Data Vases: 2D and 3D Plots for Visualizing Multiple Time Series

Transcription

1 Data Vases: 2D and 3D Plots for Visualizing Multiple Time Series Sidharth Thakur and Theresa-Marie Rhyne Renaissance Computing Institute, North Carolina, USA Abstract. One challenge associated with the visualization of time-dependent data is to develop graphical representations that are effective for exploring multiple time-varying quantities. Many existing solutions are limited either because they are primarily applicable for visualizing nonnegative values or because they sacrifice the display of overall trends in favor of value-based comparisons. We present a two-dimensional representation we call Data Vases that yields a compact pictorial display of a large number of numeric values varying over time. Our method is based on an intuitive and flexible but less widely-used display technique called a kite diagram. We show how our interactive two-dimensional method, while not limited to time-dependent problems, effectively uses shape and color for investigating temporal data. In addition, we extended our method to three dimensions for visualizing time-dependent data on cartographic maps. 1 Introduction In this paper we address challenges associated with the graphical representation and exploration of multiple time-dependent quantities. Our motivation is to support visual analytic tasks of exploring data such as census records that can have a large number of interesting correlations and trends in the temporal domain. Some specific challenges and issues addressed in our work are: Displaying several time-dependent or time-varying quantities simultaneously without causing overplotting. Developing effective graphical representations that engage a human user s visual and cognitive abilities to detect interesting temporal patterns of changes and quickly get overviews of data having multiple time-varying quantities. Census records and many other temporal data often contain a geo-spatial context such as cartographic maps. A challenge is how to expose patterns in the temporal and spatial domains while maintaining the ability to inspect several time-varying quantities. We present a two-dimensional graphical arrangement for displaying multiple time-varying numeric quantities that avoids the problem of overplotting. Our approach is based on a two-dimensional plot called a kite diagram. Our method creates what we call Data Vases: interesting and intuitive graphical patterns G. Bebis et al. (Eds.): ISVC 2009, Part II, LNCS 5876, pp , c Springer-Verlag Berlin Heidelberg 2009

2 930 S. Thakur and T.-M. Rhyne of time-varying data. Data vases can be used in many analysis tasks such as quick comparison of global and local time-varying patterns across many data sets, identification of outliers, and exploration of data with multiple levels of temporal granularity. We begin the remainder of this paper with a discussion in Section 2 on background and related work. In Section 3 we describe kite diagrams and their applications. Sections 4 and 5 describe our visualization methods in two and three dimensions. In Section 6 we conclude the paper with a discussion of our approaches and directions for future work. 2 Background and Related Work Time constitutes an inherent and often a principal independent quantity in many data sets and possesses unique characteristics compared to the other fundamental data entities, namely space and populations [1,2]. Although many effective visualization techniques and interactive methods have been developed for exploring time-dependent data [3,4,5,6,7,8], some important challenges remain. For example, a common problem with many existing methods (e.g., line graphs) is over plotting as shown in figure 1 (a). Another important limitation of many available techniques available for visualizing multiple time series is that few of them can effectively display positive and negative data values. Among the existing methods for visualizing multiple time-varying data is an effective two-dimensional representation called ThemeRiver [9], in which the time-dependent quantities are displayed using smooth area-filled and layered profiles to create aesthetically pleasing currents representing the data stream. However, the ThemeRiver metaphor is mostly limited to the visualization of nonnegative data values. On the other hand, a different approach, namely Horizon Graphs [10], can handle negative and positive data values by effectively exploiting layering and color-coding to create dense, space-conserving visualizations. However, the method achieves the efficiency in the spatial layout by sacrificing the ability to compare overall profiles of the time-varying quantities. Another interesting time series visualization is called wiggle traces [11] and employs individual line traces or wiggles to plot the profiles of seismic waves obtained during the exploration of sub-surface strata. However, this technique can not be generalized because it is difficult, in general, to visually compare multiple line graphs that do not share the same set of coordinate axes. We address some of the challenges in visualizing multiple time series using a method that is an evolution of two-dimensional charts called kite diagrams [12]. Kite diagrams are useful for plotting simple statistical data but have not been exploited for displaying more complex data. We apply our methods for visualizing census-related data, which often contain a huge set of individual time series and can have potentially many interesting correlations among the recorded social and economic indicators that may be studied. In our work we have also explored three-dimensional visualizations to investigate potentially interesting spatial relationships in census data that have an inherent geo-spatial context (e.g., census tract, counties, and states). Our visualizations

3 Data Vases: 2D and 3D Plots for Visualizing Multiple Time Series 931 Fig. 1. (a) A dense plot of multiple time series. (b) Illustration of the steps involved in the creation of a kite diagram of a single data series shown in step 1. exploit a standard three-dimensional geo-spatial representation called the spacetime cube [13], in which spatial data are plotted in the X Y ground plane and temporal data are plotted along a vertical Z axis. This space-time cube metaphor has been used to generate effective visualizations of spatial-temporal data in some previous works [14,15,16]. However, three-dimensional information visualizations are generally challenging due to the problem of inter-object occlusion. We employ user-driven data filtering to reduce clutter, though some other techniques are also available for overcoming the occlusion-related problem [17]. We begin the discussion on our visualizations of multiple time series by discussing a two-dimensional layout based on kite diagrams. 3 Kite Diagrams A kite diagram is a two-dimensional data representation technique that employs closed, symmetric glyphs (graphical widgets) to represent simple quantitative data [12]. Figure 1 (b) illustrates the construction of a kite diagram of a line graph profile shown in step 1 in the figure. The underlying motivation in using kite diagrams is that for small data sets the differences in the shapes of the kites can reveal differences in the trends and values values of one or more data series. An effective application of kite diagrams is shown in figure 2, where kite diagrams have been used along with a standard tree view for visualizing species diversification during the Mesozoic era [18]. The horizontal temporal axes in the kite diagrams correspond to the different geologic periods of the Mesozoic era and the thickness of the kites along the vertical axis indicates the estimated populations during the corresponding periods. Colors of the kite shapes pertain to the different mammalian orders or families shown in the phylogenetic tree. Discussion. Kite diagrams are an easy-to-create and straightforward representations of simple time-series data sets. However, to visualize complex data using kite diagrams the following limitations of the kite diagrams need to be addressed: Kite diagrams are limited to the display of positive data values and there is no option to encode negative data values or missing data. Kite diagrams are suitable for comparing gross values of variables and attributes; however, detailed analysis that involves the comparison of exact values across multiple charts is tedious.

4 932 S. Thakur and T.-M. Rhyne Fig. 2. Species distribution and diversification in Mesozoic Era (courtesy of [18]) shown using (left) phylogenetic tree, and (right) kite diagrams Kite diagrams are useful mostly for exposing large differences between and within different data series; using kite charts it is difficult to compare adjacent values that vary only slightly. We next discuss a two-dimensional approach for visualizing time-dependent data that exploits the useful characteristics of kite diagrams and avoids some of its limitations. Although in this work we consider primarily time-varying data, our methods are also applicable for visualizing other types of multi-variate data that may not involve a temporal domain. 4 Data Vases: Display of Multiple Time Series We present an approach for visualizing multiple time series that combines kite diagrams and standard visualization techniques to create information-rich and interesting glyph-based representations of the data 1. At the very least, our approach generates dense, space-filling representations of time-dependent data by plotting kite diagrams corresponding to multiple time series and using markers to highlight unusual data values such as missing data. An example based on our approach is shown in figure 3, which shows in a single view data vases for a hundred crime-related time series 2. Our technique avoids over plotting (compared to standard methods such as line graphs shown in figure 1 (a)) and allows encoding of additional interesting characteristics in a given data set. Our approach exploits many of the salient perceptual organizing principles of graphical representations available in kite diagrams such as bilateral symmetry, closure of shapes, and distinction between figure and ground [20]. Our visualizations are intended to engage an observer s visual perceptual capabilities for detecting and pre-attentively processing interesting patterns in the emergent data vase shapes [21]. 1 The resulting shapes in our approach look like profiles of flower vases; we therefore use the term data vases to refer to our representation of time series data. 2 The design choice pertaining to the alignment of the temporal axis is governed primarily by the principle of creating space-filling representations of the data [19]. The temporal axes in data vases might easily be swapped to have a horizontal alignment in case of a data with larger number of time steps relative to other data dimensions.

5 Data Vases: 2D and 3D Plots for Visualizing Multiple Time Series 933 Fig. 3. Kite diagram-based Data Vases showing the time series of crime rates (numbers) in North Carolina s (USA) 100 counties during Individual kite diagrams are arranged alphabetically from left to right based on county names and colored based on geographic regions in North Carolina (see the map in figure 4). Fig. 4. Data vases corresponding to net migration rates for North Carolina s 100 counties using (a) interpolated profiles, and (b) discrete or stepped profiles The data vase chart shown in figure 3 provide a useful tool for the simultaneous comparison of multiple time series; however, our straightforward representation is not sufficient for performing more complex data analysis tasks. We next present some enhancements to our data vase charts that exploit some of the standard visualization techniques for exploring and representing data. Interpolated Versus Discrete Profiles of Data Vases. The data vases shown in figure 3 are constructed using profiles of line graphs, which employ a linear interpolation between consecutive time steps to represent a continuous data series. However, in many data, such as census surveys, the quantities may not vary linearly between each time step. We therefore provide an option to use profiles of bar graphs or histograms to generate discrete representations of the data. figure 4 shows the two versions of data vases that are based on interpolated and discrete profiles.

6 934 S. Thakur and T.-M. Rhyne Fig. 5. Data vases showing US oil imports from different countries (1970 and 2007) Fig. 6. Data filtering with data vases using simple techniques like range selection to show (left) negative data values, and (right) positive data values. Color Coding. The symmetric shapes of data vases are limited to conveying the absolute values of time-dependent variables. We exploit different color coding schemes to improve differentiation of the data values and to represent additional information such as negative data values. An example is shown in figure 4 where two different color hues are used for encoding positive values (blue-green scheme) and negative values (orange-red scheme). Figure 5 illustrates a different coloring scheme that is based on a discretized or segmented color palette, which can reveal interesting patterns in data such as time ranges corresponding to major changes and time periods over which different values persisted. Other useful color coding schemes that are sensitive to statistical properties in data are also available [22]. Data Vases and Data Filtering. Data filtering is an indispensable analytic tool in any type of visualization for investigating dense data. Some standard data filtering methods include user-driven dynamic queries that employ straight forward graphical widgets like sliders and range selectors [23]. These and other data filtering tools can be used effectively with data vases for exploring time-varying data and to answer some analytic questions, for example, when certain data values of interest appear in the data. An example is shown in figure 6 where the data vases corresponding to estimated net migration rates for the counties in North Carolina (USA) have been filtered to show either the negative or the positive migration rates. Exploration of Different Levels of Granularity. An important characteristic in some time-varying data is the different levels of granularity of the temporal domain [2] (e.g., months and years in census data). In our data vase approach multiple levels of temporal granularity can be displayed by summarizing data values by their averages over the higher granularity levels.

7 Data Vases: 2D and 3D Plots for Visualizing Multiple Time Series 935 Fig. 7. Charts showing vases corresponding to different levels of temporal granularity in a data set: (background) unemployment rates averaged for each year, and (foreground) all time series expanded to show monthly unemployment rates An example is shown in figure 7 where two levels of granularity in a data are shown in two different charts. In addition, interactive methods are used in our approach to collapse and expand the different temporal levels, which nicely affords the exploration of the data with the multiple levels of details. Interaction with Data Vases. Interactive tools can be particularly effective for exploring dense data sets using data vases. For example, in a prototype implementation of our methods region-wise patterns in census data can be explored by rearranging the glyphs on the horizontal axis according to the different regions in the data (figure 4). The glyphs may also be sorted to highlight data vases with large averages over the entire time series or for particular time steps. Some other useful options include option to switch between the representation of data vases basedonrawvaluesandper-capita values and to interactively change the width of the glyphs to reduce overlaps. 5 Display of Multiple Time Series on Maps Many time-dependent data often also involve an inherent geo-spatial context. For example, census survey data are usually associated with geographic regions like census tracts, districts, counties, and states. We present an approach using three-dimensional versions of data vases for exploring spatial relationships in data with multiple time series. We create the 3D visualizations of data series for different geographic regions by stacking polygonal disks for each time step along a corresponding vertical temporal axis. In this representation, time increases from bottom to top and the value of a variable at each time step is encoded by the width of the corresponding disk. The disks are color coded using the coloring schemes discussed in Section 4 for better discrimination of data values. We employ orthographic projections in our visualizations to avoid the distortion of the 3D shapes and to preserve the relative sizes of the disks in different rotationally-transformed views. Figure 8 shows a 3D visualization of the monthly unemployment rates for North Carolina s (USA) 100 counties. The visualization employs color coding and interactive methods like rotation and zooming to reveal interesting patterns in space and time. For example, closer inspection of the two right-most 3D vases in figure 8(a) reveals highly fluctuating unemployment rates, which might be due to the changes in the employment rates during different agricultural seasons.

8 936 S. Thakur and T.-M. Rhyne Fig. 8. 3D data vase diagrams of a dense data set. (a) Vases corresponding to unemployment rates in North Carolina s 100 counties from January 1999 to December (b) A filtered view of the data corresponding to a user-selected range (inset). One problem in our approach is due to occlusion (see figure 8(a)), which makes it difficult to compare the 3D shapes of the data values. Some effective methods for reducing occlusion in 3D visualizations have been suggested in [17]. We improve the readability of the 3D data glyphs by reducing the number of data elements displayed using a data-filtering mechanism (see figure 8(b)). The problem due to occlusion can also be overcome to some extent using interactive camera control (e.g., using rotation, panning, and zooming). 6 Discussion and Conclusion In this paper we have highlighted a visualization technique for creating engaging and informative displays of multiple time series and is based on an intuitive twodimensional graphical plot entitled kite diagrams. Although we have primarily considered historic data (i.e., recorded census data), our graphical representations can be adapted for visualizing streaming data (e.g., network traffic). An important consideration in the generation of the vase shapes pertains to the distribution of values in a data set: data with high standard deviations often result in vases of highly varying widths. For example, in figure 5, which shows USA s oil imports in millions of barrels from different countries, the vases corresponding to small import values are highly shrunk. A standard solution to generate more homogeneous shapes might be to rescale the data values using a log scale. Another option in domains like census surveys is to use per-capita values, which are sometimes more meaningful and often also eliminate large differences in data values. Another important issue in our representations is that it can be difficult to compare the profiles of the vase shapes that are far apart in the chart. Some possible solutions might be to interactively rearrange the locations of the vases on the chart or to selectively compare up to a few glyphs in a separate window. To discuss the different exploratory tasks supported by our approach we turn to a comprehensive framework in [24] that introduces a systematic and functional description of data and tasks. A distilled description of the framework, particularly its task topology, has been presented in [22]. The first and basic tasks in the task topology are elementary tasks and involve the determination of the values of dependent variables when the values of independent variables have been specified (and vice versa). For example, in the

9 Data Vases: 2D and 3D Plots for Visualizing Multiple Time Series 937 data vase charts in figure 5 showing USA s crude oil imports an analyst can pose and answer questions like How much crude oil did the US import from Canada in 2007?, and When did the highest value of crude oil imports occur? Other types of elementary tasks involve the investigation of relationships between independent and dependent variables, for example, Compare import rates of crude oil between OPEC and non-opec countries. A different and more complex set of tasks are synoptic tasks, which, unlike elementary tasks, involve exploring relationships between and within the entire sets of dependent and independent quantities in the data. In the synoptic tasks concrete patterns are specified and a goal is to find the sets of values of the dependent and independent variables that exhibit the target patterns. Synoptic tasks are generally considered more important tasks because they can expose the general behavior of a phenomenon or a system. Some synoptic tasks can be specified using the data vase approach; for example, in figure 5 some synoptic tasks are From 1980 to 2000 how did crude oil imports vary?, or During what time interval(s) did the crude oil imports change from decreasing to increasing? Synoptic tasks often require queries that involve complex patterns specified over multiple independent variables. For example, a hypothetical task of moderate complexity pertaining to census data can be: Find the time interval(s) when poverty rates in Western North Carolina were decreasing and per capita income was increasing. Data vases in the current form are limited to the exploration of analytical queries that combine only up to a few data variables; we therefore need to adapt our approach for exploring complex data sets with multiple variables. We conducted an informal discussion session within our organization to assess our data vase-based approaches using snap shots of our visualizations in a webbased format. As a future work we would like to evaluate our methods using a formal comparison with the other standard methods for representing timevarying data. Another interesting direction to pursue is to experiment with nongeographic maps (e.g., tree maps) with our 3D versions of data vases. Acknowledgment This work was conducted at the Renaissance Computing Institute s Engagement Facility at North Carolina State University (NCSU). Data vases grew out of a visualization framework that was developed with NCSU s Institute for Emerging Issues. We thank Steve Chall and Chris Williams for their contributions. References 1. Müller, W., Schumann, H.: Visualization methods for time-dependent data - an overview. In: Chick, S., Sanchez, P., Ferrin, D., Morrice, D. (eds.) Proc. of Winter Simulation 2003 (2003) 2. Aigner, W., Bertone, A., Miksch, S., Tominski, C., Schumann, H.: Towards a conceptual framework for visual analytics of time and time-oriented data. In: WSC 2007: Proceedings of the 39th conference on Winter simulation, Piscataway, NJ, USA, pp IEEE Press, Los Alamitos (2007)

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