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Chapter DM:I (continued) I. Introduction ❑ Data Mining Overview ❑ On Data DM:I-17 Introduction © STEIN 2005-2020
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Chapter DM:I (continued)
I. Introductionq Data Mining Overviewq On Data
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On Data [Tan et al. 2005]
q An object o ∈ O is described by a set of attributes.An object is also known as record, point, case, sample, entity, or instance.
q An attribute A is a property of an object.An attribute is also known as variable, field, characteristic, or feature.
q A measurement scale is a system (often a convention) of assigninga numerical or symbolic value to an attribute of an object.
Attributes
Objects
ID Check Status Income Risk
1 + single 125 000 No
2 - married 100 000 No
3 - single 70 000 No
4 + married 120 000 No
5 - divorced 95 000 Yes
6 - married 60 000 No
7 + divorced 220 000 No
8 - single 85 000 Yes
9 - married 75 000 No
10 - single 90 000 Yes
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On Data [Tan et al. 2005]
q An object o ∈ O is described by a set of attributes.An object is also known as record, point, case, sample, entity, or instance.
q An attribute A is a property of an object.An attribute is also known as variable, field, characteristic, or feature.
q A measurement scale is a system (often a convention) of assigninga numerical or symbolic value to an attribute of an object.
Attributes
Objects
ID Check Status Income Risk
1 + single 125 000 No
2 - married 100 000 No
3 - single 70 000 No
4 + married 120 000 No
5 - divorced 95 000 Yes
6 - married 60 000 No
7 + divorced 220 000 No
8 - single 85 000 Yes
9 - married 75 000 No
10 - single 90 000 Yes
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On Data [Tan et al. 2005]
q An object o ∈ O is described by a set of attributes.An object is also known as record, point, case, sample, entity, or instance.
q An attribute A is a property of an object.An attribute is also known as variable, field, characteristic, or feature.
q A measurement scale is a system (often a convention) of assigninga numerical or symbolic value to an attribute of an object.
Attributes
Objects
ID Check Status Income Risk
1 + single 125 000 No
2 - married 100 000 No
3 - single 70 000 No
4 + married 120 000 No
5 - divorced 95 000 Yes
6 - married 60 000 No
7 + divorced 220 000 No
8 - single 85 000 Yes
9 - married 75 000 No
10 - single 90 000 Yes
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On Data [Tan et al. 2005]
q Attribute values may vary from one object to another or one time to another.
q The same attribute can be mapped to different attribute values.Example: height can be measured in feet or meters.
q Different attributes can be mapped to the same set of values.Example: attribute values for person ID and age are integers.
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On Data [Tan et al. 2005]
q Attribute values may vary from one object to another or one time to another.
q The same attribute can be mapped to different attribute values.Example: height can be measured in feet or meters.
q Different attributes can be mapped to the same set of values.Example: attribute values for person ID and age are integers.
The way an attribute is measured may not match the attribute’s properties:
1
10
8
7
3
1
5
4
3
2
Measuringlengths
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On Data [Tan et al. 2005]
Types of Attributes
Type Comparison Statistics Examples
categorical nominal(qualitative)
values are names,only information todistinguish objects
= 6=
mode, entropy,contingency,correlation, χ2 test
zip codes,employee IDs,eye color,gender: {male, female}
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On Data [Tan et al. 2005]
Types of Attributes
Type Comparison Statistics Examples
categorical nominal(qualitative)
values are names,only information todistinguish objects
= 6=
mode, entropy,contingency,correlation, χ2 test
zip codes,employee IDs,eye color,gender: {male, female}
ordinal enough information toorder objects
< > ≤ ≥
median, percentiles,rank correlation,run tests, sign tests
hardness of minerals,grades, street numbers,quality: {good, better,best}
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On Data [Tan et al. 2005]
Types of Attributes
Type Comparison Statistics Examples
categorical nominal(qualitative)
values are names,only information todistinguish objects
= 6=
mode, entropy,contingency,correlation, χ2 test
zip codes,employee IDs,eye color,gender: {male, female}
ordinal enough information toorder objects
< > ≤ ≥
median, percentiles,rank correlation,run tests, sign tests
hardness of minerals,grades, street numbers,quality: {good, better,best}
numeric interval(quantitative)
differences aremeaningful, a unit ofmeasurement exists
+ −
mean,standard deviation,Pearson’s correlation,t-test, F -test
calendar dates,temperature in Celsius,temperature inFahrenheit
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On Data [Tan et al. 2005]
Types of Attributes
Type Comparison Statistics Examples
categorical nominal(qualitative)
values are names,only information todistinguish objects
= 6=
mode, entropy,contingency,correlation, χ2 test
zip codes,employee IDs,eye color,gender: {male, female}
ordinal enough information toorder objects
< > ≤ ≥
median, percentiles,rank correlation,run tests, sign tests
hardness of minerals,grades, street numbers,quality: {good, better,best}
numeric interval(quantitative)
differences aremeaningful, a unit ofmeasurement exists
+ −
mean,standard deviation,Pearson’s correlation,t-test, F -test
calendar dates,temperature in Celsius,temperature inFahrenheit
ratio differences and ratiosare meaningful
∗ /
geometric mean,harmonic mean,percent variation
temperature in Kelvin,monetary quantities,counts, age, length,electrical current
DM:I-26 Introduction © STEIN 2005-2020
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On Data [Tan et al. 2005]
Types of Attributes
Type Permissible transformation Comment
categorical nominal(qualitative)
any one-to-one mapping,permutation of values
A reassignment of employee IDnumbers will not make anydifference.
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On Data [Tan et al. 2005]
Types of Attributes
Type Permissible transformation Comment
categorical nominal(qualitative)
any one-to-one mapping,permutation of values
A reassignment of employee IDnumbers will not make anydifference.
ordinal any order-preserving change ofvalues: x 7→ f(x), where f is amonotonic
An attribute encompassing thenotion of {good, better, best} can berepresented equally well by thevalues {1, 2, 3}.
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On Data [Tan et al. 2005]
Types of Attributes
Type Permissible transformation Comment
categorical nominal(qualitative)
any one-to-one mapping,permutation of values
A reassignment of employee IDnumbers will not make anydifference.
ordinal any order-preserving change ofvalues: x 7→ f(x), where f is amonotonic
An attribute encompassing thenotion of {good, better, best} can berepresented equally well by thevalues {1, 2, 3}.
numeric interval(quantitative)
x 7→ a · x+ b, where a and b areconstants
The Fahrenheit and Celsiustemperature scales differ in terms ofwhere their zero value is, as well asthe size of a unit (degree).
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On Data [Tan et al. 2005]
Types of Attributes
Type Permissible transformation Comment
categorical nominal(qualitative)
any one-to-one mapping,permutation of values
A reassignment of employee IDnumbers will not make anydifference.
ordinal any order-preserving change ofvalues: x 7→ f(x), where f is amonotonic
An attribute encompassing thenotion of {good, better, best} can berepresented equally well by thevalues {1, 2, 3}.
numeric interval(quantitative)
x 7→ a · x+ b, where a and b areconstants
The Fahrenheit and Celsiustemperature scales differ in terms ofwhere their zero value is, as well asthe size of a unit (degree).
ratio x 7→ a · x, where a is a constant Length can be measured in metersor feet.
DM:I-30 Introduction © STEIN 2005-2020
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Remarks:
q Identifying, considering, and measuring an attribute A of an object O is the heart of modelformation and always goes along with a sort of abstraction. Formally, this abstraction isoperationalized by a model formation function α : O → X. [
::::ML
:::::::::::::Introduction]
q The terms “attribute” and “feature” can be used synonymously. However, a slight distinction isthe following: attributes are often associated with objects, O, while features usually designatethe dimensions of the feature space, X.
q The type of an attribute is also referred to as the type of a measurement scale or level ofmeasurement.
q We call a transformation of an attribute permissible if its meaning is unchanged after thetransformation.
q Distinguish between discrete attributes and continuous attributes. The former can only take afinite or countably infinite set of values, the latter can be measured in infinitely small units.Be careful when deriving from this distinction an attribute’s type.
q We will encode attributes of interval type or ratio type by real numbers. Note that attributes ofnominal type and ordinal type can also be encoded by real numbers.
q Particular learning methods require particular attribute types.
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On Data [Tan et al. 2005]
Types of Data Sets
Data sets may not be a homogeneous collection of objects but come along withdifferently intricate characteristics:
1. Inhomogeneity of attributes:Consider the combination of different attribute types within a single object.
2. Inhomogeneity of objects:Consider the combination of different objects in a single data set.
3. Inhomogeneity of distributions:The correlation between attributes varies in the sample space.
4. Resolution:The attributes may be given at different resolutions.
5. Curse of dimensionality:Attribute number and object density stand in exponential relation.
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On Data [Tan et al. 2005]
Types of Data Sets
Data sets may not be a homogeneous collection of objects but come along withdifferently intricate characteristics:
1. Inhomogeneity of attributes:Consider the combination of different attribute types within a single object.
2. Inhomogeneity of objects:Consider the combination of different objects in a single data set.
3. Inhomogeneity of distributions:The correlation between attributes varies in the sample space.
4. Resolution:The attributes may be given at different resolutions.
5. Curse of dimensionality:Attribute number and object density stand in exponential relation.
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On Data [Tan et al. 2005]
Types of Data Sets: Record Data
Collection of records, each of which consists of a fixed set of attributes:
ID Check Status Income Risk
1 + single 125 000 No
2 - married 100 000 No
3 - single 70 000 No
4 + married 120 000 No
5 - divorced 95 000 Yes
6 - married 60 000 No
7 + divorced 220 000 No
8 - single 85 000 Yes
9 - married 75 000 No
10 - single 90 000 Yes
q If all elements in a data set have the same fixed set of numeric attributes, theycan be thought of as points in a multi-dimensional space.
q Such data can be represented by a matrix, where each row stores an objectand each column stores an attribute.Example: term-document matrices in information retrieval.
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On Data [Tan et al. 2005]
Types of Data Sets: Graph Data
Graph of the Linked Open Data cloud [lod-cloud.net] :
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On Data [Tan et al. 2005]
Types of Data Sets: Ordered Data
Average monthly temperature of land and ocean (= spatio-temporal data) :
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On Data [Tan et al. 2005]
Data Quality
When repeating measurements of a quantity, measurement errors and datacollection errors may occur during the measurement process. Questions:
1. What kinds of data quality problems exist?
2. How to detect data quality problems?
3. How to address data quality problems?
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On Data [Tan et al. 2005]
Data Quality
When repeating measurements of a quantity, measurement errors and datacollection errors may occur during the measurement process. Questions:
1. What kinds of data quality problems exist?
2. How to detect data quality problems?
3. How to address data quality problems?
Definition 1 (Precision, Bias, Accuracy)
Given a set of repeated measurements of the same quantity. Then, the closenessof the measurements to one another is called precision, a possible systematicvariation is called bias, and the closeness to the true value is called accuracy.
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On Data [Tan et al. 2005]
Data Quality
When repeating measurements of a quantity, measurement errors and datacollection errors may occur during the measurement process. Questions:
1. What kinds of data quality problems exist?
2. How to detect data quality problems?
3. How to address data quality problems?
Definition 1 (Precision, Bias, Accuracy)
Given a set of repeated measurements of the same quantity. Then, the closenessof the measurements to one another is called precision, a possible systematicvariation is called bias, and the closeness to the true value is called accuracy.
Examples for data quality problems:
q noise, artifacts, outliersq missing valuesq duplicate data
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On Data [Tan et al. 2005]
Data Quality: Noise
Noise refers to random modifications of attributes that often have a spatial ortemporal characteristics:
sine waves sine waves with noise
Noise represents the intrinsic variability of data. [Bishop 2006, p.47]
Artifacts refer to deterministic distortions of a measurement process.
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On Data [Tan et al. 2005]
Data Quality: Outliers
Outliers are members in the data set with characteristics that are considerablydifferent than most of the other elements:
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On Data [Tan et al. 2005]
Data Quality: Outliers
Outliers are members in the data set with characteristics that are considerablydifferent than most of the other elements:
Cluster
Noise
Outlier
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On Data [Tan et al. 2005]
Data Quality: Missing Values
Main reasons for missing values:
1. Information is not collected.Example: people decline to give their age or weight.
2. Attributes may not be applicable to all elements in O.Example: annual income is not applicable to children.
3. Information is not trustworthy.Example: profile data on Facebook is intentionally misleading.
Strategies for handling missing values:
q eliminate members of the data
q estimate missing values
q ignore the missing value during analysis
q replace with all possible values weighted by their probabilities
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On Data [Tan et al. 2005]
Data Preprocessing
q sampling of object set O
q modeling of objects, α : O → X
q sampling of feature space X [::::ML
:::::::::::::Introduction]
q selection of attributes (features) [attributes versus features]
q transformation of attributes (features)
q discretization and binarization of attributes (features)
q dimensionality reduction of feature space X
DM:I-44 Introduction © STEIN 2005-2020
