DMTM Lecture 05 Data representation

Prof. Pier Luca Lanzi
Data Representation
Data Mining andText Mining (UIC 583 @ Politecnico di Milano)

Readings
• “Data Mining and Analysis” – Chapter 1
• “Mining of Massive Datasets” – Chapter 1
2

syllabusdescribing data

Contact Lenses Data 4
NoneReducedYesHypermetropePre-presbyopic
NoneNormalYesHypermetropePre-presbyopic
NoneReducedNoMyopePresbyopic
NoneNormalNoMyopePresbyopic
NoneReducedYesMyopePresbyopic
HardNormalYesMyopePresbyopic
NoneReducedNoHypermetropePresbyopic
SoftNormalNoHypermetropePresbyopic
NoneReducedYesHypermetropePresbyopic
NoneNormalYesHypermetropePresbyopic
SoftNormalNoHypermetropePre-presbyopic
NoneReducedNoHypermetropePre-presbyopic
HardNormalYesMyopePre-presbyopic
NoneReducedYesMyopePre-presbyopic
SoftNormalNoMyopePre-presbyopic
NoneReducedNoMyopePre-presbyopic
hardNormalYesHypermetropeYoung
NoneReducedYesHypermetropeYoung
SoftNormalNoHypermetropeYoung
NoneReducedNoHypermetropeYoung
HardNormalYesMyopeYoung
NoneReducedYesMyopeYoung
SoftNormalNoMyopeYoung
NoneReducedNoMyopeYoung
Recommended lensesTear production rateAstigmatismSpectacle prescriptionAge

Data Representation
• Data are typically abstracted as a matrix, with n rows and d
columns, given as
• Rows are called instances, examples, records, transactions,
objects, points, feature-vectors, etc.
• Columns are called attributes, properties, features, dimensions,
variables, fields, etc.
5

Instances, Attributes, Concepts
• Instances (observations, case)
§ The atomic elements of information from a dataset
§ Also known as records, prototypes, or examples
• Attributes (variable)
§ Measures aspects of an instance
§ Also known as features or variables
§ Each instance is composed of a certain number of attributes
• Concepts
§ Special content inside the data
§ Kind of things that can be learned
§ Intelligible and operational concept description
7

Two Versions of the Weather Data 8
……………
YesFalseNormalMildRainy
YesFalseHighHotOvercast
NoTrueHighHotSunny
NoFalseHighHotSunny
PlayWindyHumidityTemperatureOutlook
……………
YesFalse8075Rainy
YesFalse8683Overcast
NoTrue9080Sunny
NoFalse8585Sunny
PlayWindyHumidityTemperatureOutlook

syllabusattribute types

Attributes
• Numeric Attributes
§Real-valued or integer-valued domain
§Interval-scaled when only differences are meaningful
(e.g., temperature)
§Ratio-scaled when differences and ratios are meaningful
(e.g., Age)
• Categorical Attributes
§Set-valued domain composed of a set of symbols
§Nominal when only equality is meaningful
(e.g., domain(Sex) = { M, F})
§Ordinal when both equality (are two values the same?) and
inequality (is one value less than another?) are meaningful
(e.g., domain(Education) = { High School, BS, MS, PhD})
10

Numerical Attributes
• Not only ordered but measured in fixed and equal units
• Examples
§Attribute “temperature” expressed in degrees
§Attribute “year”
• Characteristics
§Difference of two values makes sense
§Sum or product doesn’t make sense
§Zero point is not defined
• Sometimes they are divided into “discrete” and “continuous”
11

Nominal Attributes (or Categorical)
• Values are distinct symbols
• Values themselves serve only as labels or names
• Example
§Attribute “outlook” from weather data
§Values: “sunny”, “overcast”, and “rainy”
• Characteristics
§No relation is implied among nominal values
§No ordering
§No distance measure
§Only equality tests can be performed
12

Other Types of Attributes
• Ratio Attributes
§Numerical attributes for which the measurement scheme
defines a zero point (e.g., an attribute representing distance)
• Ordinal Attributes
§Categorical attributes with an imposed order on values
§No distance between values defined
§For instance, the attribute “temperature” in weather data
“hot” > “mild” > “cool”
13

Nominal or Ordinal?
• Attribute “age” nominal
§If age = young and astigmatic = no
and tear production rate = normal
then recommendation = soft
• Attribute “age” ordinal
(e.g. “young” < “pre-presbyopic” < “presbyopic”)
§If age≤pre-presbyopic and astigmatic = no
and tear production rate = normal
then recommendation = soft
14

Why Specifying Attribute Types?
• Some algorithms fit some specific data types best
• Express the best possible patterns into data
• Make the most adequate comparisons
• Example
§Outlook > “sunny” does not make sense, while
§Temperature > “cool” or
§Humidity > 70 does
• Additional uses of attribute type
§Check for valid values
§Deal with missing values, etc.
15

syllabusmissing values

Why Missing Values Exist?
• Faulty equipment, incorrect measurements, missing cells in manual
data entry, censored/anonymous data
• Review scores for movies, books, etc.
• Very frequent in questionnaires for medical scenarios
• Censored/anonymous data
• In practice, a low rate of missing values may be suspicious
• Interview data (“Did you ever …”)
17

Missing Values
• Frequently indicated by out-of-range entries (e.g. max/min float),
Nan or special values (e.g., zero)
• Missing value may have significance in itself
§E.g. missing test in a medical examination
• Most schemes assume that is not the case
§“missing” may need to be coded as additional value
• Does absence of value have some significance?
§If it does, “missing” is a separate value
§If it does not, “missing” must be treated in a special way
18

What Types of Missing Values?
• Missing completely at random (MCAR)
§ The distribution of an example having a missing value for an attribute does not depend on
either the observed data or the missing data
§ Example: some survey questions contain a random sample of the whole questionnaire
• Missing at random (MAR)
§ The distribution of an example having a missing value for an attribute depends on the
observed data, but does not depend on the missing data
§ Missing at Random means the propensity for a data point to be missing is not related to the
missing data, but it is related to some of the observed data
§ Whether or not someone answered #13 on your survey has nothing to do with the missing
values, but it does have to do with the values of some other variable
§ For example, people who don’t declare their salary not because of the amount of it but just
because they don’t want to.
• Not missing at random (NMAR)
§ The distribution of an example having a missing depends on the missing values.
§ For example, respondents with high income less likely to report income
• Note that NMAR and MAR might be difficult to identify and often require domain knowledge
19

Dealing with Missing Values
• Use what you know
§ Why data is missing
§ Distribution of missing data
• Decide on the best strategy to yield the least biased estimates
§ Deletion Methods (listwise deletion, pairwise deletion)
§ Single Imputation Methods (mean/mode substitution, dummy variable
method, single regression)
§ Model-Based Methods (maximum Likelihood, multiple imputation
20

Strategies for missing values handling
• The handling of missing data depends on the type
• Discarding all the examples with a missing values
§ Simplest approach
§ Allows the use of unmodified data mining methods
§ Only practical if there are few examples with missing values. Otherwise, it
can introduce bias
• Fill in the missing value manually J
• Convert the missing values into a new value
§ Use a special value for it
§ Add an attribute that indicates if value is missing or not
§ Greatly increases the difficulty of the data mining process
• Imputation methods
§ Assign a value to the missing one, based on the rest of the dataset. Use
the unmodified data mining methods.
21

Listwise Deletion
(Complete Case Analysis)
• Only analyze cases with available data
on each variable
• Simple, but reduces the data
• Comparability across analyses
• Does not use all the information
• Estimates may be biased if data not
MCAR
22

Pairwise deletion
(Available Case Analysis)
• Analysis with all cases in which
the variables of interest are
present
• Advantage
§Keeps as many cases as
possible for each analysis
§Uses all information
possible with each analysis
• Disadvantage
§Can’t compare analyses
because sample different
each time
23

Imputation methods
• Extract a model from the dataset to perform the imputation
• Suitable for MCAR and, to a lesser extent, for MAR
• Not suitable for NMAR type of missing data
• For NMAR we need to go back to the source of the data to
obtain more information
• Survey of imputation methods available at
http://sci2s.ugr.es/MVDM/index.php
http://sci2s.ugr.es/MVDM/biblio.php
24

Single Imputation Methods
• Mean/mode substitution (most common value)
§ Replace missing value with sample mean or mode
§ Run analyses as if all complete cases
§ Advantages: Can use complete case analysis methods
§ Disadvantages: Reduces variability
• Dummy variable control
§ Create an indicator for missing value (1=value is missing for observation;
0=value is observed for observation)
§ Impute missing values to a constant (such as the mean)
§ Include missing indicator in the algorithm
§ Advantage: uses all available information about missing observation
§ Disadvantage: results in biased estimates, not theoretically driven
• Regression Imputation
§ Replaces missing values with predicted score from a regression equation.
25

Do Not Impute (DNI)
• Simply use the default policy of the data mining method
• Works only if the policy exists
26

syllabusinaccurate values

Inaccurate Values
• Data has not been collected for mining it
• Errors and omissions that don’t affect original purpose of data
(e.g. age of customer)
• Typographical errors in nominal attributes,
thus values need to be checked for consistency
• Typographical and measurement errors in numeric attributes,
thus outliers need to be identified
• Errors may be deliberate (e.g. wrong zip codes)
28

syllabusthe geometric view

The Geometrical View of the Data
• When the data matrix contains only numerical values
§Every row can be viewed as a point in a d-dimension space
§Every column as a point in a n-dimensional space
30

syllabusthe probabilistic view

syllabusdata format

Data Format
• Most commercial tools have their own proprietary format
• Most tools import excel files and comma-separated value files
37
Year,Make,Model,Length
1997,Ford,E350,2.34
2000,Mercury,Cougar,2.38
Year;Make;Model;Length
1997;Ford;E350;2,34
2000;Mercury;Cougar;2,38

Attribute-Relation File Format
(ARFF)
38
%
% ARFF file for weather data with some numeric features
%
@relation weather
@attribute outlook {sunny, overcast, rainy}
@attribute temperature numeric
@attribute humidity numeric
@attribute windy {true, false}
@attribute play? {yes, no}
@data
sunny, 85, 85, false, no
sunny, 80, 90, true, no
overcast, 83, 86, false, yes
...
http://www.cs.waikato.ac.nz/~ml/weka/arff.html

Additional Attribute Types
• ARFF supports string attributes:
• Similar to nominal attributes but list of values
is not pre-specified
• ARFF also supports date attributes:
• Uses the ISO-8601 combined date
and time format yyyy-MM-dd-THH:mm:ss
39
@attribute description string
@attribute today date

Additional Attribute Types
• ARFF supports sparse data, for instance the following examples,
• Can also be represented as,
40
0, 26, 0, 0, 0 ,0, 63, 0, 0, 0, “class A”
0, 0, 0, 42, 0, 0, 0, 0, 0, 0, “class B”
{1 26, 6 63, 10 “class A”}
{3 42, 10 “class B”}

Missing Values in ARFF 41
@relation labor
@attribute 'duration' real
@attribute 'wage-increase-first-year' real
@attribute 'wage-increase-second-year' real
@attribute 'wage-increase-third-year' real
@attribute 'cost-of-living-adjustment' {'none','tcf','tc'}
@attribute 'working-hours' real
@attribute 'pension' {'none','ret_allw','empl_contr'}
@attribute 'standby-pay' real
@attribute 'shift-differential' real
@attribute 'education-allowance' {'yes','no'}
@attribute 'statutory-holidays' real
@attribute 'vacation' {'below_average','average','generous'}
@attribute 'longterm-disability-assistance' {'yes','no'}
@attribute 'contribution-to-dental-plan' {'none','half','full'}
@attribute 'bereavement-assistance' {'yes','no'}
@attribute 'contribution-to-health-plan' {'none','half','full'}
@attribute 'class' {'bad','good'}
@data
1,5,?, ?, ?,40, ?, ?,2, ?,11,'average', ?, ?,'yes',?,'good'
2,4.5,5.8, ?, ?,35,'ret_allw', ?, ?,'yes',11,'below_average', ?,'full', ?,'full','good'
?, ?, ?, ?, ?,38,'empl_contr', ?,5, ?,11,'generous','yes','half','yes','half','good'
3,3.7,4,5,'tc', ?, ?, ?, ?,'yes', ?, ?, ?, ?,'yes', ?,'good'

Attribute Types and Interpretation
• Interpretation of attribute types in ARFF depends
on the mining scheme
• Numeric attributes are interpreted as
§Ordinal scales if less-than and greater-than are used
§Ratio scales if distance calculations are performed
(normalization/standardization may be required)
• Instance-based schemes define distance between nominal values
(0 if values are equal, 1 otherwise)
• Integers in some given data file: nominal, ordinal, or ratio scale?
42

DSPL: Dataset Publishing Language
• Open format by Google available at
http://code.google.com/apis/publicdata/
• Use existing data: add an XML metadata file existing CSV
• Read by the Google Public Data Explorer, which includes
animated bar chart, motion chart, and map visualization
• Allow linking to concepts in other datasets
• Geo-enabled: allows adding latitude and longitude data to your
concept definitions
43

syllabusmodel representation

Predictive Model Markup Language
• XML-based markup language developed by the Data Mining
Group (DMG) to provide a way for applications to define models
related to predictive analytics and data mining
• The goal is to share models between applications
• Vendor-independent method of defining models
• Allow to exchange of models between applications.
• PMML Components: data dictionary, data transformations, model,
mining schema, targets, output
45

syllabusdata repositories

Publicly Available Datasets
• UCI repository
§http://archive.ics.uci.edu/ml/
§Probably the most famous collection of datasets
• Kaggle
§http://www.kaggle.com/
§It is not a static repository of datasets, but a site that manages
Data Mining competitions
§Example of the modern concept of crowdsourcing
• KDNuggets
§http://www.kdnuggets.com/datasets/
47

DMTM Lecture 05 Data representation

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