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