Data mining Practical Connection Assignment

profileBuddhaland
ITS_632_Week3_Chapter2.pdf

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Dr. Oner Celepcikay

ITS 632

Data Mining

Summer 2019Week 3: Data and Data Exploration

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Chapter 2: Data

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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 u Example: height can be measured in feet or meters

– Different attributes can be mapped to the same set of values u Example: Attribute values for ID and age are integers u But properties of attribute values can be different

– ID has no limit but age has a maximum and minimum value – Some operations are meaningful on age but meaningless on ID

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Types of Attributes

● There are different types of attributes

– Nominal

u Examples: ID numbers, eye color, zip codes

– Ordinal

u Examples: rankings (e.g., taste of potato chips on a scale

from 1-10), grades, height in {tall, medium, short}

– Interval

u Examples: calendar dates, temperatures in Celsius or

Fahrenheit.

– Ratio

u Examples: temperature in Kelvin, length, time, counts

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. (=, ¹)

zip codes, employee ID numbers, eye color, sex: {male, female}

mode, entropy, contingency correlation, c2 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.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Properties of Attribute Values

● The type of an attribute depends on which of the

following properties it possesses:

– Distinctness: = ¹ – Order: < >

– Addition: + -

– Multiplication: * /

– Nominal attribute: distinctness

– Ordinal attribute: distinctness & order

– Interval attribute: distinctness, order & addition

– Ratio attribute: all 4 properties

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Types of data sets

● Record – Data Matrix – Document Data – Transaction Data

● Graph – World Wide Web – Molecular Structures

● Ordered – Spatial Data – Temporal Data – Sequential Data – Genetic Sequence Data

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Important Characteristics of Structured Data

– Dimensionality u Curse of Dimensionality

– Sparsity u Only presence counts

– Resolution u Patterns depend on the scale

– Examples: Texas data, Aleks, Simpson’s Paradox

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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

1.12.216.226.2512.65

1.22.715.225.2710.23

Thickness LoadDistanceProjection of y load

Projection of x Load

1.12.216.226.2512.65

1.22.715.225.2710.23

Thickness LoadDistanceProjection of y load

Projection of x Load

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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. – In practice only non-0 is stored

Document 1

season

tim eout

lost

w in

gam e

score

ball

play

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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Graph Data

● Examples: Generic graph and HTML Links

● Data objects are nodes, links are properties

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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Chemical Data

● Benzene Molecule: C6H6

● Nodes are atoms, links are chemical bonds ● helps to identify substructures.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Ordered Data

● Sequences of transactions

An element of the sequence

Items/Events

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Ordered Data

● Genomic sequence data

● Similar to sequential data but no time stamps

GGTTCCGCCTTCAGCCCCGCGCC CGCAGGGCCCGCCCCGCGCCGTC GAGAAGGGCCCGCCTGGCGGGCG GGGGGAGGCGGGGCCGCCCGAGC CCAACCGAGTCCGACCAGGTGCC CCCTCTGCTCGGCCTAGACCTGA GCTCATTAGGCGGCAGCGGACAG GCCAAGTAGAACACGCGAAGCGC TGGGCTGCCTGCTGCGACCAGGG

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Ordered Data

● Spatio-Temporal Data

Average Monthly Temperature of land and ocean

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Data Quality

● Precision: The closeness of repeated measurements (of the same quantity) to other measurements.

● Bias: A systematic variation of measurements from the quantity being measured.

● Accuracy: The closeness of measurements to the true value of the quantity being measurement.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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

Two Sine Waves Two Sine Waves + Noise

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Outliers

● Outliers are data objects with characteristics that are considerably different than most of the other data objects in the data set (diff. than noise)

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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 (unless many missing)

– Estimate Missing Values (avg., most common val.)

– Ignore the Missing Value During Analysis

– Replace with all possible values (weighted by their

probabilities)

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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 – Also attention needed to avoid combining 2 very

similar objects into 1.

● Examples: – Same person with multiple email addresses

● Data cleaning – Process of dealing with duplicate data issues

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Data Preprocessing

● Aggregation

● Sampling

● Dimensionality Reduction

● Feature subset selection

● Feature creation

● Discretization and Binarization

● Attribute Transformation

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Aggregation

● Combining two or more attributes (or objects) into a single attribute (or object)

● Purpose – Data reduction

u Reduce the number of attributes or objects

– Change of scale u Cities aggregated into regions, states, countries, etc

– More �stable� data u Aggregated data tends to have less variability

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Aggregation-Why?

● Less memory & less processing times – Aggregation allows to use very expensive Algorithms

● High level view of the data – Store example

● Behavior of groups of objects often more stable than individual objects. – A disadvantage of this is losing information or

patterns, – e.g. if you aggregate days into months, you might

miss the sales peak in Valentine’s Day.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Aggregation

Standard Deviation of Average Monthly Precipitation

Standard Deviation of Average Yearly Precipitation

Variation of Precipitation in Australia

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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

– If mean is of interest then the mean of the sample,

should be similar to mean of the full data.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Types of Sampling

● Simple Random Sampling – There is an equal probability of selecting any particular item

● Sampling without replacement – As each item is selected, it is removed from the population

● Sampling with replacement – Objects are not removed from the population as they are

selected for the sample. u In sampling with replacement, the same object can be picked up more than once (easier to analyze, probability is constant)

● Stratified sampling – Split the data into several partitions; then draw random samples

from each partition (handles representation of less freq. objects)

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Sample Size

8000 points 2000 Points 500 Points

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Sample Size

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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Curse of Dimensionality

● 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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Dimensionality Reduction

● Purpose: – 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 – Principle Component Analysis – Singular Value Decomposition – Others: supervised and non-linear techniques

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Dimensionality Reduction: PCA

● Goal is to find a projection that captures the largest amount of variation in data

x2

x1

e

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Dimensionality Reduction: PCA

● Find the eigenvectors of the covariance matrix

● The eigenvectors define the new space

● Tends to identify strongest patterns in data.

x2

x1

e

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Dimensions = 10Dimensions = 40Dimensions = 80Dimensions = 120Dimensions = 160Dimensions = 206

Dimensionality Reduction: PCA

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Face detection and recognition

Detection Recognition “Sally”

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Feature Subset Selection

● Another way to reduce dimensionality of data

● 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

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Feature Subset Selection

● Techniques: – Brute-force approch:

uTry all possible feature subsets as input to data mining algorithm

– Embedded approaches: u Feature selection occurs naturally as part of the data mining algorithm

– Filter approaches: u Features are selected before data mining algorithm is run

– Wrapper approaches: u Use the data mining algorithm as a black box to find best subset of attributes

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Feature Subset Selection

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

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

u domain-specific

– Mapping Data to New Space – Feature Construction

u combining features (pixels à edges for face recognition) u e.g. using density instead of mass, volume in identifying artifacts such as gold, bronze, clay, etc…

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Similarity and Dissimilarity

● Similarity – Numerical measure of how alike two data objects are. – Is higher when objects are more alike. – Often falls in the range [0,1]

● Dissimilarity – Numerical measure of how different are two data

objects – Lower when objects are more alike – Minimum dissimilarity is often 0 – Upper limit varies

● Proximity refers to a similarity or dissimilarity

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Similarity/Dissimilarity for Simple Attributes

p and q are the attribute values for two data objects.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Similarity/Dissimilarity for Simple Attributes

● An example: quality of a product (e.g. candy) {poor, fair, OK, good, wonderful}

● P1->Wonderful, P->2 good, P3->OK ● P1 is closer to P2 than it is to P3 ● Map ordinal attributes into integers:

{poor=0, fair=1, OK=2, good=3, wonderful=4} ● Estimate the distance values for each pair. ● Normalize if you want [1,1] interval

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Euclidean Distance

● Euclidean Distance

Where n is the number of dimensions (attributes) and pk and qk are, respectively, the kth attributes (components) or data objects p and q.

● Standardization is necessary, if scales differ.

å =

-= n

k kk qpdist

1

2)(

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Euclidean Distance

0

1

2

3

0 1 2 3 4 5 6

p1

p2

p3 p4

point x y p1 0 2 p2 2 0 p3 3 1 p4 5 1

Distance Matrix

p1 p2 p3 p4 p1 0 2.828 3.162 5.099 p2 2.828 0 1.414 3.162 p3 3.162 1.414 0 2 p4 5.099 3.162 2 0

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Minkowski Distance

● Minkowski Distance is a generalization of Euclidean

Distance

Where r is a parameter, n is the number of dimensions (attributes) and pk and qk are, respectively, the kth attributes (components) or data objects p and q.

r n

k

r kk qpdist

1

1 )||( å

= -=

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Minkowski Distance: Examples

● r = 1. City block (Manhattan, taxicab, L1 norm) distance. – A common example of this is the Hamming distance, which is just the

number of bits that are different between two binary vectors

● r = 2. Euclidean distance

● r ® ¥. �supremum� (Lmax norm, L¥ norm) distance. – This is the maximum difference between any component of the vectors

● Do not confuse r with n, i.e., all these distances are defined for all numbers of dimensions.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Minkowski Distance

Distance Matrix

point x y p1 0 2 p2 2 0 p3 3 1 p4 5 1

L1 p1 p2 p3 p4 p1 0 4 4 6 p2 4 0 2 4 p3 4 2 0 2 p4 6 4 2 0

L2 p1 p2 p3 p4 p1 0 2.828 3.162 5.099 p2 2.828 0 1.414 3.162 p3 3.162 1.414 0 2 p4 5.099 3.162 2 0

L¥ p1 p2 p3 p4 p1 0 2 3 5 p2 2 0 1 3 p3 3 1 0 2 p4 5 3 2 0

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Common Properties of a Distance

● Distances, such as the Euclidean distance,

have some well known properties.

1. d(p, q) ³ 0 for all p and q and d(p, q) = 0 only if p = q. (Positive definiteness)

2. d(p, q) = d(q, p) for all p and q. (Symmetry) 3. d(p, r) £ d(p, q) + d(q, r) for all points p, q, and r.

(Triangle Inequality)

where d(p, q) is the distance (dissimilarity) between points (data objects), p and q.

● A distance that satisfies these properties is a

metric

● Examples 2.14 and 2.15

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Common Properties of a Similarity

● Similarities, also have some well known properties.

1. s(p, q) = 1 (or maximum similarity) only if p = q.

2. s(p, q) = s(q, p) for all p and q. (Symmetry)

where s(p, q) is the similarity between points (data objects), p and q.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

SMC versus Jaccard: Example

p = 1 0 0 0 0 0 0 0 0 0 q = 0 0 0 0 0 0 1 0 0 1

M01 = 2 (the number of attributes where p was 0 and q was 1) M10 = 1 (the number of attributes where p was 1 and q was 0) M00 = 7 (the number of attributes where p was 0 and q was 0) M11 = 0 (the number of attributes where p was 1 and q was 1)

SMC = (M11 + M00)/(M01 + M10 + M11 + M00) = (0+7) / (2+1+0+7) = 0.7

J = (M11) / (M01 + M10 + M11) = 0 / (2 + 1 + 0) = 0

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Cosine Similarity

● If d1 and d2 are two document vectors, then cos( d1, d2 ) = (d1 • d2) / ||d1|| ||d2|| ,

where • indicates vector dot product and || d || is the length of vector d.

● Example:

d1 = 3 2 0 5 0 0 0 2 0 0 d2 = 1 0 0 0 0 0 0 1 0 2

d1 • d2= 3*1 + 2*0 + 0*0 + 5*0 + 0*0 + 0*0 + 0*0 + 2*1 + 0*0 + 0*2 = 5

||d1|| = (3*3+2*2+0*0+5*5+0*0+0*0+0*0+2*2+0*0+0*0)0.5 = (42) 0.5 = 6.481 ||d2|| = (1*1+0*0+0*0+0*0+0*0+0*0+0*0+1*1+0*0+2*2) 0.5 = (6) 0.5 = 2.245

cos( d1, d2 ) = .3150

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Correlation

● Correlation measures the linear relationship between objects

● To compute correlation, we standardize data objects, p and q, and then take their dot product

)(/))(( pstdpmeanpp kk -=¢

)(/))(( qstdqmeanqq kk -=¢

qpqpncorrelatio ¢•¢=),(

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Correlation

● Correlation measures the linear relationship between objects

● To compute correlation, we standardize data objects, p and q, and then take their dot product

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Visually Evaluating Correlation

Scatter plots showing the similarity from –1 to 1.

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Density

● Density-based clustering require a notion of density

● Examples: – Euclidean density

u Euclidean density = number of points per unit volume

– Probability density

– Graph-based density

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Euclidean Density – Cell-based

● Simplest approach is to divide region into a number of rectangular cells of equal volume and define density as # of points the cell contains

© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 ‹#›

Euclidean Density – Center-based

● Euclidean density is the number of points within a specified radius of the point