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 & 4 Assignment
[Dharmin Nareshbhai Patel]
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.
Ans) MATLAB and R have excellent facilities for visualization. Most of the figures in this chapter
were created using MATLAB. R is freely available from http://www.r-project.org/.
Identify at least two advantages and two disadvantages of using color to visually represent
Ans) Advantages: Color makes it much easier to visually distinguish visual elements from one
another. For example, three clusters of two-dimensional points are more readily distinguished if the
markers representing the points have different colors, rather than only different shapes. Also,
figures with color are more interesting to look at.
Disadvantages: Some people are color blind and may not be able to properly interpret a color
figure. Grayscale figures can show more detail in some cases. Color can be hard to use properly.
For example, a poor color scheme can be garish or can focus attention on unimportant
What are the arrangement issues that arise with respect to three-dimensional plots?
Ans) It would have been better to state this more generally as “What are the issues . ” since
selection, as well as arrangement plays a key issue in displaying a three-dimensional plot. The key
issue for three dimensional plots is how to display information so that as little information is
obscured as possible. If the plot is of a twodimensional surface, then the choice of a viewpoint is
critical. However, if the plot is in electronic form, then it is sometimes possible to interactively
change the viewpoint to get a complete view of the surface. For three dimensional solids, the
situation is even more challenging. Typically, portions of the information must be omitted in order
to provide the necessary information. For example, a slice or cross-section of a three dimensional
object is often shown. In some cases, transparency can be used. Again, the ability to change the
arrangement of the visual elements interactively can be helpful.
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?
Ans) Simple random sampling is not the best approach since it will eliminate most of the points in
sparse regions. It is better to under sample the regions where data objects are too dense while
keeping most or all of the data objects from sparse regions.
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
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
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
Ans) (a) Computer networks. Be sure to include both the static aspects of the network, such as
connectivity, and the dynamic aspects, such as traffic.
The connectivity of the network would best be represented as a graph, with the nodes being
routers, gateways, or other communications devices and the links representing the connections.
The bandwidth of the connection could be represented by the width of the links. Color could be
used to show the percent usage of the links and nodes.
(b) The distribution of specific plant and animal species around the world for a specific moment
The simplest approach is to display each species on a separate map of the world and to shade
the regions of the world where the species occurs. If several species are to be shown at once,
then icons for each species can be placed on a map of the world.
(c) The use of computer resources, such as processor time, main memory, and disk, for a set of
benchmark database programs.
The resource usage of each program could be displayed as a bar plot of the three quantities.
Since the three quantities would have different scales, a proper scaling of the resources would
be necessary for this to work well. For example, resource usage could be displayed as a
percentage of the total. Alternatively, we could use three bar plots, one for type of resource
usage. On each of these plots there would be a bar whose height represents the usage of the
corresponding program. This approach would not require any scaling. Yet another option would
be to display a line plot of each program’s resource usage. For each program, a line would be
constructed by (1) considering processor time, main memory, and disk as different x locations,
(2) letting the percentage resource usage of a particular program for the three quantities be the
y values associated with the x values, and then (3) drawing a line to connect these three points.
Note that an ordering of the three quantities needs to be specified, but is arbitrary. For this
approach, the resource usage of all programs could be displayed on the same plot.
(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
For each gender, the occupation breakdown could be displayed as an array of pie charts, where
each row of pie charts indicates a particular level of education and each column indicates a
particular year. For convenience, the time gap between each column could be 5 or ten years.
Alternatively, we could order the occupations and then, for each gender, compute the
cumulative percent employment for each occupation. If this quantity is plotted for each gender,
then the area between two successive lines shows the percentage of employment for this
occupation. If a color is associated with each occupation, then the area between each set of
lines can also be colored with the color associated with each occupation. A similar way to show
the same information would be to use a sequence of stacked bar graphs.
Describe one advantage and one disadvantage of a stem and leaf plot with respect to a standard
Ans) A stem and leaf plot shows you the actual distribution of values. On the other hand, a stem and
leaf plot becomes rather unwieldy for a large number of values.
How might you address the problem that a histogram depends on the number and location of
Ans) The best approach is to estimate what the actual distribution function of the data looks like
using kernel density estimation. This branch of data analysis is relatively well-developed and is more
appropriate if the widely available, but simplistic approach of a histogram is not sufficient.
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?
Ans) (a) If the line representing the median of the data is in the middle of the box, then the data is
symmetrically distributed, at least in terms of the 75% of the data between the first and third quartiles.
For the remaining data, the length of the whiskers and outliers is also an indication, although, since
these features do not involve as many points, they may be misleading.
(b) Sepal width and length seem to be relatively symmetrically distributed, petal length seems to be
rather skewed, and petal width is somewhat skewed.
Compare sepal length, sepal width, petal length, and petal width, using Figure3.12.
Ans) For Setosa, sepal length > sepal width > petal length > petal width. For Versicolour and Virginiica,
sepal length > sepal width and petal length > petal width, but although sepal length > petal length, petal
length > sepal width.
10. Comment on the use of a box plot to explore a data set with four attributes: age, weight, height,
Ans) A great deal of information can be obtained by looking at (1) the box plots for each attribute, and
(2) the box plots for a particular attribute across various categories of a second attribute. For example, if
we compare the box plots of age for different categories of ages, we would see that weight increases
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.
Ans) We would expect such a distribution if the three species of Iris can be ordered according to
their size, and if petal length and width are both correlated to the size of the plant and each other.
12. Use Figures 3.14 and 3.15 to identify a characteristic shared by the petal width and petal length
Ans) There is a relatively flat area in the curves of the Empirical CDF’s and the percentile plots for both
petal length and petal width. This indicates a set of flowers for which these attributes have a relatively
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?
Ans) The fact that the attribute values are ordered.
14.Describe the types of situations that produce sparse or dense data cubes. Illustrate with
examples other than those used in the book.
Ans) Any set of data for which all combinations of values are unlikely to occur would produce sparse
data cubes. This would include sets of continuous attributes where the set of objects described by
the attributes doesn’t occupy the entire data space, but only a fraction of it, as well as discrete
attributes, where many combinations of values don’t occur. A dense data cube would tend to arise,
when either almost all combinations of the categories of the underlying attributes occur, or the level
of aggregation is high enough so that all combinations are likely to have values. For example,
consider a data set that contains the type of traffic accident, as well as its location and date. The
original data cube would be very sparse, but if it is aggregated to have categories consisting single or
multiple car accident, the state of the accident, and the month in which it occurred, then we would
obtain a dense data cube.
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?
Ans) A summary statistics that would be of interest would be the frequencies with which values or
combinations of values, target and otherwise, occur. From this we could derive conditional
relationships among various values. In turn, these relationships could be displayed using a graph
similar to that used to display Bayesian networks.
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.
Ans) The data cube is shown in belowTable , It is a dense cube; only two cells are empty.
17.Discuss the diﬀerences between dimensionality reduction based on aggregation and
dimensionality reduction based on techniques such as PCA and SVD.
Ans) The dimensionality of PCA or SVD can be viewed as a projection of the data onto a reduced set
of dimensions. In aggregation, groups of dimensions are combined. In some cases, as when days are
aggregated into months or the sales of a product are aggregated by store location, the aggregation
can be viewed as a change of scale. In contrast, the dimensionality reduction provided by PCA and
SVD do not have such an interpretation.
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