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FAMILY ASSESSMENT 1
FAMILY ASSESSMENT
Institution Affiliation
Student Name
Date
Family-Focused Functional Assessment
The questions asked in the interview with the family that agreed
to participate were based on the eleven functional health
patterns. The family that participated in the family health
assessment program was a single parent structure, a mother with
two children. The questions were directed towards the personal
life of the respondent; therefore, their names will not be
mentioned. It was an African American parent who is single,
middle class income. The family is religious, Christians and live
in the Chicago neighbourhood. It is a mother who is always
there for her daughters and works hard to meet their needs.
The overall health behaviour of the family include eating
healthy meals, drink plenty of fluids, and children are given
junk once in a while. The children snore and the mother works
two jobs and gets time to sleep for only 5hours in a day because
she works in the afternoon and evening. The family’s bowel
movements are normal and temporary changes are experienced
but it’s nothing to worry about. The mother creates time to
engage in physical activities, twice a week and the types of
exercises she does are morning runs and home work-out just to
keep fit. She makes all the decisions that involve her children’s
schooling and future plans, and she reported that she doesn’t get
confused. She has healthy eyesight. She feels that the future
will be great because she has done several investments that will
yield positive outcomes.
Children are disciplined using praise positive behaviour because
she wants her children to grow into a functional family that
does not instil fear and reflect negative behaviour when they
become adults. She has started seeing someone recently and has
never experienced any sexual dysfunction. The most recent
stressful event she experienced is increased pressure from work
and creating time to spend with her children. Unfortunately,
coping strategies were not well defined. The current health of
the family is moderate considering the constraints that the
single parent has to undergo to ensure that the children are
happy and safe. The family eats a healthy diet that includes
vegetables and fruits with less junk food.
Based on the findings of the role relationship, I saw this as
strength because the parent disciplines her daughters through
praise positive behaviour. Descriptive praise is what she
mentioned that works best for her children. Descriptive praise
means that a parent takes the initiative to tell their children
exactly what they like. Praise helps change a child’ negative
behaviour and based on what I observed her children are
disciplined, they have confidence and self-esteem, (Campbell-
Salome, et.al, 2019). At times, she has to use rewards to
encourage her two daughters to perform well in academics and
at home. The healthy diet and drinking more fluids habit is
another strength that the family practices. This is because
healthy diet that has plenty vegetables and water reduces the
chances of getting chronic diseases such as cancer, obesity and
heart disease.
Stress from work and long hours are a barrier to the health of
the mother and children as well because they do not get enough
attention from their mother. Another barrier to health is lack of
enough sleep because she only gest to rest for 4 hours. Lack of
enough sleep impedes good health; it can escalate to serious
conditions such as high blood pressure and diabetes, (Kaakinen,
et.al, 2018). Lack of coping strategies also impedes an
individual’s ability to make sound decisions. Being able in a
position to be able to deal with stress is detrimental because it
can affect other aspects of life and overall health of a person.
Family systems theory is a theoretical framework of human
behaviour that views the family as an emotional unit and
provides insights about the complex interactions in the unit.
Family systems theory can help to solicit changes in family
members because families tend to affect an individual’s
thoughts, actions and feelings, (Healy & Allen, 2019).
Emotional interdependence can help promote cooperation and
cohesiveness which requires one to feed, shelter and protect
their family members. Family members’ actions and emotions
may be affected positively or negatively because a change in
one person’s sparks changes in how other people around are
them will act and feel. In every family, there is that one person
who absorbs all the emotions of the family and may suffer
depression and even physical health. Families can work together
to alleviate their problems instead of letting the negative
emotions to take a toll on the entire family. Families need to be
emotionally independent to achieve positive changes in family
functions.
Questions
Values/Health Perception: How healthy is your family?
Nutrition: How many hours of sleep do you get on working
days? Does anyone in your family snore?
Sleep/Rest: How would you describe your diet?
Elimination: Have you ever experienced any abnormal bowel
movements?
Activity/Exercise: Do you create time to exercise? What types
of exercise do you engage in?
Cognitive: Do you ever experience confusion? How do you
make decisions in the house?
Sensory-Perception: How healthy is your eyesight?
Self-Perception: Where do you see yourself in future?
Role Relationship: How do you discipline your children?
Sexuality: How often do you have sex? Have you experienced a
sexual dysfunction?
Coping: Have you experienced any form of stress recently?
What methods do you use to when coping with stress?
References
Campbell-Salome, G., Rauscher, E. A., & Freytag, J. (2019).
Patterns of Communicating About Family Health History:
Exploring Differences in Family Types, Age, and Sex. Health
Education & Behavior, 46(5), 809-817.
Healy, R. W., & Allen, L. R. (2019). Bowen Family Systems
Therapy with Transgender Minors: A Case Study. Clinical
Social Work Journal, 1-10.
Kaakinen, J. R., Coehlo, D. P., Steele, R., & Robinson, M.
(2018). Family health care nursing: Theory, practice, and
research. FA Davis.
Data Mining: Exploring Data
Lecture Notes for Chapter 3
Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler
Look for accompanying R
code on the course web site.
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© Tan,Steinbach, Kumar Introduction to Data Mining
8/05/2005 ‹#›
Techniques Used In Data Exploration
Tukey
– The focus was on visualization
– Clustering and anomaly detection were viewed as
exploratory techniques
– In data mining, clustering and anomaly detection are
major areas of interest, and not thought of as just
exploratory
of data exploration, we focus on
– Summary statistics
– Visualization
– Online Analytical Processing (OLAP)
brins
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What is data exploration?
• Key motivations of data exploration include
- Helping to select the right tool for preprocessing or analysis
- Making use of humans’ abilities to recognize patterns
• People can recognize patterns not captured by data analysis
tools
• Related to the area of Exploratory Data Analysis (EDA)
- Created by statistician John Tukey
- Seminal book is "Exploratory Data Analysis" by Tukey
- A nice online introduction can be found in Chapter 1 of the
NIST
Engineering Statistics Handbook
http://www.itl.nist.gov/div898/handbook/index.htm
A preliminary exploration of the data to
better understand its characteristics.
http://www.itl.nist.gov/div898/handbook/index.htm
Iris Sample Data Set
• Many of the exploratory data techniques are illustrated
with the Iris Plant data set.
- Can be obtained from the UCI Machine Learning Repository
http://www.ics.uci.edu/~mlearn/MLRepository.html
- From the statistician R.A. Fisher
- Three flower types (classes):
• Setosa
• Virginica
• Versicolour
- Four (non-class) attributes
• Sepal width and length
• Petal width and length Virginica. Robert H. Mohlenbrock.
USDA
NRCS. 1995. Northeast wetland flora: Field
office guide to plant species. Northeast
National Technical Center, Chester, PA.
Courtesy of USDA NRCS Wetland Science
Institute.
Summary Statistics
• Summary statistics are numbers that summarize
properties of the data
- Summarized properties include location and
spread for continuous data
• Examples: location - mean
spread - standard deviation
- Most summary statistics can be calculated in a
single pass through the data
Frequency and Mode
• The frequency of an attribute value is the
percentage of time the value occurs in the
data set
- For example, given the attribute ‘gender’ and a
representative population of people, the gender
‘female’ occurs about 50% of the time.
• The mode of an attribute is the most frequent attribute
value
• The notions of frequency and mode are typically used
with categorical data
Measures of Location: Mean and Median
• The mean is the most common measure of the
location of a set of points.
• However, the mean is very sensitive to outliers.
• Thus, the median or a trimmed mean is also
commonly used.
Measures of Spread: Range and Variance
• Range is the difference between the max and min
• The variance or standard deviation is the most
common measure of the spread of a set of points.
• However, this is also sensitive to outliers, so that
other measures are often used.
Percentiles
x p
x p
Median – 50% of the
cases has a smaller value & 50%
are larger
Multivariate Summary Statistics
Object x
1
x
2
1 12 15
2 2 4
... ... ...
m 18 4
• Covariance between
features i and j
• Correlation
si is the variance of
feature i
sij=
1
m−1
∑
k=1
m
( xki− x̄ i)(xkj−x̄ j)
r ij=
sij
si s j
Topics
• Exploratory Data Analysis
• Summary Statistics
• Visualization
Visualization
Visualization is the conversion of data into a visual
or tabular format so that the characteristics of the
data and the relationships among data items or
attributes can be analyzed or reported.
• Visualization of data is one of the most powerful and
appealing techniques for data exploration.
- Humans have a well developed ability to analyze
large amounts of information that is presented
visually
- Can detect general patterns and trends
- Can detect outliers and unusual patterns
Example: Sea Surface Temperature
• The following shows the Sea Surface Temperature
(SST) for July 1982
- Tens of thousands of data points are
summarized in a single figure
Representation
• Is the mapping of information to a visual format
• Data objects, their attributes, and the relationships
among data objects are translated into graphical
elements such as points, lines, shapes, and colors.
• Example:
- Objects are often represented as points
- Their attribute values can be represented as the
position of the points or the characteristics of the
points, e.g., color, size, and shape
- If position is used, then the relationships of points,
i.e., whether they form groups or a point is an
outlier, is easily perceived.
Arrangement
• Is the placement of visual elements within a
display
• Can make a large difference in how easy it is to
understand the data
• Example:
Selection
• Is the elimination or the deemphasis of certain objects and
attributes
• Selection may involve the choosing a subset of attributes
- Dimensionality reduction is often used to reduce the
number of dimensions to two or three
- Alternatively, pairs of attributes can be considered
• Selection may also involve choosing a subset of objects
- A region of the screen can only show so many points
- Can sample, but want to preserve points in sparse areas
Histograms
• Usually shows the distribution of values of a single variable
• Divide the values into bins and show a bar plot of the number
of objects in each bin.
• The height of each bar indicates the number of objects
• Shape of histogram depends on the number of bins
• Example: Petal Width (10 and 20 bins, respectively)
Empirical Cumulative Distribution
Function (ECDF)
• Probability Density
Function (PDF): describes
the relative likelihood for
this random variable to take
on a given value
• Cumulative Distribution
Function (CDF): Shows
the distribution of data as
the fraction of points that
are less than this value.
CDF
PDF
Example: ECDF
Two-Dimensional Histograms
• Show the joint distribution of the values of two attributes
• Example: petal width and petal length
- What does this tell us?
Box Plots
• Invented by J. Tukey
• Another way of displaying the distribution of data
• Following figure shows the basic part of a box plot
outlier
25th percentile
– 1.5 IQR
25th percentile
75th percentile
50th percentile
75th percentile
+ 1.5 IQR
IQR
Q1 Q3
IQR
Median
Q3 + 1.5 × IQRQ1 − 1.5 × IQR
−0.6745 σ 0.6745 σ 2.698 σ−2.698 σ
50%24.65% 24.65%
68.27% 15.73%15.73%
−4 σ −3 σ −2 σ −1 σ 0 σ 1 σ 3 σ2 σ 4 σ
−4 σ −3 σ −2 σ −1 σ 0 σ 1 σ 3 σ2 σ 4 σ
−4 σ −3 σ −2 σ −1 σ 0 σ 1 σ 3 σ2 σ 4 σ
Example of Box Plots
• Box plots can be used to compare attributes
Scatter Plots
- Attributes values determine the position
- Two-dimensional scatter plots most common,
but can have three-dimensional scatter plots
- Often additional attributes can be displayed by
using the size, shape, and color of the markers
that represent the objects
- It is useful to have arrays of scatter plots can
compactly summarize the relationships of
several pairs of attributes
• See example on the next slide
Scatter Plot Array of Iris Attributes
Contour Plots
- Useful when a continuous attribute is measured
on a spatial grid
- They partition the plane into regions of similar
values
- The contour lines that form the boundaries of
these regions connect points with equal values
- The most common example is contour maps of
elevation
- Can also display temperature, rainfall, air
pressure, etc.
provided on the next slide
Contour Plot Example: SST Dec, 1998
Celsius
Matrix Plots
- Can plot a data matrix
- Can be useful when objects are sorted
according to class
- Typically, the attributes are normalized to
prevent one attribute from dominating the plot
- Plots of similarity or distance matrices can also
be useful for visualizing the relationships
between objects
Visualization of the Iris Data Matrix
standard
deviation
Deviation form feature mean
Visualization of the Iris Correlation Matrix
Parallel Coordinates
– Used to plot the attribute values of high-
dimensional data
– Instead of using perpendicular axes, use a set of
parallel axes
– The attribute values of each object are plotted as a
point on each corresponding coordinate axis and
the points are connected by a line
– Thus, each object is represented as a line
– Often, the lines representing a distinct class of
objects group together, at least for some attributes
– Ordering of attributes is important in seeing such
groupings
Parallel Coordinates Plots for Iris Data
Reordered features
Other Visualization Techniques
Star Plots
- Similar approach to parallel coordinates, but axes radiate
from a central point
- The line connecting the values of an object is a polygon
Chernoff Faces
- Approach created by Herman Chernoff
- This approach associates each attribute with a characteristic
of a face
- The values of each attribute determine the appearance of the
corresponding facial characteristic
- Each object becomes a separate face
- Relies on human’s ability to distinguish faces
Star Plots for Iris Data
Setosa
Versicolor
Virginica
Chernoff Faces for Iris Data
Setosa
Versicolor
Virginica
OLAP
• On-Line Analytical Processing (OLAP) was
proposed by E. F. Codd, the father of the
relational database.
• Relational databases put data into tables, while
OLAP uses a multidimensional array
representation.
– Such representations of data previously existed in
statistics and other fields
• There are a number of data analysis and data
exploration operations that are easier with such
a data representation.
Creating a Multidimensional Array
• Two key steps in converting tabular data into a
multidimensional array.
– First, identify which attributes are to be the dimensions
and which attribute is to be the target attribute whose
values appear as entries in the multidimensional array.
• The attributes used as dimensions must have discrete values
• The target value is typically a count or continuous value, e.g.,
the cost of an item
• Can have no target variable at all except the count of objects
that have the same set of attribute values
– Second, find the value of each entry in the
multidimensional array by summing the values (of the
target attribute) or count of all objects that have the
attribute values corresponding to that entry.
Example: Iris data
• We show how the attributes, petal length, petal
width, and species type can be converted to a
multidimensional array
– First, we discretized the petal width and length to
have categorical values: low, medium, and high
– We get the following table - note the count
attribute
Example: Iris data (continued)
• Each unique tuple of petal width, petal length,
and species type identifies one element of the
array.
• This element is assigned the corresponding
count value.
• The figure illustrates
the result.
• All non-specified
tuples are 0.
Example: Iris data (continued)
• Slices of the multidimensional array are shown
by the following cross-tabulations
• What do these tables tell us?
OLAP Operations: Data Cube
• The key operation of a OLAP is the formation of a
data cube
• A data cube is a multidimensional representation
of data, together with all possible aggregates.
• By all possible aggregates, we mean the aggregates
that result by selecting a proper subset of the
dimensions and summing over all remaining
dimensions.
• For example, if we choose the species type
dimension of the Iris data and sum over all other
dimensions, the result will be a one-dimensional
entry with three entries, each of which gives the
number of flowers of each type.
Data Cube Example
• Consider a data set that records the sales of
products at a number of company stores at
various dates.
• This data can be represented
as a 3 dimensional array
• There are 3 two-dimensional
aggregates (3 choose 2 ),
3 one-dimensional aggregates,
and 1 zero-dimensional
aggregate (the overall total)
Data Cube Example (continued)
• The following figure table shows one of the two
dimensional aggregates, along with two of the
one-dimensional aggregates, and the overall
total
OLAP Operations: Slicing and Dicing
• Slicing is selecting a group of cells from the
entire multidimensional array by specifying a
specific value for one or more dimensions.
• Dicing involves selecting a subset of cells by
specifying a range of attribute values.
– This is equivalent to defining a subarray from the
complete array.
• In practice, both operations can also be
accompanied by aggregation over some
dimensions.
OLAP Operations: Roll-up and Drill-down
• Attribute values often have a hierarchical
structure.
– Each date is associated with a year, month, and week.
– A location is associated with a continent, country, state
(province, etc.), and city.
– Products can be divided into various categories, such as
clothing, electronics, and furniture.
• Note that these categories often nest and form a
tree or lattice
– A year contains months which contains day
– A country contains a state which contains a city
OLAP Operations: Roll-up and Drill-down
• This hierarchical structure gives rise to the roll-
up and drill-down operations.
– For sales data, we can aggregate (roll up) the sales
across all the dates in a month.
– Conversely, given a view of the data where the time
dimension is broken into months, we could split the
monthly sales totals (drill down) into daily sales
totals.
– Likewise, we can drill down or roll up on the
location or product ID attributes.
ITS-632 Intro to Data Mining
Dr. Patrick Haney
Dept. of Information Technology &
School of Computer and Information Sciences
University of the Cumberlands
Chapter 3 Assignment
[Your Name Here]
1. Obtain one of the data sets available at the UCI Machine
Learning Repository and apply as many of the different
visualization techniques described in the chapter as possible.
The bibliographic notes and book Web site provide pointers to
visualization software.
2. Identify at least two advantages and two disadvantages of
using color to visually represent information.
3. What are the arrangement issues that arise with respect
to three-dimensional plots?
4. Discuss the advantages and disadvantages of using sampling
to reduce the number of data objects that need to be displayed.
Would simple random sampling (without replacement) be a
good approach to sampling? Why or why not?
5. Describe how you would create visualizations to display
information that de-scribes the following types of systems.
a) Computer networks. Be sure to include both the static aspects
of the network, such as connectivity, and the dynamic aspects,
such as traffic.
b) The distribution of specific plant and animal species around
the world fora specific moment in time.
c) The use of computer resources, such as processor time, main
memory, and disk, for a set of benchmark database programs.
d) The change in occupation of workers in a particular country
over the last thirty years. Assume that you have yearly
information about each person that also includes gender and
level of education.
Be sure to address the following issues:
· Representation. How will you map objects, attributes, and
relation-ships to visual elements?
· Arrangement. Are there any special considerations that need to
be taken into account with respect to how visual elements are
displayed? Specific examples might be the choice of viewpoint,
the use of transparency, or the separation of certain groups of
objects.
· Selection. How will you handle a large number of attributes
and data objects
6. Describe one advantage and one disadvantage of a stem and
leaf plot with respect to a standard histogram.
7. How might you address the problem that a histogram depends
on the number and location of the bins?
8. Describe how a box plot can give information about whether
the value of an attribute is symmetrically distributed. What can
you say about the symmetry of the distributions of the attributes
shown in Figure 3.11?
9. Compare sepal length, sepal width, petal length, and petal
width, using Figure3.12.
10. Comment on the use of a box plot to explore a data set with
four attributes: age, weight, height, and income.
11. Give a possible explanation as to why most of the values of
petal length and width fall in the buckets along the diagonal in
Figure 3.9.
12. Use Figures 3.14 and 3.15 to identify a characteristic shared
by the petal width and petal length attributes.
13. Simple line plots, such as that displayed in Figure 2.12 on
page 56, which shows two time series, can be used to effectively
display high-dimensional data. For example, in Figure 2.12 it is
easy to tell that the frequencies of the two time series are
different. What characteristic of time series allows the effective
visualization of high-dimensional data?
14. Describe the types of situations that produce sparse or dense
data cubes. Illustrate with examples other than those used in the
book.
15. How might you extend the notion of multidimensional data
analysis so that the target variable is a qualitative variable? In
other words, what sorts of summary statistics or data
visualizations would be of interest?
16. Construct a data cube from Table 3.14. Is this a dense or
sparse data cube? If it is sparse, identify the cells that are
empty.
17. Discuss the differences between dimensionality reduction
based on aggregation and dimensionality reduction based on
techniques such as PCA and SVD.

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FAMILY ASSESSMENT 1FAMILY ASSESSMENTIn.docx

  • 1. FAMILY ASSESSMENT 1 FAMILY ASSESSMENT Institution Affiliation Student Name Date Family-Focused Functional Assessment The questions asked in the interview with the family that agreed to participate were based on the eleven functional health patterns. The family that participated in the family health assessment program was a single parent structure, a mother with two children. The questions were directed towards the personal life of the respondent; therefore, their names will not be mentioned. It was an African American parent who is single, middle class income. The family is religious, Christians and live in the Chicago neighbourhood. It is a mother who is always there for her daughters and works hard to meet their needs. The overall health behaviour of the family include eating
  • 2. healthy meals, drink plenty of fluids, and children are given junk once in a while. The children snore and the mother works two jobs and gets time to sleep for only 5hours in a day because she works in the afternoon and evening. The family’s bowel movements are normal and temporary changes are experienced but it’s nothing to worry about. The mother creates time to engage in physical activities, twice a week and the types of exercises she does are morning runs and home work-out just to keep fit. She makes all the decisions that involve her children’s schooling and future plans, and she reported that she doesn’t get confused. She has healthy eyesight. She feels that the future will be great because she has done several investments that will yield positive outcomes. Children are disciplined using praise positive behaviour because she wants her children to grow into a functional family that does not instil fear and reflect negative behaviour when they become adults. She has started seeing someone recently and has never experienced any sexual dysfunction. The most recent stressful event she experienced is increased pressure from work and creating time to spend with her children. Unfortunately, coping strategies were not well defined. The current health of the family is moderate considering the constraints that the single parent has to undergo to ensure that the children are happy and safe. The family eats a healthy diet that includes vegetables and fruits with less junk food. Based on the findings of the role relationship, I saw this as strength because the parent disciplines her daughters through praise positive behaviour. Descriptive praise is what she mentioned that works best for her children. Descriptive praise means that a parent takes the initiative to tell their children exactly what they like. Praise helps change a child’ negative behaviour and based on what I observed her children are disciplined, they have confidence and self-esteem, (Campbell- Salome, et.al, 2019). At times, she has to use rewards to encourage her two daughters to perform well in academics and at home. The healthy diet and drinking more fluids habit is
  • 3. another strength that the family practices. This is because healthy diet that has plenty vegetables and water reduces the chances of getting chronic diseases such as cancer, obesity and heart disease. Stress from work and long hours are a barrier to the health of the mother and children as well because they do not get enough attention from their mother. Another barrier to health is lack of enough sleep because she only gest to rest for 4 hours. Lack of enough sleep impedes good health; it can escalate to serious conditions such as high blood pressure and diabetes, (Kaakinen, et.al, 2018). Lack of coping strategies also impedes an individual’s ability to make sound decisions. Being able in a position to be able to deal with stress is detrimental because it can affect other aspects of life and overall health of a person. Family systems theory is a theoretical framework of human behaviour that views the family as an emotional unit and provides insights about the complex interactions in the unit. Family systems theory can help to solicit changes in family members because families tend to affect an individual’s thoughts, actions and feelings, (Healy & Allen, 2019). Emotional interdependence can help promote cooperation and cohesiveness which requires one to feed, shelter and protect their family members. Family members’ actions and emotions may be affected positively or negatively because a change in one person’s sparks changes in how other people around are them will act and feel. In every family, there is that one person who absorbs all the emotions of the family and may suffer depression and even physical health. Families can work together to alleviate their problems instead of letting the negative emotions to take a toll on the entire family. Families need to be emotionally independent to achieve positive changes in family functions.
  • 4. Questions Values/Health Perception: How healthy is your family? Nutrition: How many hours of sleep do you get on working days? Does anyone in your family snore? Sleep/Rest: How would you describe your diet? Elimination: Have you ever experienced any abnormal bowel movements? Activity/Exercise: Do you create time to exercise? What types of exercise do you engage in? Cognitive: Do you ever experience confusion? How do you make decisions in the house? Sensory-Perception: How healthy is your eyesight? Self-Perception: Where do you see yourself in future? Role Relationship: How do you discipline your children? Sexuality: How often do you have sex? Have you experienced a sexual dysfunction? Coping: Have you experienced any form of stress recently? What methods do you use to when coping with stress? References Campbell-Salome, G., Rauscher, E. A., & Freytag, J. (2019). Patterns of Communicating About Family Health History: Exploring Differences in Family Types, Age, and Sex. Health Education & Behavior, 46(5), 809-817. Healy, R. W., & Allen, L. R. (2019). Bowen Family Systems
  • 5. Therapy with Transgender Minors: A Case Study. Clinical Social Work Journal, 1-10. Kaakinen, J. R., Coehlo, D. P., Steele, R., & Robinson, M. (2018). Family health care nursing: Theory, practice, and research. FA Davis. Data Mining: Exploring Data Lecture Notes for Chapter 3 Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler Look for accompanying R code on the course web site. brins Rectangle © Tan,Steinbach, Kumar Introduction to Data Mining 8/05/2005 ‹#› Techniques Used In Data Exploration Tukey – The focus was on visualization – Clustering and anomaly detection were viewed as exploratory techniques – In data mining, clustering and anomaly detection are major areas of interest, and not thought of as just
  • 6. exploratory of data exploration, we focus on – Summary statistics – Visualization – Online Analytical Processing (OLAP) brins Rectangle brins Rectangle What is data exploration? • Key motivations of data exploration include - Helping to select the right tool for preprocessing or analysis - Making use of humans’ abilities to recognize patterns • People can recognize patterns not captured by data analysis tools • Related to the area of Exploratory Data Analysis (EDA) - Created by statistician John Tukey - Seminal book is "Exploratory Data Analysis" by Tukey - A nice online introduction can be found in Chapter 1 of the NIST Engineering Statistics Handbook http://www.itl.nist.gov/div898/handbook/index.htm A preliminary exploration of the data to better understand its characteristics.
  • 7. http://www.itl.nist.gov/div898/handbook/index.htm Iris Sample Data Set • Many of the exploratory data techniques are illustrated with the Iris Plant data set. - Can be obtained from the UCI Machine Learning Repository http://www.ics.uci.edu/~mlearn/MLRepository.html - From the statistician R.A. Fisher - Three flower types (classes): • Setosa • Virginica • Versicolour - Four (non-class) attributes • Sepal width and length • Petal width and length Virginica. Robert H. Mohlenbrock. USDA NRCS. 1995. Northeast wetland flora: Field office guide to plant species. Northeast National Technical Center, Chester, PA. Courtesy of USDA NRCS Wetland Science Institute. Summary Statistics • Summary statistics are numbers that summarize properties of the data
  • 8. - Summarized properties include location and spread for continuous data • Examples: location - mean spread - standard deviation - Most summary statistics can be calculated in a single pass through the data Frequency and Mode • The frequency of an attribute value is the percentage of time the value occurs in the data set - For example, given the attribute ‘gender’ and a representative population of people, the gender ‘female’ occurs about 50% of the time. • The mode of an attribute is the most frequent attribute value • The notions of frequency and mode are typically used with categorical data Measures of Location: Mean and Median • The mean is the most common measure of the location of a set of points. • However, the mean is very sensitive to outliers.
  • 9. • Thus, the median or a trimmed mean is also commonly used. Measures of Spread: Range and Variance • Range is the difference between the max and min • The variance or standard deviation is the most common measure of the spread of a set of points. • However, this is also sensitive to outliers, so that other measures are often used. Percentiles x p x p Median – 50% of the cases has a smaller value & 50% are larger Multivariate Summary Statistics Object x
  • 10. 1 x 2 1 12 15 2 2 4 ... ... ... m 18 4 • Covariance between features i and j • Correlation si is the variance of feature i sij= 1 m−1 ∑ k=1 m ( xki− x̄ i)(xkj−x̄ j) r ij= sij si s j
  • 11. Topics • Exploratory Data Analysis • Summary Statistics • Visualization Visualization Visualization is the conversion of data into a visual or tabular format so that the characteristics of the data and the relationships among data items or attributes can be analyzed or reported. • Visualization of data is one of the most powerful and appealing techniques for data exploration. - Humans have a well developed ability to analyze large amounts of information that is presented visually - Can detect general patterns and trends - Can detect outliers and unusual patterns Example: Sea Surface Temperature • The following shows the Sea Surface Temperature (SST) for July 1982 - Tens of thousands of data points are summarized in a single figure
  • 12. Representation • Is the mapping of information to a visual format • Data objects, their attributes, and the relationships among data objects are translated into graphical elements such as points, lines, shapes, and colors. • Example: - Objects are often represented as points - Their attribute values can be represented as the position of the points or the characteristics of the points, e.g., color, size, and shape - If position is used, then the relationships of points, i.e., whether they form groups or a point is an outlier, is easily perceived. Arrangement • Is the placement of visual elements within a display • Can make a large difference in how easy it is to understand the data • Example:
  • 13. Selection • Is the elimination or the deemphasis of certain objects and attributes • Selection may involve the choosing a subset of attributes - Dimensionality reduction is often used to reduce the number of dimensions to two or three - Alternatively, pairs of attributes can be considered • Selection may also involve choosing a subset of objects - A region of the screen can only show so many points - Can sample, but want to preserve points in sparse areas Histograms • Usually shows the distribution of values of a single variable • Divide the values into bins and show a bar plot of the number of objects in each bin. • The height of each bar indicates the number of objects • Shape of histogram depends on the number of bins • Example: Petal Width (10 and 20 bins, respectively) Empirical Cumulative Distribution Function (ECDF)
  • 14. • Probability Density Function (PDF): describes the relative likelihood for this random variable to take on a given value • Cumulative Distribution Function (CDF): Shows the distribution of data as the fraction of points that are less than this value. CDF PDF Example: ECDF Two-Dimensional Histograms • Show the joint distribution of the values of two attributes • Example: petal width and petal length - What does this tell us? Box Plots • Invented by J. Tukey • Another way of displaying the distribution of data • Following figure shows the basic part of a box plot
  • 15. outlier 25th percentile – 1.5 IQR 25th percentile 75th percentile 50th percentile 75th percentile + 1.5 IQR IQR Q1 Q3 IQR Median Q3 + 1.5 × IQRQ1 − 1.5 × IQR −0.6745 σ 0.6745 σ 2.698 σ−2.698 σ 50%24.65% 24.65% 68.27% 15.73%15.73% −4 σ −3 σ −2 σ −1 σ 0 σ 1 σ 3 σ2 σ 4 σ −4 σ −3 σ −2 σ −1 σ 0 σ 1 σ 3 σ2 σ 4 σ −4 σ −3 σ −2 σ −1 σ 0 σ 1 σ 3 σ2 σ 4 σ
  • 16. Example of Box Plots • Box plots can be used to compare attributes Scatter Plots - Attributes values determine the position - Two-dimensional scatter plots most common, but can have three-dimensional scatter plots - Often additional attributes can be displayed by using the size, shape, and color of the markers that represent the objects - It is useful to have arrays of scatter plots can compactly summarize the relationships of several pairs of attributes • See example on the next slide Scatter Plot Array of Iris Attributes Contour Plots - Useful when a continuous attribute is measured
  • 17. on a spatial grid - They partition the plane into regions of similar values - The contour lines that form the boundaries of these regions connect points with equal values - The most common example is contour maps of elevation - Can also display temperature, rainfall, air pressure, etc. provided on the next slide Contour Plot Example: SST Dec, 1998 Celsius Matrix Plots - Can plot a data matrix - Can be useful when objects are sorted according to class - Typically, the attributes are normalized to prevent one attribute from dominating the plot - Plots of similarity or distance matrices can also
  • 18. be useful for visualizing the relationships between objects Visualization of the Iris Data Matrix standard deviation Deviation form feature mean Visualization of the Iris Correlation Matrix Parallel Coordinates – Used to plot the attribute values of high- dimensional data – Instead of using perpendicular axes, use a set of parallel axes – The attribute values of each object are plotted as a point on each corresponding coordinate axis and the points are connected by a line – Thus, each object is represented as a line – Often, the lines representing a distinct class of objects group together, at least for some attributes – Ordering of attributes is important in seeing such
  • 19. groupings Parallel Coordinates Plots for Iris Data Reordered features Other Visualization Techniques Star Plots - Similar approach to parallel coordinates, but axes radiate from a central point - The line connecting the values of an object is a polygon Chernoff Faces - Approach created by Herman Chernoff - This approach associates each attribute with a characteristic of a face - The values of each attribute determine the appearance of the corresponding facial characteristic - Each object becomes a separate face - Relies on human’s ability to distinguish faces Star Plots for Iris Data
  • 20. Setosa Versicolor Virginica Chernoff Faces for Iris Data Setosa Versicolor Virginica OLAP • On-Line Analytical Processing (OLAP) was proposed by E. F. Codd, the father of the relational database. • Relational databases put data into tables, while OLAP uses a multidimensional array representation. – Such representations of data previously existed in statistics and other fields • There are a number of data analysis and data exploration operations that are easier with such a data representation.
  • 21. Creating a Multidimensional Array • Two key steps in converting tabular data into a multidimensional array. – First, identify which attributes are to be the dimensions and which attribute is to be the target attribute whose values appear as entries in the multidimensional array. • The attributes used as dimensions must have discrete values • The target value is typically a count or continuous value, e.g., the cost of an item • Can have no target variable at all except the count of objects that have the same set of attribute values – Second, find the value of each entry in the multidimensional array by summing the values (of the target attribute) or count of all objects that have the attribute values corresponding to that entry. Example: Iris data • We show how the attributes, petal length, petal width, and species type can be converted to a multidimensional array – First, we discretized the petal width and length to have categorical values: low, medium, and high
  • 22. – We get the following table - note the count attribute Example: Iris data (continued) • Each unique tuple of petal width, petal length, and species type identifies one element of the array. • This element is assigned the corresponding count value. • The figure illustrates the result. • All non-specified tuples are 0. Example: Iris data (continued) • Slices of the multidimensional array are shown by the following cross-tabulations • What do these tables tell us?
  • 23. OLAP Operations: Data Cube • The key operation of a OLAP is the formation of a data cube • A data cube is a multidimensional representation of data, together with all possible aggregates. • By all possible aggregates, we mean the aggregates that result by selecting a proper subset of the dimensions and summing over all remaining dimensions. • For example, if we choose the species type dimension of the Iris data and sum over all other dimensions, the result will be a one-dimensional entry with three entries, each of which gives the number of flowers of each type. Data Cube Example • Consider a data set that records the sales of products at a number of company stores at various dates. • This data can be represented as a 3 dimensional array • There are 3 two-dimensional aggregates (3 choose 2 ), 3 one-dimensional aggregates, and 1 zero-dimensional aggregate (the overall total)
  • 24. Data Cube Example (continued) • The following figure table shows one of the two dimensional aggregates, along with two of the one-dimensional aggregates, and the overall total OLAP Operations: Slicing and Dicing • Slicing is selecting a group of cells from the entire multidimensional array by specifying a specific value for one or more dimensions. • Dicing involves selecting a subset of cells by specifying a range of attribute values. – This is equivalent to defining a subarray from the complete array. • In practice, both operations can also be accompanied by aggregation over some dimensions. OLAP Operations: Roll-up and Drill-down • Attribute values often have a hierarchical
  • 25. structure. – Each date is associated with a year, month, and week. – A location is associated with a continent, country, state (province, etc.), and city. – Products can be divided into various categories, such as clothing, electronics, and furniture. • Note that these categories often nest and form a tree or lattice – A year contains months which contains day – A country contains a state which contains a city OLAP Operations: Roll-up and Drill-down • This hierarchical structure gives rise to the roll- up and drill-down operations. – For sales data, we can aggregate (roll up) the sales across all the dates in a month. – Conversely, given a view of the data where the time dimension is broken into months, we could split the monthly sales totals (drill down) into daily sales totals. – Likewise, we can drill down or roll up on the location or product ID attributes. ITS-632 Intro to Data Mining
  • 26. Dr. Patrick Haney Dept. of Information Technology & School of Computer and Information Sciences University of the Cumberlands Chapter 3 Assignment [Your Name Here] 1. Obtain one of the data sets available at the UCI Machine Learning Repository and apply as many of the different visualization techniques described in the chapter as possible. The bibliographic notes and book Web site provide pointers to visualization software. 2. Identify at least two advantages and two disadvantages of using color to visually represent information. 3. What are the arrangement issues that arise with respect to three-dimensional plots? 4. Discuss the advantages and disadvantages of using sampling to reduce the number of data objects that need to be displayed. Would simple random sampling (without replacement) be a good approach to sampling? Why or why not? 5. Describe how you would create visualizations to display information that de-scribes the following types of systems. a) Computer networks. Be sure to include both the static aspects of the network, such as connectivity, and the dynamic aspects, such as traffic. b) The distribution of specific plant and animal species around the world fora specific moment in time. c) The use of computer resources, such as processor time, main
  • 27. memory, and disk, for a set of benchmark database programs. d) The change in occupation of workers in a particular country over the last thirty years. Assume that you have yearly information about each person that also includes gender and level of education. Be sure to address the following issues: · Representation. How will you map objects, attributes, and relation-ships to visual elements? · Arrangement. Are there any special considerations that need to be taken into account with respect to how visual elements are displayed? Specific examples might be the choice of viewpoint, the use of transparency, or the separation of certain groups of objects. · Selection. How will you handle a large number of attributes and data objects 6. Describe one advantage and one disadvantage of a stem and leaf plot with respect to a standard histogram. 7. How might you address the problem that a histogram depends on the number and location of the bins? 8. Describe how a box plot can give information about whether the value of an attribute is symmetrically distributed. What can you say about the symmetry of the distributions of the attributes shown in Figure 3.11? 9. Compare sepal length, sepal width, petal length, and petal width, using Figure3.12. 10. Comment on the use of a box plot to explore a data set with four attributes: age, weight, height, and income.
  • 28. 11. Give a possible explanation as to why most of the values of petal length and width fall in the buckets along the diagonal in Figure 3.9. 12. Use Figures 3.14 and 3.15 to identify a characteristic shared by the petal width and petal length attributes. 13. Simple line plots, such as that displayed in Figure 2.12 on page 56, which shows two time series, can be used to effectively display high-dimensional data. For example, in Figure 2.12 it is easy to tell that the frequencies of the two time series are different. What characteristic of time series allows the effective visualization of high-dimensional data? 14. Describe the types of situations that produce sparse or dense data cubes. Illustrate with examples other than those used in the book. 15. How might you extend the notion of multidimensional data analysis so that the target variable is a qualitative variable? In other words, what sorts of summary statistics or data visualizations would be of interest? 16. Construct a data cube from Table 3.14. Is this a dense or sparse data cube? If it is sparse, identify the cells that are empty. 17. Discuss the differences between dimensionality reduction
  • 29. based on aggregation and dimensionality reduction based on techniques such as PCA and SVD.