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.

2 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. 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.

3 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.

4 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 .

5 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. 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].

6 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.

7 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.

8 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,()..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.

9 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. 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.

10 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.