Multi-temporal Flow Maps

Looking Back to Look Forward

Alberto Debiasi and Raffaele De Amicis

Fondazione Graphitech, Trento, Italiy

1 STAGE OF THE RESEARCH

A flow map is a thematic map that is been used to

emphasize the spatial pattern of one or more

geographic attributes. Although most flow maps are

still drawn by hand, a few algorithms exist to

automatically generate this kind of thematic maps.

The flow magnitude is represented as the width

of each line, and the sum of all flow line branches

should add up to the width of the flow line (Dent,

1990). Usually the traces depicted by lines do not

correspond to the real route. In many instances the

flow magnitude is not placed over the map, so the

reader must judge relative amounts visually, without

the legend (Dent, 1990).

At present we proposed a novel algorithm for the

automatic generation of flow maps, which is

theoretically grounded on physics’ laws to describe

the motion and force of attraction or repulsion

between points. Properties associated to these laws

are then used to merge different flows, as well as for

the improvement of the maps’ visual quality (see

Figure 1f). Finally, we evaluate our work by

generating a set of flow maps and we make a

comparison with flow maps produced by existing

algorithms.

1.1 Outline of Objectives

The graphical representation of numbers started in

1750 – 1800 with the invention of time-series,

scatter plots, multivariate displays. Geographic maps

were used in the seventeenth century combining

cartographic and statistical elements. (Tufte and

Graves-Morris, 1983). Nowadays with the advent of

calculators some innovations open new possibilities

described in the following section.

1.2 The Use of the 3D

We have the ability to create more information-rich,

and dynamic visualization processes using 3D

(Spence and Press, 2000). Usually when there is the

need to represent spatio-temporal data, the time

dimension is simply associated to the z axis and this

is a limit. A smart use of this dimension can open

big opportunities to novel visualization techniques.

1.3 The Possibility to Interact

Interaction techniques allow the data analyst to

directly interact with the visualizations and

dynamically change the visualizations according to

the exploration objectives. Besides, they also make it

possible to relate and combine multiple independent

visualizations (Spence and Press, 2000). A single

static view can rarely give the whole detailed

information of the data being analysed. With the

appropriate interactive exploration techniques allow

the user to analyse the data in every detail for

example providing support for multiple tasks in a

single visualization tool.

1.4 The Use of Animations

In a visualization, animation might help a viewer

work through the logic behind an idea by showing

the intermediate steps and transitions, or show how

data collected over time changes. Animation can be

a powerful technique when used appropriately, but it

can be very bad when used poorly. Some animations

can enhance the visual appeal of the visualization

being presented, but may make exploration of the

dataset more difficul

t (Steele and Iliinsky, 2010).

The aforementioned aspects can enrich the

capabilities of the flow maps. The possibility to

visualize more than a variable will be studied, in

particular the time dimension is an aspect that lacks

in the flow maps.

Analysis of movement is currently a hot research

topic in visual analytics. Andrienko et al.,

(Andrienko et al., Visual analytics tools for analysis

of movement data, 2007) provided an overview on

the methods and tools studied for the analysis of

movement data. The problem stated in this research

regards the visualization of origin-destination data

such as flow of goods or immigration trends where

Debiasi A. and De Amicis R..

Multi-temporal Flow Maps - Looking Back to Look Forward.

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

only the origins and the destinations of the flows and

the flow magnitudes are known, but not the exact

movement routes.

Flow maps represent in a simple and clear way

origin-destination data.

The main objective is to automatically generate

flow maps and represent also multivariate attributes

with temporal dimensions through interaction

techniques, animations and the use of the 3D.

2 RESEARCH PROBLEM

The research problem faced so far is the automatic

generation of flow maps. The main aspect to take

into consideration is the necessity to reduce the

visual clutter while keeping a good visual

appearance. Due to the fact that the flows can be

considered as a rooted acyclic graph the research

problem regards the graph drawing problems. In the

graph drawing domain the emphasis is on finding a

layout, i.e., positions of nodes and edges of a given

graph that satisfies certain aesthetic criteria, e.g., few

edge crossings

device.

In visualization techniques, the usefulness of a

drawing of a graph depends on its readability, that is,

the capability of conveying the meaning of the

diagram quickly and clearly. These issues are

expressed by means of aesthetics, which can be

formulated as optimization goals for the drawing

algorithms. (Battista et al., 1994).

The major challenge is how to bring together the

spatial and temporal dimensions in a way which

makes it possible to explore the relationships

between these two aspects of the data.

In general, not much has been written on the

exploration of temporal changes in origin-

destination data. Marble et al., (1997) noted in 1997

Figure 1: Different maps representing the migration from California in 1995-2000. (a) the first software that automatically

generate flow maps (Tools, 2001), (b) algorithm taking into account aggregation of flows (Phan et al., 2005), (c) (d) the

force directed algorithms in graph drawing domain (Cui et al., 2008), (Holten and Van Wijk, 2009), (e) the algorithm based

on spiral tree (Verbeek et al., 2011), (f) the force directed algorithm described in the stage of the research.

(a)

(b)

(c)

(d)

(e)

(f)

Multi-temporalFlowMaps-LookingBacktoLookForward

that the limitations of the data and the empirical

difficulties encountered in their analysis have

restricted researchers to the examination of flows

within a single time period. This situation has not

changed much since then, and there is still a strong

need for techniques capturing the spatio-temporal

aspects simultaneously.

3 STATE OF THE ART

3.1 Automatic Generation of Flow

Maps

This section focuses on a specific domain of the

analysis of the movement that is related to the flow

maps. There are other methods used to represent

origin-destination data, anyway maps are well

familiar to everybody and allow to reason about the

geographic patterns of the movement as no other

representation.

The book “Handbook of Graph Drawing and

Visualization” (Tamassia, 2007) gives an overview

of the actual technique for the automatic generation

of flowmaps. Tobler in 1987 developed a computer

program called FlowMapper (Tools, 2001) used to

visualize migration maps; this mapper produces

generic maps without any optimization with respect

to the visualization of the data. For each flow, it

generates an arrow on the map with a width varying

accordingly to its magnitude. As the number of links

increases, it becomes increasingly difficult to

represent new flows without creating a visual clutter

(see Figure 1a). Tobler not only created the software

for basic flow mapping, but also investigated various

approaches for making flow maps more readable by

addressing their problems.

The main aspect of a flow map is the aggregation

of the flows. In 2005 Phan et al. (Phan, Xiao, Yeh,

& Hanrahan, 2005) introduced a method to reduce

the visual clutter by merging the flows (see Figure

1b). The author used a binary hierarchical clustering

formulating the layout in a simple and recursive

manner. To make the final layout of the flow map

more aesthetically pleasing, the polygonal paths that

represent the edges are drawn as Catmull-Rom

splines, that is, as special cubic curves that go

through the given points. The advantage of this

algorithm is its Ο



 time complexity, where  is

the total number of nodes used in the algorithm.

However this algorithm has a few limitations: during

the first step the nodes are moved if their proximity

is too small. Hence, it might lose the geographical

reference associated to each node. Furthermore, if

there are too many destination nodes in a small area,

by forcing binary splits introduces too many extra

routing nodes, which then leads to clutter.

Verbeek et al., (2011) describes a method to

overcome the aforementioned limitations through

the use of spiral trees. The authors used spiral spline

(Buchin et al., 2011), which have Ο log 

complexity, to generate maps that are crossing-free.

Another key property concerns the weights of the

leaves. If there are two flow maps with the same

origin and destinations but with different

magnitudes, then the layout of the flow map will be

represented differently. Moreover the flow tree

produced is constrained to avoid crossing its own

nodes, as well as user-specified obstacles (see Figure

1e). In order to have a high-quality map, a quality

function that takes into account the obstacles, the

smoothness, the angles and the straightness, has to

be minimized. The time required to perform a flow

map is mentioned in the paper as a “couple of

minutes”. Two limitations of this algorithm are the

complexity in the construction of the tree structure

and the non-intuitive body cost function used to

improve the aesthetic results.

The reduction of visual clutter has been studied

extensively in the graph drawing domain. The

objectives are not the same of the methods described

above but the following works have some points in

common. Cui et al., (2008) use a control mesh that

reflects the underlying control pattern reducing the

visual clutter (see figure Figure 1c). Holten and van

Wijk (2009) presented a force-directed algorithm in

which the edges are modelled as flexible springs that

can attract each other while node positions remain

fixed (see Figure 1d). The input to these methods is

a graph rather than a tree; in the output, the curved

edges are bundled in order to better reflect the

structure of the graph.

The automatic method for the flow map

generators do not permits to visualize multivariate

variables and in particular the time dimension. Some

techniques to use in conjunction with the flow maps

are developed in order to overcome the above

limitations.

The “small multiples” display is one of the most

often used techniques for representing temporal data.

It uses multiple charts laid side-by-side and

corresponding to consecutive time periods or

moments in time (Boyandin et al., Using flow maps

to explore migrations over time, 2010). The problem

with this technique is the scalability: the more small

multiples are represented, the more difficult it is to

see the details. Animation can be used to show how

flows of subsequent time periods change (Becker et

VISIGRAPP2014-DoctoralConsortium

Figure 2: Some examples of multivariate visualizations with the 3rd dimension used to depict time.

al., 1995). An animated flow map showing

thousands of flow lines could hardly be accurately

perceived as it would be too difficult to keep track of

changes in it.

A direct embedding into a flow map would mean

representing the temporal changes by mapping

temporal data to each of the visual features of the

flow lines (color, size etc). A more sophisticated

way of embedding might be able to overcome this

problem though (Boyandin et al., 2011).

3.2 Alternative Techniques for

Origin-destination Data

There are also techniques that are able to represent

also the time dimension such as the “flowstrates”

(Boyandin et al., 2011). It provides means of

interaction for controlling filtering, zooming and

aggregation: the origins and the destinations of the

flows are displayed in two separate maps, and the

changes over time of the flow magnitudes are

represented in a separate heatmap view in the

middle. Mosaic diagrams were introduced in

(Andrienko and Andrienko, Spatio-temporal

aggregation for visual analysis of movements, 2008)

for displaying spatiotemporal patterns in traffic

situations. A set of multiple small calendar-like

views representing temporal data are displayed in a

regular rectangular grid on top of a geographic map.

Distorting map projections are sometimes used to

make geographic maps more readable or to highlight

the most important elements in them. (Stefaner,

2010), (Wood and Dykes, 2008) and (Brunet, 1986)

provided some techniques.

When the 3D representation is included one of

the dimensions is used to show the temporal changes

and the two others for a 2D representation of the

data at each specific moment in time. (Proulx,

Khamisa and Harper), (Adali, Eren, Turk and

Balcisoy); (Tominski et al., 2005) are some example

of this approach.

Multi-temporalFlowMaps-LookingBacktoLookForward

Figure 3: This maps show some kind of connections in a 2D map using arcs in 3D. The main idea is to merge the flows with

the same origin in order to reduce the visual clutter. The concept is the same of aggregation techniques in 2D flow maps but

in a 3D environment.

Figure 4: Sketch of a possible visualization technique. Two 2D maps connected with flows. Each flow line depicts the

temporal pattern.

4 METHODOLOGY

The methodology of this research is divided into the

following steps:

1. Study the available techniques for temporal OD-

data visualization, describing in which way the

animation, the interaction and the 3rd dimension

are used.

VISIGRAPP2014-DoctoralConsortium

2. Define which are the tasks the tool can support;

3. Define in which way the interaction metaphor,

the 3D and the animation techniques can be used

in order to represent multivariate attributes with

temporal dimensions.

4. Implement the algorithm on a target platform.

5. Perform a user study to evaluate the proposed

tool. Interview will be done and an analysis on

the user interaction must be performed.

5 EXPECTED OUTCOME

The first results will be a list of novel methods for

the depiction of origin destination data, using the 3

dimension in conjunction with interaction metaphors

and animations. The basic idea is to use the 3

dimension not only as a way to depict the time

dimension.

A first idea can be the definition of an algorithm

for the creation of flow maps with aggregation

techniques but enriched for a 3D environment (see

Figure 3).

Another idea can be the use of 2D maps but in a

3D environment with flows connecting both maps,

one representing the origin and the other

representing the destinations. In this way should be

possible to use flows as temporal indicator (see

Figure 4).

The next outcome will be a developed tool with

the algorithms implemented. This tool will be used

to evaluate the techniques with the users.

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