UNIT -1

UNIT-I:
Introduction and Data Foundation: Basics - Relationship between Visualization and Other Fields-
The Visualization Process - Pseudo code Conventions - The Scatter plot. Data Foundation - Types of
Data - Structure within and between Records - Data Preprocessing - Data Sets

References:
1.Matthew Ward, Georges Grinstein and Daniel Keim, : Interactive Data Visualization Foundations,
Techniques, Applications “,2010

1.1Basics:
Visualization
• We define visualization as the communication of information using
graphical representations.
• Pictures have been used as a mechanism for communication since
before the formalization of written language
• A single picture can contain a wealth of information that can be
processed much more quickly than a comparable page of words
• This is because image interpretation is performed in parallel within the
human perceptual system, while the speed of text analysis is limited by
the sequential process of reading.
Visualization in everyday life:
It is an interesting exercise to consider the number and types of data and
information visualization that we encounter in our normal activities
• a table in a newspaper, representing data being discussed in an article
• a train and subway map with times used for determining train arrivals
and departures
• a map of the region, to help select a route to a new destination
• a weather chart showing the movement of a storm front that might
influence your weekend activities
• a graph of stock market activities that might indicate an upswing (or
downturn) in the economy
 • a plot comparing the effectiveness of your pain killer to that of the
leading brand
an instruction manual for putting together a bicycle, with views specific to
each part as it is added;
• a highway sign indicating a curve, merging of lanes, or an intersection.
• Visualization is used on a daily basis in many areas of employment as
well, such as
• the result of a financial and stock market analysis;
• a mechanical and civil engineering rotary bridge design and systems
analysis;
• a breast cancer MRI for diagnosis and therapy;
• a comet path data and trend analysis;
• the analysis of human population smoking behaviors;
• the study of actuarial data for confirming and guiding quantitative
analysis;
• the simulation of a complex process
• the analysis of a simulation of a physical system;
• a visual representation of Facebook friends and their connections;
• marketing posters and advertising
Importance of Visualization:
• There are many reasons why visualization is important.
• Perhaps the most obvious reason is that we are visual beings who use
sight as one of our key senses for information understanding.
• The two examples below highlight why visualization is so important in
decision making, and the role of human preferences and training.
One example focuses on data distortion, and the other on human
interpretation
1.4 Various Visual representations:

• it is obvious that Marketing has the most consultants and that the Driver
has the longest chain of command
• The flood of data, its democratization, and the web have brought about
an increasing use of both static and interactive visualizations that are
much more aesthetic and understandable to the user
• The exploration and analysis of large marketing, financial, security,
medical, and biological data sets has led to results needing to be
explained,
An organizational chart.:
Early Visualizations:
• Perhaps the first technique for graphically recording and presenting
information was that used by early man.
• An example is the early Chauvet-Pont-d’Arc Cave, located near Vallon-
Pont-d’Arc in southern France [421].
• The Chauvet Cave contains over 250 paintings, created approximately
30,000 years ago.
• These were likely meant to pass on information to future generations.
Cave painting:

Mesopotamia Graphics:
Visualization today:
• Visualization most often provides different levels of both qualitative
and quantitative views of the information being communicated
• For example, Figure below shows a map of the Tokyo underground
• It provides an easy-toread yet logically distorted view of the criss-
crossing network of the subway system to facilitate interpretation
 • similar techniques have been used for a number of subway and other
transportation systems as well as for processes and their flows
Visualization Today:

Google maps

1.2. Relationship between Visualization and Other Fields:

Visualization, as a field, has significant relationships with several other fields
due to its multidisciplinary nature
• Here are some key relationships between visualization and other fields:
Data Science and Analytics:
 • Visualization plays a crucial role in data science and analytics by helping
to understand and communicate complex data patterns and insights
• Data visualization techniques enable analysts to explore large datasets,
identify trends, outliers, and correlations, and present their findings
effectively to both technical and non-technical audiences
Computer Science and Information Technology
• Visualization is closely linked to computer science and information
technology, particularly in terms of developing algorithms and software
tools for creating interactive and immersive visual representations.
• Computer graphics, image processing, and human-computer interaction
are among the subfields that contribute to visualization techniques and
technologies.
• Design and User Experience (UX): Visualization heavily relies on design
principles and user experience considerations to create effective and
aesthetically pleasing visual representations.
• Designers play a crucial role in developing visually engaging and intuitive
interfaces for data visualization applications, ensuring that the
information is presented in a user-friendly and accessible manner.
Difference between Visualization and Computer Graphics
Originally, visualization was considered a subfield of computer graphics,
primarily because visualization uses graphics to display information via
images. As illustrated by any of the computer-generated images shown earlier,
visualization applies graphical techniques to generate visual displays of data.
Here, graphics is used as the communication medium.
In all visualizations, one can clearly see the use of the graphics primitives
(points, lines, areas, and volumes). Beyond the use of graphics, the most
important aspect of all visualizations is their connection to data. Computer
graphics focuses primarily on graphical objects and the organization of graphic
primitives; visualizations go one step further and are based on the underlying
data, and may include spatial positions, populations, or physical measures.
Consequently, visualization is the application of graphics to display data by
mapping data to graphical primitives and rendering the display.
 However, visualization is more than simply computer graphics. The field of
visualization encompasses aspects from numerous other disciplines, including
human-computer interaction, perceptual psychology, databases, statistics, and
data mining, to name a few. While computer graphics can be used to define
and generate the displays that are used to communicate the information, the
sources of data and the way users interact and perceive the data are all
important components to understand when presenting information,
Our view is that computer graphics is predominantly focused on the creation
of interactive synthetic images and animations of three-dimensional objects,
most often where visual realism is one of the primary goals. A secondary
application of computer graphics is in art and entertainment, with video
games, cartoons, advertisements, and movie special effects as typical
examples. Visualization, on the other hand, does not emphasize visual realism
as much as the effective communication of information. Many types of
visualizations do not deal with physical objects, and those that do are often
communicating attributes of the objects that would normally not be visible,
such as material stress or fluid flow patterns. Thus, while computer graphics
and visualization share many concepts, tools, and techniques, the underlying
models (the information to be visualized) and goals (what the viewer hopes to
extract) are fundamentally different.
Thus, computer graphics consists of the tools that display the visualizations .
This includes the graphics-programming language (OpenGL, DirectX,
Processing, Java3D), the underlying graphics hardware (NVidia or ATI/AMD
graphics cards), the rendering process (flat, Gouraud, Phong, ray tracing, or
radiosity), the output format (JPEG, TIFF, AVI, MPEG), and more. We consider
computer graphics to be the underpinning of visualization and thus need to
keep abreast of it.
Scientific Data Visualization vs. Information Visualization

• Although during the 1990s and early 2000s the visualization community
differentiated between scientific visualization and information
visualization, we do not.
• Both provide representations of data.
 • However the data sets are most often different. Figure 1.25 highlights
the importance and value of having both.
• Biomolecular chemistry, which once only considered the visual
representation of molecules as stick and balls, has migrated over time

• to representations as spheres with rods, to more realistic ones, to now

including information visualizations (scatterplots and other
visualizations).

1.3. The Visualization Process

 • To visualize data, one needs to define a mapping from the data to the
display (see Figure ). There are many ways to achieve this mapping.
• The user interface consists of components, some of which deal with data
needing to be entered, presented, monitored, analyzed, and computed.
• These user interface components are often input via dialog boxes, but
they could be visual representations of the data to facilitate the
selections required by the user.
• Visualizations can provide mechanisms for translating data and tasks
into more visual and intuitive formats for users to perform their tasks.
• This means that the data values themselves, or perhaps the attributes of
the data, are used to define graphical objects, such as points, lines, and
shapes; and their attributes, such as size, position, orientation, and
color. Thus, for example, a list of numbers can be plotted by mapping
each number to the y-coordinate of a point and the number’s index in
the list to the xcoordinate. Alternatively, we could map the number to
the height of a bar or the color of a square to get a different way to view
the data.
• Visualization is often part of a larger process, which may be exploratory
data analysis, knowledge discovery, or visual analytics. In this discovery
process, the preparation of data depends upon the task and often
requires massaging erroneous or noisy data. Visualization and analysis
go hand in hand with the goal of building a model that represents or
approximates the data. Visualization in data exploration is used to
convey information, discover new knowledge, and identify structures,
patterns, anomalies, trends, and relationships.
• The process of starting with data and generating an image, a
visualization, or a model via the computer is traditionally described as
a pipeline—a sequence of stages that can be studied independently in
terms of algorithms, data structures, and coordinate systems. These
processes or pipelines are different for graphics, visualization, and
knowledge discovery, but overlap a great deal. All start with data and
end with the user.
Computer Graphics Pipeline
• Modeling. A three-dimensional model, consisting of planar polygons
defined by vertices and surface properties, is generated using a world
coordinate system.
• Viewing. A virtual camera is defined at a location in world coordinates,
along with a direction and orientation (generally given as vectors).
• All vertices are transformed into a viewing coordinate system based on
the camera parameters

• Clipping:- By specifying the bounds of the desired image (usually given

by corner positions on a plane of projection placed in front of the
• camera), objects out of view can be removed, and those that are
partially visible can be clipped.
• Objects may be transformed into a normalized viewing coordinates to
simplify the clipping process.
• Clipping can actually be performed at many different stages of the
pipeline.
• Hidden surface removal:- Polygons facing away from the camera, or
those obscured by others, are removed or clipped.
• This process may be integrated into the projection process.
 • Projection:- Three-dimensional polygons are projected onto the
twodimensional plane of projection, usually using a perspective
transformation.
• The results may be in a normalized 2D coordinate system or
device/screen coordinates
• Rendering:- The actual color of the pixels associated with a visible
polygon depends on a number of factors, including the material
properties being synthesized (base color, texture, surface roughness,
shininess), the type(s), location(s), color, and intensity of the light
source(s), the degree of occlusion from direct light exposure, and the
amount and color of light being reflected off of other objects onto the
polygon
• This process may also be applied at different stages of the pipeline (e.g.,
vertex colors can be assigned during the modeling process); however,
due to its computational complexity, it is usually performed in
conjunction with projection.
The Visualization Pipeline

The data/information visualization pipeline has some similarities to the

graphics pipeline, at least on an abstract level. The stages of this pipeline
(see Figure ) are as follows:

Data modeling. The data to be visualized, whether from a file or a database,

has to be structured to facilitate its visualization. The name, type, range,
and semantics of each attribute or field of a data record must be available
in a format that ensures rapid access and easy modification
Data selection. Similar to clipping, data selection involves identifying the
subset of the data that will be potentially visualized. This can occur totally
under user control or via algorithmic methods, such as cycling through time
slices or automatically detecting features of potential interest to the user
Data to visual mappings. The heart of the visualization pipeline is performing
the mapping of data values to graphical entities or their attributes. Thus, one
component of a data record may map to the size of an object, while others
might control the position or color of the object. This mapping often involves
processing the data prior to mapping, such as scaling, shifting, filtering,
interpolating, or subsampling
Scene parameter setting (view transformations). As in traditional graphics, the
user must specify several attributes of the visualization that are relatively
independent of the data. These include color map selection (for different
domains, certain colors have clearly defined meaning), sound map selection (in
case the auditory channels will be conveying information as well), and lighting
specifications (for 3D visualizations).
Rendering or generation of the visualization. The specific projection or
rendering of the visualization objects varies according to the mapping being
used; techniques such as shading or texture mapping might be involved,
although many visualization techniques only require drawing lines and
uniformly shaded polygons. Besides showing the data itself, most visualizations
also include supplementary information to facilitate interpretation, such as
axes, keys, and annotations
The Knowledge Discovery Pipeline
The knowledge discovery (also called data mining) field has its own pipeline.
As with the graphics and visualization pipelines, we start with data; in this case
we process it with the goal of generating a model, rather than some graphics
display.
Note that the visualization pipeline can be overlaid on this knowledge
discovery (KD) pipeline. If we were to look at a pipeline for typical statistical
analysis procedures, we would find the same process structure:
Data. In the KD pipeline there is more focus on data, as the graphics and
visualization processes often assume that the data is already structured to
facilitate its display.
Data integration, cleaning, warehousing and selection. These involve
identifying the various data sets that will be potentially analyzed. Again, the
user may participate in this step. This can involve filtering, sampling,
subsetting, aggregating, and other techniques that help curate and manage the
data for the data mining step.
Data mining. The heart of the KD pipeline is algorithmically analyzing the data
to produce a model.
Pattern evaluation. The resulting model or models must be evaluated to
determine their robustness, stability, precision, and accuracy.
Rendering or visualization. The specific results must be presented to the user.
It does not matter whether we think of this as part of the graphics or
visualization pipelines; the fact is that a user will eventually need to see the
results of the process.
Interactive visualization can be used at every step of the KD pipeline. One can
think of this as computational steering.
1.4. Pseudo-code Conventions
• In our pseudo-code, we aim to convey the essence of the algorithms at
hand, while leaving out details required for user interaction, graphics
nuances, and data management
• We therefore assume that the following global variables and functions
exist in the environment of the pseudo-code
• data—The working data table
• This data table is assumed to contain only numeric values. In practice,
dimensions of the original data table that contain non-numeric values
must be somehow converted to numeric values
• When visualizing a subset of the entire original data table, the working
data table is assumed to be the subset
• m—The number of dimensions (columns) in the working data table.
Dimensions are typically iterated over using j as the running dimension
index
• n—The number of records (rows) in the working data table. Records are
typically iterated over using i as the running record index
• Normalize(record, dimension), Normalize(record, dimension, min,
max)—A function that maps the value for the given record and
dimension in the working data table to a value between min and max, or
between zero and one if min and max are not specified
• The normalization is typically linear and local to a single dimension
• However, in practice, code must be structured such that various kinds of
normalization could be used (logarithmic or square root, for example)
either locally (using the bounds of the current dimension), globally
 (using the bounds of all dimensions), or local to the active dimensions
(using the bounds of the dimensions being displayed)
• Also, in practice, one must accommodate multiple kinds of normalization
within a single visualization. For example, a scatter plot may require a
linear normalization for the x-axis and a logarithmic normalization for
the y-axis.
• Color(color)—A function that sets the color state of the graphics
environment to the specified color (whose type is assumed to be an
integer containing RGB values)
• MapColor(record, dimension)—A function that sets the color state of the
graphics environment to be the color derived from applying the global
color map to the normalized value of the given record and dimension in
the working data table
• Circle(x, y,radius)—A function that fills a circle centered at the given (x,
y)-location, with the given radius, with the color of the color state of the
graphics environment. The plotting space for all visualizations is the unit
square. In practice, this function must map the unit square to a square in
pixel coordinates
• Polyline(xs, ys)—A function that draws a polyline (many connected line
segments) from the given arrays of x- and y-coordinates.
• Polyline(xs, ys)—A function that draws a polyline (many connected line
segments) from the given arrays of x- and y-coordinates.
For geographic visualizations, the following functions are assumed to exist
in the environment:
• GetLatitudes(record), GetLongitudes(record)—Functions that retrieve
the arrays of latitude and longitude coordinates, respectively, of the
geographic polygon associated with the given record. For example, these
polygons could be outlines of the countries of the world.
• ProjectLatitudes(lats, scale), ProjectLongitudes(longs, scale) —Functions
that project arrays of latitude values to arrays of y values, and arrays of
longitude values to arrays of x values, respectively.
• For graph and 3D surface data sets, the following is provided:
 • GetConnections(record)—A function that retrieves an array of record
indices to which the given record is connect.
Arrays are indexed starting at zero.

1.5. The Scatter plot:

The scatterplot is one of the earliest and most widely used visualizations
developed. It is based on the Cartesian coordinate system.
A scatter plot uses dots to represent values for two different numeric
variables. The position of each dot on the horizontal and vertical axis indicates
values for an individual data point. Scatter plots are used to observe
relationships between variables.

The example scatter plot above shows the diameters and heights for a
sample of fictional trees.

Scatter plots’ primary uses are to observe and show relationships between two
numeric variables. The dots in a scatter plot not only report the values of
individual data points, but also patterns when the data are taken as a
whole.

Identification of correlational relationships are common with scatter plots. In

these cases, we want to know, if we were given a particular horizontal
value, what a good prediction would be for the vertical value. You will
often see the variable on the horizontal axis denoted an independent
variable, and the variable on the vertical axis the dependent variable.
 Relationships between variables can be described in many ways: positive
or negative, strong or weak, linear or nonlinear.

• The following pseudo-code renders a scatter plot of circles.

• Records are represented in the scatter plot as circles of varying location,
color, and size
• The x- and y-axes represent data from dimension numbers xDim and
yDim, respectively
• The color of the circles is derived from dimension number cDim
• The radius of the circles is derived from dimension number rDim, as well
as from the upper and lower bounds for the radius, rM in and rM ax
• Scatter plot(xDim, yDim, cDim, rDim, rM in, rM ax)

• Step1:- for each record i ✄ For each record,

• Step2:- do x ← Normalize(i, xDim) ✄ derive the location,

• Step3:- y ← Normalize(i, yDim)
 • Step4:- r ← Normalize(i, rDim, rM in, rM ax) ✄ radius,

• Step5:- MapColor(i, cDim) ✄ and color, then

• Step6:- Circle(x, y, r) ✄ draw the record as a circle.

1.6. Data Foundations:

Since every visualization starts with the data that is to be displayed, a first step
in addressing the design of visualizations is to examine the characteristics of
the data. Data comes from many sources; it can be gathered from sensors or
surveys, or it can be generated by simulations and computations. Data can be
raw (untreated), or it can be derived from raw data via some process, such as
smoothing, noise removal, scaling, or interpolation. It also can have a wide
range of characteristics and structures.
A typical data set used in visualization consists of a list of n records,
(r1, r2,...,rn)
Each record ri consists of m (one or more) observations or variables,
(v1, v2,...vm)
• An observation may be a single number/symbol/ string or a more
complex structure (discussed in more detail later in this chapter)
• A variable may be classified as either independent or dependent. An
independent variable ivi is one whose value is not controlled or affected
by another variable, such as the time variable in a time-series data set
• A dependent variable dvj is one whose value is affected by a variation in
one or more
• associated independent variables
• Temperature for a region would be considered a dependent variable, as
its value could be affected by variables such as date, time, or location
• Thus we can formally represent a record as
• ri = (iv1, iv2, . . . ivmi , dv1, dv2, . . . dvmd ),
• where mi is the number of independent variables and md is the number
of dependent variables
• With this notation we have, m = mi + md
• In many cases, we may not know which variables are dependent or
independent
Types of Data
• In its simplest form, each observation or variable of a data record
represents a single piece of information. We can categorize this
information as being ordinal (numeric) or nominal (nonnumeric).
Subcategories of each can be readily defined.
• Ordinal. The data take on numeric values:
binary—assuming only values of 0 and 1;
discrete—taking on only integer values or from a specific
subset (e.g., (2, 4, 6)); continuous—representing real values (e.g., in
the interval [0, 5]).
Nominal
The data take on nonnumeric values:
• Categorical—a value selected from a finite (often short) list of
possibilities (e.g., red, blue, green);
• Ranked—a categorical variable that has an implied ordering (e.g., small,
medium, large);
• Arbitrary—a variable with a potentially infinite range of values with no
implied ordering (e.g., addresses)
• Another method of categorizing variables is by using the mathematical
concept of scale.
Scale
Three attributes that define a variable’s measure are as follows:
• Ordering relation, with which the data can be ordered in some fashion
By definition, ranked nominal variables and all ordinal variables exhibit
this relation
• Distance metric, with which the distances can be computed between
different records. This measure is clearly present in all ordinal variables,
but is generally not found in nominal variables.
 • Existence of absolute zero, in which variables may have a fixed lowest
value. This is useful for differentiating types of ordinal variables. A
variable such as weight possesses an absolute zero, while bank balance
does not. A variable possesses an absolute zero if it makes sense to
apply all four mathematical operations (+, −, ×, ÷) to it [129].

1.7.Structure within and between Records

• Data sets have structure, both in terms of the means of representation
(syntax ), and the types of interrelationships within a given record and
between records (semantics)
Scalars, Vectors, and Tensors
• Scalars and vectors are simple variants on a more general structure
known as a tensor
• A tensor is defined by its rank and by the dimensionality of the space
within which it is defined. It is generally represented as an array or
matrix
• A scalar is a tensor of rank 0, while a vector is a tensor of rank 1. One
could use a 3 × 3 matrix to represent a tensor of rank 2 in 3D space, and
in general, a tensor of rank M in D-dimensional space requires DM data
values
• An example of a tensor that might be found in a data record would be a
transformation matrix to specify a local coordinate system.
Geometry and Grids:
Geometric structure can commonly be found in data sets, especially
those from scientific and engineering domains. The simplest method of
incorporating geometric structure in a data set is to have explicit
coordinates for each data record. Thus, a data set of temperature
readings from across the country might include the longitude and
latitude associated with the sensors, as well as the sensor values. In
modeling of 3D objects, the geometry constitutes the majority of the
data, with coordinates given for each vertex.
There are many different coordinate systems that are used for
gridstructured data, including Cartesian, spherical, and hyperbolic
 coordinates. Often, the choice of coordinate system is domain-specific,
and is partially dependent on how the data is acquired/computed, and
on the structure of the space in which the data resides.
Nonuniform, or irregular , geometry is also common.
Other Forms of Structure:
A timestamp is an important attribute that can be associated with a data
record. Time perhaps has the widest range of possible values of all
aspects of a data set, since we can refer to time with units from
picoseconds to millennia. It can also be relative or absolute in terms of
its base value. Data sets with temporal attributes can be uniformly
spaced, such as in the sampling of a continuous phenomenon, or
nonuniformly spaced, as in a business transaction database.
The following are examples of various structured data:
MRI (magnetic resonance imagery). Density (scalar), with three spatial
attributes, 3D grid connectivity;
CFD (computational fluid dynamics). Three dimensions for displacement,
with one temporal and three spatial attributes, 3D grid connectivity
(uniform or nonuniform)
Financial. No geometric structure, n possibly independent components,
nominal and ordinal, with a temporal attribute;
CAD (computer-aided design). Three spatial attributes with edge and
polygon connections, and surface properties.
Remote sensing. Multiple channels, with two or three spatial attributes,
one temporal attribute, and grid connectivity;
Census. Multiple fields of all types, spatial attributes (e.g., addresses),
temporal attribute, and connectivity implied by similarities in fields;
Social Network. Nodes consisting of multiple fields of all types, with
various connectivity attributes that could be spatial, temporal, or
dependent on other attributes, such as belonging to the same group or
having some common computed values.

•
1.8. Data Preprocessing
In most circumstances, it is preferable to view the original raw data. In
many domains, such as medical imaging, the data analyst is often
opposed to any sort of data modifications, such as filtering or
smoothing, for fear that important information will be lost or deceptive
artifacts will be added.
Viewing raw data also often identifies problems in the data set, such as
missing data, or outliers that may be the result of errors in computation
or input.
Depending on the type of data and the visualization techniques to be
applied, however, some forms of preprocessing might be necessary.

common methods for preprocessing data:

Metadata and Statistics
Information regarding a data set of interest (its metadata) and statistical
analysis can provide invaluable guidance in preprocessing the data.
Metadata may provide information that can help in its interpretation,
such as the format of individual fields within the data records.
It may also contain the base reference point from which some of the
data fields are measured, the units used in the measurements, the
symbol or number used to indicate a missing value (see below), and the
resolution at which measurements were acquired.
This information may be important in selecting the appropriate
preprocessing operations, and in setting their parameters.
Missing Values and Data Cleansing
One of the realities of analyzing and visualizing “real” data sets is that
they often are missing some data entries or have erroneous entries.
Missing data may be caused by several reasons, including, for example, a
malfunctioning sensor, a blank entry on a survey, or an omission on the
part of the person entering the data.
Segmentation involves dividing data into different regions, where each region represents a specific category or classification.

For example, in an MRI scan, data might have 256 possible values initially. These values can then be grouped into categories like bone, muscle,
fat, and skin.

Simple segmentation maps specific ranges of values directly to categories.

However, in many cases, assigning values to a category isn't straightforward and can be unclear or uncertain.
Erroneous data is most often caused by human error and can be difficult
to detect. In either case, the data analyst must choose a strategy for
dealing with these common events.
Normalization
Normalization is the process of transforming a data set so that the
results satisfy a particular statistical property.
A simple example of this is to transform the range of values a particular
variable assumes so that all numbers fall within the range of 0.0 to 1.0.
Other forms of normalization convert the data such that each
dimension has a common mean and standard deviation.
Normalization is a useful operation since it allows us to compare
seemingly unrelated variables.

Segmentation
In many situations, the data can be separated into contiguous regions,
where each region corresponds to a particular classification of the data.
For example, an MRI data set might originally have 256 possible value
point, and then be segmented into specific categories, such as bone,
muscle, fat, and skin.
Simple segmentation can be performed by just mapping disjoint ranges
of the data values to specific categories. However, in most situations,
the assignment of values to a category is ambiguous.
Sampling and Subsetting
Often it is necessary to transform a data set with one spatial resolution
into another data set with a different spatial resolution.
For example, we might have an image we would like to shrink or
expand, or we might have only a small sampling of data points and wish
to fill in values for locations between our samples.
In each case, we assume that the data we possess is a discrete sampling
of a continuous phenomenon, and therefore we can predict the values
at another location by examining the actual data nearest to it.
Sometimes, we need to change the resolution of a dataset, such as resizing an image to make it smaller or larger.

Another example is when we have only a few data points and want to estimate values for the gaps between them.

In both cases, we treat the data as samples from a continuous process and use nearby data points to predict the missing values. This approach
relies on the idea that nearby data can help us approximate unknown values.
The process of interpolation is a commonly used resampling method in
many fields, including visualization.
Dimension Reduction
In situations where the dimensionality of the data exceeds the
capabilities of the visualization technique, it is necessary to investigate
ways to reduce the data dimensionality, while at the same time
preserving, as much as possible, the information contained within.
This can be done manually by allowing the user to select the dimensions
deemed most important, or via computational techniques, such as
principal component analysis (PCA) , multidimensional scaling (MDS) ,
Kohonen self-organizing maps (SOMs) , and Local Linear Embedding (LLE)
Mapping Nominal Dimensions to Numbers
In many domains, one or more of the data dimensions consist of
nominal values.
We may have several alternative strategies for handling these
dimensions within our visualizations, depending on how many nominal
dimensions there are, how many distinct values each variable can take
on, and whether an ordering or distance relation is available or can be
derived.
The key is to find a mapping of the data to a graphical entity or attribute
that doesn’t introduce artificial relationships that don’t exist in the data.

Aggregation and Summarization

In the event that too much data is present, it is often useful to group
data points based on their similarity in value and/or position and
represent the group by some smaller amount of data.
This can be as simple as averaging the values, or there might be more
descriptive information, such as the number of members in the group
and the extents of their positions or values.

Smoothing and Filtering

In graphics and visualization:

Raster data is pixel-based (like an image).

Vector data uses shapes like lines and polygons (e.g., maps with roads).
Sometimes, we need to convert raster data into vector forms to extract meaningful structures, like roads from a satellite image.

A common process in signal processing is to smooth the data values, to

reduce noise and to blur sharp discontinuities.
A typical way to perform this task is through a process known as
convolution, which for our purposes can be viewed as a weighted
averaging of neighbors surrounding a data point.
Raster-to-Vector Conversion
In computer graphics, objects are typically represented by sets of
connected, planar polygons (vertices, edges, and triangular or
quadrilateral patches), and the task is to create a raster (pixel-level)
image representing these objects, their surface properties, and their
interactions with light sources and other objects.
In spatial data visualization, our objects can be points or regions, or they
can be linear structures, such as a road on a map.
It is sometimes useful to take a raster-based data set, such as an image,
and extract linear structures from it.

1.9 Data Sets

• djia-100.xls. A univariate, nonspatial data set consisting of 100+ years of
daily Dow Jones Industrial Averages
Source—http://www.analyzeindices.com/dow-jones-
history.shtml
Format—Excel spreadsheet. After the header, each entry is
of the form YYMMDD followed by the closing value
Code—file can be viewed with Excel
• colorado elev.vit. A two-dimensional, uniform grid, scalar field
representing the elevation of a square region of Colorado
Source—included with the distribution of OpenDX (http://www.opendx
.org/)
Format—binary file with a 268-byte header followed by a
400 × 400 array of 1-byte elevations
 Code—file can be rendered with Topo-Surface, a Processing
program included in Appendix C and on the book’s web site
• cars.xls, detroit.xls, cereal.xls. Several multivariate, non-spatial data sets
commonly used in multivariate data analysis
Source—http://lib.stat.cmu.edu
Format—Excel spreadsheets, mostly with no headers
Code—files can be viewed with Excel
• Health-related multivariate data sets. Subsets from UNICEF’s basic
indicators by country and the CDC’s obesity by state; several
multivariate, spatial data sets used with Geospatial Information Systems
Source—http://OpenIndicators.org
Format—Excel spreadsheets

Code—files can be viewed with Excel, with Weave, and with

many other visualization systems.
• iris.csv. Size data for Iris plants classified by type
Source—http://archive.ics.uci.edu/ml/datasets/Iris
Format—comma-separated values
Code—The file can be viewed with Excel or as text
city temp.xls. A two-dimensional, nonuniform, geo-spatial, scalar data
set containing the average January temperature for 56 U.S. cities.
Source—Peixoto, J.L. (1990), “A Property of Well-Formulated Polynomial
Regression Models.” American Statistician, 44, 26–30. Also found in:
Hand, D.J., et al. (1994) A Handbook of Small Data Sets, London:
Chapman & Hall, 208–210. Downloaded from http://lib.stat .cmu.edu
uvw.dat. A three-dimensional uniform grid vector field representing a
simulated flow field. The data shows one frame of the unsteady velocity
field in a turbulent channel flow, computed by a finite volume method.
The streamwise velocity (u) is much larger than the secondary velocities
in the transverse direction (v and w).
 Source—Data courtesy of Drs. Jiacai Lu and Gretar Tryggvason, ME
Department, Worcester Polytechnic Institute (http://www.me.wpi
.edu/Tryggvason).
Format—plain text. After the header, each entry is a set of 6 float values,
3 for position, 3 for displacement. There is roughly a 20:1:1 ratio
between the 3 displacements.
Code—file can be rendered with FlowSlicer, a Processing program, and
FlowView, a Java program (also need Voxel.java)