Visualizing Time-Series on Spirals

1 Visualizing Time-Series on SpiralsMarc WeberMarc AlexaWolfgang M llerc-cop GmbHTechnische Universit t this paper, we present a new approach for the visualiza-tion of Time-Series data based on Spirals . Different to classi-cal bar charts and line graphs, the spiral is suited tovisualize large data sets and supports much better the iden-tification of periodic structures in the data. Moreover, it sup-ports both the visualization of nominal and quantitative databased on a similar visualization metaphor. The extension ofthe spiral visualization to 3D gives access to concepts forzooming and focusing and linking in the data set. The spiralcomes with additional tools to further enhance the identifi-cation of Information Visualization, graph Drawing, Vi-sualization of Time-Series Data, Data Mining1.

2 IntroductionThe analysis of time series data is one of the most widelyappearing problems in science, engineering, and data is analyzed in order to discover the un-derlying processes, to identify trends, and to predict futuredevelopments. Often, the analyzed data displays a periodicbehavior, providing a model to better estimate such for time series data with periodic structures arenatural phenomena such as temperatures and radiation oflight in a month or year. Some theories assume that econom-ic cycles also show periodic has been successfully used to analyze Time-Series data for a long time . Especially line graphs have prov-en to be very effective in this more sensitive sensors in science and engineeringand the widespread use of computers in corporations have in-creased the amount of time series data collected by manymagnitudes.

3 Existing approaches to the visualization of suchlarge data sets are insufficiently suited in supporting peoplein discovering underlying structures. In this paper we present the spiral graph a new approachfor the visualization of Time-Series data. The spiral Graphcan visualize large data sets and is ideally suited to supportthe human ability to detect structures. Such structures areclues to hidden, underlying cyclic processes behind the data2. State of the ArtTime series data is characterized by data elements beinga function of time . In general, this data takes the followingform:withThe data elements can represent different data we differentiate between nominal, ordinal, andquantitative data or tuples of these in the case of multivariatedata.

4 The purpose of a visualization is to detect and validatecharacteristic properties of the unknown function f. The visualization of Time-Series data has a long series plots appear for the first time in the illustrationof planetary orbits in a text from a monastery school [14]. Inscience, Time-Series charts have been rediscovered not earlierthan in the 18th century by Lambert to display periodic vari-ation in soil temperature in relation to depth under the sur-face [9]. Playfair was the first to an of the analyze theeffectiveness of line graphs and bar charts [11]; he appliedthese graphs for the analysis of economic data. A detaileddiscussion of the history of Time-Series plots can be found in[14]. Today the visualization of Time-Series data differs onlylittle from these early most important visualization techniques for time se-ries data are sequence charts, point charts, bar charts, linegraphs, and circle graphs:Sequence charts represent time -dependent data on a one-axis chart in chronological order.

5 Data elements are visua-lized by marks at the corresponding distances to the origin ofthe axis. Using marks for the visualization of the data ele-ments, sequence charts are restricted to the visualization ofnominal Time-Series data. Point graphs extend sequence charts into the second di-mension and use the remaining dimension to visualizequantitative data aspects by the distance from the main charts use bars instead of points to represent the dataenhancing the comparability of the data graphs extend point graphs by linking the data markswith lines to emphasize the temporal sequences can be combined in a single graph toallow for a comparison of these sequences, leading to multi-ple bar charts and multiple line graphs. Depending on the da-ta, this combination is restricted to 2-8 sequences in oneDt1y1,()t2y2,().

6 Tnyn,(),,{}=yifti =yigraph. In addition, cycle and cycle length of the data have tobe known in advance to allow for a graphs map line graphs into the spherical are usually used to visualize quantitative data with (as-sumed) periodic background and with a known cycle to multiple sequences ca be combined in one cyclegraph. Hereby, multiple cycles of a data set can be compared. Lately, 3D versions of line and bar charts have been usedto visualize Time-Series data in relation to a second free vari-able. Animation is used to visualize temporal aspects. Agood overview on graphical representation for time -seriesdata can be found in [5].Bertin [1] performed a broader analysis of visual at-tributes which can be exploited in the visualization of dataand their effectiveness to communicate certain types of in-formation.

7 Cleveland [3] further improved these studies andgives measures for the efficiency of a number of graph typesin various graphs and charts can be enhanced by differentinteractive techniques, such as scrolling, zooming, brushing,as well as focusing&linking: Scrolling extends the display area and allows for therepresentation of larger data sets. However, a compari-son of data elements is only possible in the currently vis-ible subset. Zooming is another approach to the visualization oflarge data sets. Initially a low resolution view is pre-sented and the user can decide to zoom into interestingregions. Again, comparisons are only possible across thevisible subset and important detail might not be visiblein the overview. Focusing&linking [2] extends the idea of zooming byproviding not only zoomed versions of the detail data,applying also different, more effective visualizationtechniques for the selected frame.

8 Brushing provides such additional information as pop-ups which are automatically displayed as a roll-overeffect. The information mural [7] is a visualization techniqueproviding an initial view of the whole data set as thebasis for further analysis with the above-mentionedinteractive techniques. An overview on interactive visualization techniques fortime series data can be found in [13].While all these techniques proved to be very effective inmany cases, some general problems stay for the visualizationof Time-Series data. The visualization of large data sets is stilldifficult and all these techniques do not efficiently supportthe identification of serial and periodic aspects in the data ef-fectively. The detection of a periodic behavior in the data though one of the main intentions for the visualization fromthe very beginning is still difficult and often only possible,if the cycles are relatively obvious.

9 Comparisons betweendifferent cycles - needed to identify - are also difficult. Forinstance, the detection of small, varying offsets in the periodis rarely possible with today s techniques. Also, compari-sons between different periodic processes are now, Spirals have rarely been used for first example of a spiral graph was presented by Gaba-glio in 1888 [4].Bertin [1] presented a single example for the visualizationof Time-Series data using a spiral graph . However, he doesnot discuss this visualization technique in much detail. Mackinlay et. al. [10] used a spiral for calendar visualiza-tion; iconic representations of past daily calendar entries arepositioned on the spiral to display the development of thecalendar. However, though using the spiral for temporal da-ta, this solution does not present a general approach to thevisualization of Time-Series et.

10 Al. [7] introduced a pixel-based visualizationtechnique for data mining in databases, where entries arerepresented as colored pixels or color icons. Keim et al. po-sitions these entries on a roughly approximated spiral depen-ding on their relevance to generate 2d iconic displays. Yet,they do not apply the spiral to the visualization of et. al. [6] used 2d and 3d Spirals to visualizetemporal and spatiotemporal spiral graph which we present in the following sec-tions puts the focus on the put the focus on the goals of com-paring data elements, both in a neighborhood and betweencycles, and the identification of patterns and periodic beha-viors in Time-Series data. These goals correspond to the as-pects of comparative and summary reading introduced byBertin [1].