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Tile-based parallel coordinates and its application in financial visualization
Jamal Alsakran, Ye Zhao
Kent State University, Department of Computer
Science, Kent, OH
and Xinlei Zhao
Kent State University, Department of Finance, Kent, OH
Office of the Comptroller of the Currency, Washington, USA
Motivation
Visual clutter usually weakens or even diminishes
parallel coordinates ability when the data size increases
Visualization interactivity allows users to gain wider
insight into the data
Financial data analysis is a significant application domain
for visual analytics
Background
Johansson et al (05,06) propose high textures to
represent the data, and first introduced an opacity
transfer function to reveal structures of the data
Zhou et al (08) propose energy minimization to perform
visual clustering, where they used transfer functions to
assign opacity and colors to different clusters
In financial data, Theme River, Growth Matrix, Pixel-
based …etc
Tile-based Parallel Coordinates
Parallel coordinates plotting area defines an image,
I(W,H), with width W and height H
Each data item q is projected as a polyline on the image,
I(W,H)
For each fragment I(x,y), where 0 ≤ x < W and 0 ≤ y < H,
we compute the number of lines intersecting with it,
denoting as D(x,y)
A polyline-intersection density image D(W,H) is
generated.
Tile-based Parallel Coordinates
Tile-based PC promotes the traditional pixel-based
perspective of plotting to a new stage, by defining each
fragment as a rectangular region of the image space with
a user-specified size
A classical PC plot can simply be achieved by assigning
each fragment for one pixel in the image space
Tile-based Parallel Coordinates
X Y
W
H
I(x,y)
Tile-based Parallel Coordinates
X Y
W
H
I(x,y)
Tile-based Parallel Coordinates
X Y
W
H
I(x,y)
Tile-based Parallel Coordinates
X Y
W
H
I(x,y)
Color and Opacity TFs
Transfer functions are employed to assign local optical
attributes according to the density values
For each fragment I(x,y), we define four transfer
functions TF to determine the three color elements, R, G,
B, and the opacity, O, from its density value D(x,y)
The histogram of the densities is plotted to facilitate the
manipulation of the transfer functions
Color and Opacity TFs
density
Occurrence
Histogram
Fast Computing of Line-Tile Intersection
Immediate visual feedback when users continuously
change the tile size is crucial to guarantee interactivity
A fast computing algorithm is employed (Bresenham
algorithm)
To fully utilize Bresenham algorithm, we perform a
coordinates transformation, which scales each tile to one
pixel
Fast Computing of Line-Tile Intersection
Example
Original plot # tiles = 450
# tiles = 20# tiles = 150
U.S. stocks during years (2000 to 2007)477,074 data items
Case Study: Mutual Funds
Mutual fund allows a group of investors to pool their
money together and invest.
In our study, we have 5785 funds
Each data item represents one mutual fund, whose
characteristics are investigated to find its correlation with
the annual return
The study examines the most significant characteristics
including total net asset size, cash holdings, front-end
load, rear-end load, expense ratios, and turnovers
Front Load vs. Return
# of tiles = 100
# of tiles = 20
Turnover vs. Return with Outliers
It easily accommodate emphasized outliers together with the main trend
It emphasizes crucial data items while keeping the whole data as a background view
outliers are more easily to be compared with mainstream data
Analyzing Statistical Regression with Visualization
Tile-based PC is used to visually analyze the performance of a traditional statistical method widely used by financial analysts
The standard linear regression model that assumes a linear relation between the explanatory variables and the dependent variable
Estimated return = coef * characteristic + interp.
Comparison shows that our method is more informative
Analyzing Statistical Regression with Visualization
Real Data Regression Data
Multiple Clusters Visualization
Full Attributes Visualization with Outliers
The red polyline represents the best performer, Dreyfus Premier Greater China B (DPCBX), which produced 85% return for investors.
The purple polyline is the second-best mutual fund, Old Mutual Clay Finlay China C (OMNCX)
The best performers achievement in the year 2006 has no direct relation with their fund properties and managing activities
Conclusion
A novel tile-based density and transfer functions to for
visual cluttering reduction
The tile-based parallel coordinates technique improves
the performance, yields more controllability and
promotes the visual understanding
Visual analytical results on financial data set of 2006 U.S
mutual funds illustrate the potential of using the method
in financial economics