.
• Statisticians sample because obtaining the entire set of data
of interest is too expensive or time consuming.
• Sampling is used in data mining because processing the
entire set of data of interest is too expensive or time
consuming.
• In some cases, using a sampling algorithm can reduce the
data size to the point where a better, but more expensive
algorithm can be used.

Sampling …
• The key principle for effective sampling is the following:
– using a sample will work almost as well as using the entire
data sets, if the sample is representative
– A sample is representative if it has approximately the same
property (of interest) as the original set of data
• Sampling is a statistical process, the representativeness
of any particular sample will vary, and the best that we
can do is choose a sampling scheme that guarantees
a high probability of getting a representative sample.

Types of Sampling
• Simple Random Sampling
– There is an equal probability of selecting any particular item
1. Sampling without replacement
• As each item is selected, it is removed from the population
2. Sampling with replacement
• Objects are not removed from the population as they are selected for the sample.
– In sampling with replacement, the same object can be picked up more than once
• Stratified sampling
– Split the data into several partitions; then draw random
samples from each partition

8000 points 2000 Points 500 Points
Sample Size

• What sample size is necessary to get at least
one object from each of 10 groups.
Sample Size

• 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
• Randomly generate 500 points
• Compute difference between max and min
distance between any pair of points
Curse of Dimensionality

Dimensionality Reduction
• Techniques to reduce the dimensionality of a data set by
creating new attributes that are a combination of the old
attributes
• Purpose:
– Avoid curse of dimensionality
– Reduce amount of time and memory required by data mining
algorithms
– Lead to a more understandable model
– Allow data to be more easily visualized
– May help to eliminate irrelevant features or reduce noise
• Techniques
– Principle Component Analysis
– Singular Value Decomposition
– Others: supervised and non-linear techniques

Dimensionality Reduction: PCA
• Most common approach for dimensionality reduction
• PCA is a linear algebra technique for continuous
attributes that find new attributes (principal components)
that are linear combination of the original attributes
• Goal is to find a projection that captures the largest
amount of variation in data

Feature Subset Selection
• Another way to reduce dimensionality of data to use only a
subset of the features
• Redundant features
– duplicate much or all of the information contained in one or more
other attributes
– Example: purchase price of a product and the amount of sales tax
paid
• Irrelevant features
– contain no information that is useful for the data mining task at
hand
– Example: students' ID is often irrelevant to the task of predicting
students' GPA

Feature Subset Selection
• Techniques:
– Brute-force approch:
• Try all possible feature subsets as input to data mining algorithm
– Embedded approaches:
• Feature selection occurs naturally as part of the data mining
algorithm
– Filter approaches:
• Features are selected before data mining algorithm is run
– Wrapper approaches:
• Use the data mining algorithm as a black box to find best subset
of attributes

Feature Subset Selection - Process
41

Feature Creation
• Create new attributes that can capture the important
information in a data set much more efficiently than the
original attributes
• Three general methodologies:
– Feature Extraction
• domain-specific
– Mapping Data to New Space
– Feature Construction
• combining features

Feature Extraction
• The creation of a new set of features from the original
raw data is known as feature extraction.
– For example: a set of photographs, where each photograph
is to be classified according to whether or not it contains
human face. The raw data is a set of pixels and is not
suitable for many types of classification algorithms.
– However, if the data is processed to provide higher level
features, such as the presence or absence of certain types of
edges and areas that are highly correlated with the presence
of human faces, then a much broader set of classification
techniques can be applied to this problem.
43

Two Sine Waves Two Sine Waves + Noise Frequency
 Fourier transform
 Wavelet transform
Mapping Data to a New Space

Data mining Basics and complete description

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