Applying Graphical Design Techniques to Graph Visualisation

Transcription

1 Applyig Graphical Desig Techiques to Graph Visualisatio Marty Taylor, Peter Rodgers Uiversity of Ket, Uiversity of Ket Abstract This paper cotais details of ew criteria for graph layout, based o the cocepts used i graphical desig. Curret graph layout criteria have bee show to be effective i measurig the quality of a graph layout, but they are ad-hoc ad ofte miss subtle appearace cosideratios such as balace ad distributio. We discuss how the priciples cocerig the layout of text ad diagrams from desig ca be applied to graph layout ad show how two ew metrics ca be implemeted based o these criteria. We also give prelimiary examples of layout geerated usig the ew metrics. 1. Itroductio Over the past few years there has bee much work i the field of graph visualisatio with the goal of improve the layout of graphs to icrease users comprehesio of the iformatio represeted by the diagram. A widely applied techique i this field is to measure the quality of a layout usig a umber metrics. The result of these ca the be combied to give a overall fitess for the graph drawig. At preset, commoly applied metrics are based o software desigers perceptios of what costitutes a good graph drawig, ad as such they do ot always correspod to users perceptio of what a good layout is. I this paper we attempt to improve this work by examiig the criteria used by graphical desigers i producig a pleasig ad comprehesible layout for diagrams ad text. The results of our work are ew metrics based o graphical desig techiques that may be combied with existig metrics to give a more accurate measuremet of the quality of the graph. We also give some examples of prelimiary work i usig these metrics to lay out graphs usig a multi-criteria optimiser. There are may existig metrics to measure the aesthetics or usability of a graph, listed i Sectio 2.1. However, little use of the parallel work i the field of graphical desig as bee applied to graph visualizatio. There are also may covetios used whe layig out a diagram or a page, may of these are listed i Sectio 2.2. I both fields there has bee show to be a positive correlatio betwee the criteria whe applied to displayed material ad usability [2] [7] [8]. I order to adapt graphic desig criteria for use i graph layout, it is ecessary to develop measuremet methods for them. We illustrate this with metrics that attempt to measure two criteria, Cocetratio ad Homogeeity. Cocetratio is how evely distributed a graph is withi the area it occupies. Homogeeity is how eve the distributio of graph elemets is betwee top ad bottom, or left ad right. The rest of the paper is orgaised as follows. The largest sectio, Sectio 3 describes implemetatios for both the more widely used graph drawig criteria ad two criteria, Cocetratio ad Homogeeity, which have bee used i graphic desig. Sectio 3.3 illustrates the use of the criteria i a multi-criteria graph drawig system. Sectio 4 gives our coclusios ad details some further work to move o from this prelimiary ivestigatio. 2. Desig Criteria I this sectio we cosider a umber of criteria for producig good layout. First, we briefly summarise the commoly adopted graph drawig criteria. We the look at criteria commoly used i the field of graphic desig ad discuss how they might be used i a graph cotext Graph Drawig Criteria Whe cosiderig the graph drawig metrics i isolatio, the commoly adopted aesthetics [2] [4] iclude: Edge crossigs are geerally cosidered to be oe of the maor factors i reducig uderstadig of a graph. Empirical studies support this ituitive otio [7]. Total Edge Beds: A huma eye ca follow a straight edge more easily tha a edge that zigzags through the picture. Reducig this simplifies the graph i terms of visualisatio ad for certai applicatios (such as circuit diagrams where beds i wires are trouble spots) ca be detrimetal to the overall layout. Uiform Beds: Restrictios ca be placed o the agles ad positios of beds i lies to make the diagram more regular.

2 Area: Visual space is ofte at a premium ad reducig the overall area of the boudig box of the graph is ofte desirable. The shape of the graph ca also be importat, so that it has a certai aspect ratio, hece fittig well o a page or scree. Total Edge Legth: Miimisatio of the sum of the legth of the edges should cause a reductio of the area of the graph. Miimisig the maximum edge legth ca also be beeficial. Uiform Edge Legths ofte make the regios i a graph ito regular shapes that should be easier to visualise tha complex shapes ad should give each edge the same visual emphasis. Agular Resolutio: A small agle betwee edges emaatig from a ode makes the edges difficult to distiguish. Symmetry: It is ofte importat to reflect a graph s symmetry i its visualisatio, however this is ot a trivial task. Symmetry ca be local (a subgraph of the graph) or global (the whole graph). Node Separatio: Nodes should be sufficietly far apart from their earest eighbour to be easily distiguished ad to avoid occlusio. Node Clusterig: Displayig close relatioships betwee odes by placig related odes closer together allows for good visualisatio of the groups withi a graph Graphical Desig Based Criteria These criteria are more geeralised tha the graph drawig criteria ad have bee draw from the priciples uderlyig the layout of graphics, text ad user iterface compoets. May of the criteria overlap with those relatig to graph drawig. Ngo, Teo ad Byre [6] have collated a series of fourtee metrics that ca be applied to a layout to measure its aesthetic appeal. These metrics try to quatify differet visual effects. However the ways they are calculated, ad their relative weightig, have ot bee validated for their efficiecy ad accurate represetatio of huma aesthetic measuremet. The differet metrics are described below. Balace is the distributio of optical weight withi the layout. Optical weight refers to the perceptio that some obects appear to be heavier tha others. Dark colours, uusual shapes, ad larger obects are heavier, whereas light colours, regular shapes, ad small obects are lighter. Balace is achieved by providig a equal weight of visual elemets i each quadrat. Equilibrium is the stabilisatio of the layout i the cetre of the visual area. O a scree this ivolves makig sure the overall cetre of mass of the obects is the cetre of the scree. Symmetry is the extet to which the layout is symmetrical i three directios: vertically, horizotally, ad diagoally. Sequece refers to the arragemet of obects i a layout i a way that facilitates the movemet of the eye through the iformatio displayed. Normally the eye, traied by readig, starts from the upper left ad moves back ad forth across the display to the lower right. Perceptual psychologists have foud that certai thigs attract the eye; it moves from big obects to small obects, from bright colours to subdued colours, from colour to black ad white, ad from irregular shapes to regular shapes. Aspect Ratio (Cohesio): The term aspect ratio refers to the relatioship of width to height. Chagig the aspect ratio of a visual field may affect eye movemet patters sufficietly to accout for some of the performace differeces. The aspect ratio of a visual field should stay the same durig the scaig of a display. Proportio relates to the optimum aspect ratio, as well as the optimum size for visual elemets, preferred by differet people ad cultures. Marcus [5] describes the followig shapes as aesthetically pleasig: Square (1:1), Square root of two (1:1.414), Golde rectagle (1:1.618), Square root of three (1:1.732), Double square (1:2). Aesthetically pleasig proportios should be cosidered for maor compoets i the layout. Uity: Creatig coherece, a totality of elemets that is visually all oe piece. With uity the elemets seem to belog together, dovetailig so completely that they are see as oe thig. Usig similar sizes, shapes, or colours for related iformatio ad leavig less space betwee elemets of a scree tha the space left at the margis achieves uity. Simplicity is achieved is by optimisig the umber of elemets o a scree ad miimisig the aligmet poits. Tullis [9] has derived a measure of scree complexity for text-based screes based o the work of Bosiepe [3], who proposed a method of measurig the complexity of typographically desiged pages through the applicatio of iformatio theory. Desity differs from the stadard graph otio of desity, which describes the relatioship betwee the umber of odes ad edges i a graph. I desig, this is the extet to which the layout is covered with obects. Optimal desity is achieved by miimisig the desity levels without makig the layout too sparse. This result from miimisig the umber of visual elemets beig displayed or by makig sure they are evely spaced so the desity is costat across the layout. A measure of desity, derived by Tullis [9], is the percetage of character positios o the etire frame cotaiig data. Regularity is a uiformity of elemets based o some priciple or pla. Establishig cosistetly spaced horizotal ad vertical aligmet poits for visual elemets ad miimisig the umber aligmet poits achieves regularity i scree desig. Ecoomy is the careful ad discreet use of display elemets to get the message across as simply as possible. Ecoomy is achieved by usig as few styles, displays techiques ad colours as possible. Homogeeity: The relative degree of homogeeity of a compositio is determied by how evely the obects are distributed amog the four quadrats of the

3 layout. A more eve distributio amogst the quadrats gives a more homogeeous graph. Rhythm refers to regular patters of chages i the elemets. This use of order with variatio helps to make the appearace excitig. Rhythm is accomplished through variatio of arragemet, dimesio, umber ad form of the elemets. Order (ad coversely Complexity): The measure of order is the weighted sum of the above measures for a layout. The scale may be cosidered with order at oe ed ad extreme complexity at the other. Other suggested aesthetic qualities for layouts [1] are icluded below. Hierarchy ad Focus: A obects importace i a layout ca be determied by its promiece of positio. Tesio: Usig heighteed visual weight or close positio, i moderatio, creates tesio betwee obects ad ca ehace the aesthetic quality of a layout. However over use makes a layout difficult to uderstad. Depth: Maipulatig the scale of obects ad z- order ca create a illusio of 3D positio. The obect with the largest apparet size will domiate the foregroud of the layout. Scale: As with depth, the relative size of elemets affects the promiece of obects withi the layout. Movemet Usually figurative, with elemets agled or poised like bodies i motio, movemet ca also be created with such optical effects as liear repetitio, visual vortexes ad the like. Used deliberately, suggested movemet ca have a marked emotioal ad physical impact o a viewer Desig Criteria for Graph Drawig Some of the criteria described above are very similar. For example, symmetry ad aspect ratio which both appear i graph ad graphical desig criteria. Aspect Ratio has the same meaig i both metrics, however Symmetry teds to be a global metric whe lookig at page layout i graphical desig whereas few graphs will be globally symmetric ad symmetry will ted to be localised i clusters. Some criteria seem related i a less direct way, for istace Ecoomy of layout relates to several of the graph aesthetics, as addig both edge beds ad edge crossigs creates complexity ad reduces Ecoomy. Cadidates for ew criteria for graph drawig must be both relevat to graph layout ad measurable. The ability to use a quatifiable metric represetig a particular criterio is importat whe measurig the overall goodess of a diagram. May of the criteria above are too abstract to be applied i such a way; for istace, there has bee little success i developig metrics for symmetry i graph for it to be applied as a global metric. The followig desig criteria have bee idetified as potetially useful i graph drawig. Homogeeity is a measure of effective use of area ad equal desity across the layout. A graph that is spread out equally should have odes spaced across the cavas ad thus have a homogeous umber of odes i each quadrat. A homogeous graph should be relatively well balaced ad cetred, so log as each elemet of the graph has equal visual weight, because the odes will be equally distributed across the quadrats of the layout. Desity, which we reame to Cocetratio i order to differetiate it from the traditioal graph meaig of desity, measures a graph layouts distributio of odes. A layout that has a ueve distributio of odes has a poor cocetratio, whereas a layout without dese groups of odes ad havig a eve spread of odes will have a good cocetratio. I the ext sectio we describe i detail our metrics for measurig both Homogeeity ad Cocetratio i a graph, ad demostrate how they ca be applied i a multi-criteria optimisig approach. 3. Implemetatio of the Criteria The sectio below details the implemetatios of both the graphical desig ispired criteria ad the existig graph criteria as well as a evaluatio of the prelimiary results comparig graphs laid out usig oly the existig graph criteria compared to graphs laid out usig both sets of criteria Graphical Desig Based s Cocetratio measures if there is a equal spread of odes throughout the layout. To simplify the calculatios a grid is used for a ode graph ad a optimal solutio should have a eve spread of odes throughout the grid with either zero or oe ode i each grid area. The followig formula is used to calculate cocetratio. xy, : ( x,1 x, y,1 y ) Grid( xy, ) = Cout of odes withi grid area Max ( Grid( xy, ) 1:0) M Desity = 1 I the graphs below there are always odes o the edge of the grid. This is because a boudig box aroud the graph is used to calculate the grid rather tha a fixedsized grid as it allows the metric to cater for graph that exceed the bouds of the page ad allows for later resizig of the graphs. Fiish Graph The graph above shows how applyig oly the cocetratio metric to a multi-criteria optimiser ca be

4 used to separate odes. The odes i each cluster have bee forced apart ad, although a optimal cocetratio has ot bee reached, there are ow oly oe or two odes i each grid. Fiish Graph This gives a metric value betwee 0 (optimal distributio) ad 1 (worst distributio). Agai, a boudig box aroud the graph is used to calculate the positio of the quadrats ad so some odes will always appear o the outer bouds of the grid. Fiish Graph These graphs highlight a problem with the cocetratio metric whe it is used o its ow. The metric measures the umber of odes withi each grid square but it does ot measure their positio. This meas that there ca be odes o either side of the boudary betwee grid squares ad the metric will register it as a good layout eve though the ode separatio ca be bad. Homogeeity is a measure of how evely the obects are distributed amogst the four quadrats of the display ad is measured usig a compariso betwee the combiatios of ways obects ca be orgaised for the give distributio compared to a optimal distributio. Ngo, Teo ad Byre [6] defie W as the umber of combiatios of ways a group of obects ca be arraged for a give distributio amogst the quadrats. Give obects, there are! differet ways of orderig them ( ways to pick the first obect, (-1) ways to pick the secod obect, ad so o). If the obects are split up betwee four quadrats, so there are UL, UR, LL ad LR obects i the upper-left, upper-right, lower-left ad lower-right quadrats respectively, the there are! ways of orderig the obects i quadrat. Therefore there are UL! UR! LL! LR! ways of orderig all obects i the four give quadrats. Give that the order of obects i the quadrats does ot matter the W is defied as! W =. UL! UR! LL! LR! It follows that W is maximum whe the obects are evely allocated to the quadrats. Therefore with obects each quadrat will cotai 4 obects. To esure that 4 is a iteger value, ad that W max is greater tha or equal to W for all values eve whe is ot exactly divisible by 4, 4 is rouded dow. Therefore W max is defied as: as:! W =. max ( ) 4 4! Therefore the Homogeeity metric ca be defied M Homogeeity W = 1. W max The graph above shows how the homogeeity metric moves the odes so they are spread equally throughout the quadrats of the graph. Fiish Graph Similar to the desity metric, the metric does ot measure the positio of odes withi the quadrat. As the graph above shows with little movemet a ode ca move from oe quadrat to aother ad improve the metric. The graphs also show that this factor ca produce odes with a small degree of separatio with odes o either side of the boudary betwee grids Existig Graph s I this sectio we briefly describe the stadard graph drawig metrics implemeted to allow compariso with the ew desig ispired metrics. Agular Resolutio is oly calculated for edges smaller tha the agular resolutio, i this case 15. The metric for each ode is calculated usig the square of the agle of icidece betwee edges at a ode divided by the square of the agular resolutio. Edge, Edge i i, Mi( θ,15) = = Agular : where Edge θ = Agle betwee Edge ad Edge i 2 i, i ad Edge coect to Node

5 Aspect Ratio is calculated as the proportioal differece betwee the graphs aspect ratio ad the viewig paels aspect ratio. Aspect Graph Aspect WidthGraph Width = AspectView = Height Height Graph ( Graph, AspectView ) ( Graph, AspectView ) Max Aspect = 1 Mi Aspect View View Edge Overlaps is a extesio of Edge Crossigs as it measures, for each pair of itersectig edges, the ratio of legth of the edge compared to the legth of the smallest lie-segmet created by splittig the edge at their poit of itersectio. Miimisig this has the effect of tryig to push the cetres of the edges away from each other, miimisig the distace the edges overlap by. Nearest Neighbour Distace miimises the variace i distace betwee closest eighbours, tryig to make the miimum distace betwee eighbourig odes equal. Uiform Edge Legth miimises the variace i edge legths, tryig to make each edge the same legth Prelimiary Results The graphs below were processed usig a hill climbig multi-criteria optimisig system. This system measures the quality of layout by fidig the values for several metrics, weightig each metric ad addig the weighted values to fid a overall value for the quality of the layout. The graph is the modified i a attempt to reduce this overall value, ad so improve the layout. Our hill climber iterates through the odes, testig each ode by movig it to eight compass poits. The ode is moved to the poit that has the lowest overall value for the metrics, or if the origial positio is lowest, o move is made. The hill climber starts by makig 10 pixel moves util it completes a full iteratio i which o ode has moved. At this poit it decremets the movemet value ad cotiues the process to fid a solutio with a better resolutio util the movemet value reduces to zero whe the iteratios stop. This approach was chose to allow rapid movemet towards the optimal solutio ad the fie tuig of the solutio. Weightig Agular Resolutio 0.01 Aspect Ratio Edge Overlaps 1.0 Nearest Neighbour Distace Node-Edge Distace 0.01 Uiform Edge Legth Cocetratio 1.0 Homogeeity 1.0 The graphs use six curret metrics. Each was give a weightig, show i the table above. These values were decided by the ivestigators, based o a attempt to both ormalise the metrics, so that the resultat values are i the same order of magitude. I additio, the two ew metrics are give a high relative weightig to emphasise their impact o the results. The followig graphs are produced usig the same startig graphs ad idetical weightigs for the six traditioal metrics. Value Weight Total Agular Res Aspect Ratio x10-7 Edge Overlaps Nearest N bour x10-3 N-E Distace Uiform Edges x10-4 Cocetratio Homogeeity Overall layout quality As a illustratio of the actual values of the metrics, above are the values for the metrics for the graph with the hill climber ot icludig the graphical desig metrics ad below are the results whe the desig metrics are icluded. The values for graphical desig metrics are icluded i both tables. Value Weight Total Agular Res Aspect Ratio x10-7 Edge Overlaps Nearest N bour x10-3 N-E Distace Uiform Edges x10-4 Cocetratio Homogeeity Overall layout quality The results show that cocetratio metric has improved sigificatly usig the graphical desig metrics ad this ca be see i the graph by the improved spread of odes over the cavas. This is also reflected i the earest eighbour separatio ad shows a almost 25% reductio i the variace i distace betwee the closest odes. There has, however, bee a icrease i the variace of the uiformity of edge legths but the umerical results show this is ot as sigificat as the

6 earest eighbour reductios ad does ot show upo visual ispectio of the graphs. The graphs above show improvemets i both cocetratio ad homogeeity whe usig the ew metrics. The graph produced usig oly the existig metrics has o odes i the lower left quadrat. The graphical desig based metrics chage this, movig two odes over the border betwee quadrats givig optimal values for both ew metrics. Visual compariso of the graphs show the ew metrics have produced a greater ode-edge resolutio ad the graph does ot look as cluttered. The graphical desig metrics offer a subtle improvemet over the existig metrics. Icreasig the area of the graph, spreadig the odes out ad geerally icreasig the ode-edge separatio ad agular resolutio. This gives the apparet result of makig the graph less cluttered. 4. Coclusios ad Further Work We have described our prelimiary work i applyig graphic desig criteria to graph visualizatio. The criteria make subtle alteratios to the layout, which should have a beeficial effect o users comprehesio of data represeted as a graph. A maor focus of our future ivestigatio will be the implemetatio of improvemets to the curret metrics ad the itroductio of further metrics. Criteria describig the effective use of white space, regularity ad uity are all possible criteria for which metrics could be developed. Future work will also look at applicatio areas for graph visualizatio. This paper has described the effect of the ew metrics o abstract graphs. However, to fully apply the beefit of desig techiques, the metrics must be applied i the cotext of a applicatio. This may also result i ew criteria that are applicatio depedet. 5. Refereces [1] ARTS 350 Course Euphrates, William Paterso Uiversity /aesthetics.html [2] Giuseppe Di Battista, Peter Eades, Roberto Tamassia, Ioais G. Tollis. Graph Drawig, Algorithms for the Visualisatio of Graphs. Pretice Hall 1999 ISBN [3] G. Bosiepe A Method of Quatifyig Order i Typographic Desig Joural of Typographic Research 2 (1968) [4] Michael Kaufma, Dorothea Wager (Eds). Drawig Graphs: Methods ad Models. Spriger Publishers 1998 ISBN [5] A. Marcus. Graphic Desig for Electroic Documets ad User Iterfaces ACM Press, New York, [6] David Chek Lig Ngo, Lia Seg Teo ad Joh G. Byre. Modellig Iterface Aesthetics. I Iformatio Scieces 152 (2003) Summarised at [7] Hele C. Purchase, Robert F. Cohe, Murray James. Validatig Graph Drawig Aesthetics. I F. J. Bradeburg, editor, Graph Drawig (Proc. GD 95), vol of Lecture Note i Computer Sciece, pp Spriger-Verlag, New York, [8] N. Tractisky, Aesthetics ad Apparet Usability: Empirically Assessig Cultural ad Methodological Issues. I CHI 97 Coferece Proceedigs, Associatio for Computig Machiery, New York, 1997 [9] T. S. Tullis A Evaluatio of Alphaumeric, Graphic, ad Colour Iformatio Displays Huma Factors 23 (1981) The layout produced usig the ew metrics shows a poor result i this case. By tryig to improve the spread of the odes the agular resolutio ad ode-edge separatio has bee sacrificed. This ca be improved by icreasig the weightig of these metrics.