Since high aggregation of data values with frequent overlaps in presentation graphics such as traditional bar charts and x-y-plots presents limited number of data values, a generalization is therefore proposed to allow the visualization of large amounts of data. The pixels within the bars provide detailed information by allowing effective visualization to solve complex optimization problems using real-world e-commerce data.

1. Pixel Bar Charts: A New Technique for Visualizing Large
Multi-Attribute Data Sets without Aggregation
Khaled Mosharraf
FH Kiel
Data Mining
Report for course
mosharrafkhaled@gmail.com
ABSTRACT
Since high aggregation of data values with frequent
overlaps in presentation graphics such as traditional
bar charts and x-y-plots presents limited number of
data values, a generalization is therefore proposed to
allow the visualization of large amounts of data. The
pixels within the bars provide detailed information by
allowing effective visualization to solve complex
optimization problems using real-world e-commerce
data.
1. Introduction
With increase in data generation every year that has
been reported to about 1 Exabyte, however finding
particular information from huge stack of data is a
difficult task. Most data mining systems uses simple
graphics such as bar charts, pie charts, and x-y plots
etc which shows highly aggregated and overlapping
number of data values. Multiple bar charts do not
support discovery or correlation between subsets that
is important in mining customer transaction data.
Generally, an overview of the data and its detailed
information is required which classical bar charts are
unable to represent.
Therefore, the new visualization technique called
pixel bar chart is introduced in this paper to show
that presentation paradigm of bar charts can be made
more useful by providing detailed information. The
colored pixels within the different bars enable very
large amounts of data to be presented to the user. To
make it meaningful to the user, two parameters of
data records are used for proper ordering of pixels in
x- and y- directions and combine the idea of x-y plots
and bar charts to allow an overlap free, non-
aggregated display of multi-attribute data with a
confined space.
Pixel bar charts belong to the class of pixel oriented
techniques to use each pixel to present one data value.
Examples of pixel oriented techniques includes spiral
technique, recursive pattern technique, circle
segments technique. [1]
2. From Bar Charts to Pixel Bar Charts
Bar charts help visualize large volumes of data that
require a high degree of data aggregation and show
a). Equal-Width Bar Chart b). Equal-Height Bar Chart
Figure 1: Regular Bar Charts
rather small numbers data values, by making it
ineffective for large multidimensional data. [1]
2.1 Basic Idea of Pixel Bar Chart
Unlike Bar Charts, Pixel Bar Charts present data
values directly instead of aggregating them into a few
data values .Each data item is encoded into the pixel
color and displaying it as needed. Pixels are arranged
within each bar by one or two attributes to separate
data into bars and then two additional attributes to
impose an ordering to bars, hence a combination of
traditional bar charts and x-y diagrams. Visualization
where one pixel can be represented as one customer
can be used to present large amounts of detailed
information. This correspondence allows us to use
color of the pixels to represent an additional attribute
of the customer. [1]
a). Pixel Bar Chart
2.2 Space-Filling Pixel Bar Charts
The problem in traditional Bar Charts is screen space
cannot use differing heights and large data set.
Displayable data is used in same height and width. So
the area and bar corresponds and represent the

2. number of customers. By using space-filling pixel
bar, same partitioning, ordering, and coloring
attributes as the pixel bar chart each customer is
represented by one pixel. So pixel bar chart shows
generalization of regular bar chart and significant
analysis of large original data sets. [1]
2.3 Multi-Pixel Bar Charts
In numerous case data analyzed structure can be
multiple attributes. With pixel bar charts quality
measure the values for color mappings with the same
format. So multi-pixel bar charts are the same as the
arrangement of data items and color pixel represent
the same data have different position. The example is
shown here x is number of visit dollar and y is the
quality process according to the color with spent
dollar, visit and sale quantity. [1]
3. Formal Definition of Pixel Bar Charts
Pixel bar charts need to be solved in order to
implement an effective pixel placement algorithm. [1]
3.1 Definition of Pixel Bar Charts
General definition of pixel bar charts, specify that:
- dividing attributes (for between-bar partitioning)
- ordering attributes (for within-bar ordering)
- Coloring attributes (for pixel coloring). In
traditional bar charts there is one dividing
Bars corresponding according to horizontal axis
(x).space-filling bar and screen according to X, which
is Dx and vertical axis Dy. Then we specify ordering
every pixel in pixel bar and also ordering the x axis
and y axis which is along the horizontal (Ox) and
vertical (Oy) axes inside every bar, at the end
coloring the attribute the pixel. In multi bar different
color present there different attribute and partial
relationship. Let DB = {d1, …, dn} be the data base of
n data records, each consisting of k attribute values
}, where Al is the
Attribute name of value al. formally, a pixel bar chart
is defined by a five tuple:<Dx, Dy, Ox, Oy, C >
where Dx, Dy, Ox, Oy, C {Al, …, Ak,}1and
Dx/Dy are the dividing attributes in x/y direction,
Ox/Oy are the ordering attributes in x-/y-direction,
and C is the coloring attribute. The multi-pixel bar
charts of sales transactions shown in Figure 4, for
example, are defined by the five-tuple <product
type,, no. of visits, dollar amount, C> where C corresponds to
different attributes, i.e., number of visits, dollar
amount, quantity.
3.2Formalization of the Problem
The basic idea of pixel bar charts is to produce dense
pixel visualizations which are capable of showing
large amounts of data without aggregation.
- Dense display, bars are filled completely
- Non-overlapping, no overlap of pixels in the display
- Locality, i.e., similar data records are placed close to
each other
- ordering, i.e., ordering of data record
The screen positioning function
Int Int,
which determines the x-/y-screen positions of each
data record di, i.e., f (d ) (x, y) denotes the position of
record di on screen, and f d x i ( ).. Denotes the x-
coordinate and f d y i ( ). The y-coordinate. Without
loss of generality, we assume that Ox = A1 and Oy =
A2. [1]
1. Dense Display Constraint
For equal-width
Bar charts, the width w of the bars is fixed. For a
Partition p consisting of |p| pixels, we have to
i= 1..w, j= 1..p / w: with f ( ) =(i, j) 
For equal-height bar charts of height h the
Corresponding constraint is
i= 1..p / hj= 1.. with f ( ) =(i, j)
2.No-OverlapConstraint
the no-overlap constraint means that a unique
Position is assigned to each data record.
Formally, we have to ensure that two different
Data records are placed at different positions,
Ordering Constraint
Ordering in X- and y-direction according to the
specified Attributes Ox = A1 and Oy =A2. Formally,
we have To ensure
4. The Pixel Bar Chart System
Pixel bar charts have been integrated with a data
mining visualization system to analyze large volumes
of transaction data. The web interfaces based on
standard HTML and java applets and the system uses
browser to allow real time interactive along with a
java activator. The server is integrated with the data
warehouse and the mining engine. [1]
4.1 System Architecture and Components
The pixel bar chart system connects to a data
warehouse server and uses the database to query for
detailed data as needed. The pixel bar chart system
architecture contains three basic components which
are Pixel array ordering and grouping, multiple linked
pixel bars and Interactive data exploration. [1]
4.2 Interactive Data Analysis

3. The pixel bar chart system provides interaction
capabilities like visual querying, layered drill-down /
detail-on-demand, multiple linked visualizations and
zoom in and out of the pixel bar charts. At the
execution time partitioning, ordering, and coloring
can be sleeted and changed. To identify correlations
and highlight the values of attribute within the same
display there is a subset of data item in pixel bar
chart. When you select a single data item a drill-down
technique allows you to view all the related
information. the user can select a single data item to
relate all its attribute values.
5. Application and Evaluation
The pixel bar chart technique has been prototyped in
several e-commerce applications to visually mine
large volumes of sales transactions and customer
shopping activities at HP shopping web sites. [1]
5.1 Customer Analysis
The pixel bar chart system has been applied to
customer buying patterns and behaviors to represent
customers making transactions on the web.
Customers with similar purchasing behaviors are
placed close to each other so that store manager can
use the visualization to rapidly discover customer
buying patterns and use those patterns to target
marketing campaigns. Most important facts and
objects of customer analysis is region attribute, dollar
amount attribute, number of visits attribute and
quantity attribute. [1]
5.2 Sales Transaction Analysis
The pixel bar chart provides the additional
information like Dollar amount versus product
distribution and each customer’s detail information
drilled down as needed which can helpful to an e-
commerce manager to answer his questions regarding
top sales, top dollar amount customers and so on. [1]
Conclusion
This new method for visualizing large amounts of
multi-attribute data can be a breakthrough against
generalized bar charts and x-y diagrams that usually
lose much information by aggregation or over
plotting. Pixel bar charts therefore can solve complex
optimization problem, the placement algorithm can
effectively set real data sets from e-commerce and
present significantly useful information than regular
bar charts or x-y plots. [1]
1. REFERENCES
[1] Daniel Keim1, Ming C. Hao, Julian Ladisch1,
Meichun Hsu, Umeshwar Dayal Software Technology
Laboratory. HP Laboratories Palo Alto
HPL-2001-92 April 11th , 2001