Robert M. Edsall*

Within geography, a rapidly advancing subdiscipline is that of Geographic Visualization (GVis), which applies concepts of scientific visualization, statistical graphics, and cartography toward the understanding of spatial phenomena and processes. GVis, or the "use of visual representations… to make spatial contexts and problems visible" [MacEachren, Buttenfield et al. 1992, 101], has as one of its key themes the iterative process of interacting with visual displays of geographic information, reducing complex databases to understandable patterns and structures [MacEachren and Ganter 1990].

Cartographers have long striven to make geographic phenomena visible through the use of concise graphic devices like maps and graphs. Yet the best-designed traditional paper map or graph is limited in its utility for exploring and communicating information for a number of reasons. First, it is static: ink on a page cannot be manipulated, animated, or otherwise altered (without making permanent changes). In many data analysis situations, the ability to interactively manipulate representations of information is key to complete understanding of the phenomenon: on-the-fly change classification breaks of a histogram, for example, will reveal the "stability" of the classes – if the bin distribution changes dramatically with a slight adjustment of a class break, much is learned about the data and the classification process used. Another disadvantage of traditional paper representations is their inability to effectively represent a third dimension. With the growing necessity to explore high-dimensional information, the ability to visualize three (or more) dimensions is advantageous; representing depth on a paper map is never as effective as doing so in a computing environment with the ability to rotate and/or change the depth cues of the scene. Finally, and perhaps most importantly, paper maps and graphs represent the specific viewpoint of a single graphic designer. The choices (s)he makes while creating the representation have a profound and often intentional impact on the way the data is perceived by an analyst (who may or may not be the designer). Enabling a flexible and customizable representation is vital for examination of multiple perspectives and testing (or even generation) of multiple hypotheses.

Fortunately, of course, rapidly advancing computer graphics technology is alleviating (to varying extents) the problems inherent in static geographic and statistical representations described above. Geographic information systems software is incorporating new interface designs and direct-manipulation display tools to encourage interactive exploration of data [Goodchild, Haining et al. 1992; Cook, Majure et al. 1996]. So-called geocomputational analysis methods such as knowledge discovery in databases (KDD), neural networks, and clustering algorithms are allowing examination and summarization of gigantic databases of geo-referenced information, enabling techniques like automated classification of multidimensional data [Fayyad, Piatetsky-Shapiro et al. 1996; Gahegan 1998; MacEachren, Wachowicz et al. 1999]. Sophisticated statistical software is being developed with highly graphic interface tools for the formation of insight about geographic data [Buja, Cook et al. 1996; Swayne, Cook et al. 1997]. It is from the convergence of these related developments that the work described herein originates.

This paper reports on the development of interactive tools for the inductive exploration of multivariate databases, designed specifically for the identification and interpretation of spatial and spatiotemporal patterns and features. Emphasis will be placed on the introduction of a dynamic parallel coordinate plot, using techniques of parallel coordinate geometry introduced by Inselberg [1981], and its application for the visualization of automated multivariate classification of climate data.

Recent and ongoing work in our GeoVISTA laboratory at Penn State has produced a conceptual framework and prototype implementational tools for the integration of the complementary processes of Knowledge Discovery in Databases (KDD) and Geographic Visualization (GVis) [MacEachren, Wachowicz et al. 1999]. The inductive extraction of patterns and categories from complex multidimensional data sets is one of the primary goals of both KDD [Fayyad, Piatetsky-Shapiro et al. 1996] and GVis [MacEachren and Ganter 1990].

A key step in the process of KDD is data mining, which can automatically search, classify, and summarize a data set with varying levels of human control. Each "class" in an automated data mining run might be defined by a set of related attribute values; for example, a class from a mining of climate data might be characterized by above average temperatures, zero precipitation, strong northwesterly upper-level winds, and low surface humidity. All observations sharing that multivariate "signature" would be grouped within that class.

One of the many appealing features of this technology is its ability to work iteratively and intelligently with human expert knowledge. Analysis techniques in KDD are often aided by user specification of classification and search parameters. Methods of scientific (and specifically geographic) visualization like dynamic statistical graphic displays, designed to aid expert exploration of data, can thus not only assist in these statistical techniques' interpretation but also enhance KDD performance.

Recent literature has begun to address the need for techniques for the visualization of data mining results. Keim and Kriegel [1996] concur that the integration of the human, and his or her "unmatched abilities of perception" is especially important, and that visual representation of the multidimensional data is required to allow the efficient retrieval of information from the system. Methods for visualizing large databases contained within that paper, as well as proposed by Inselberg [1997], specialize in the recognition of associations among many different dimensions of data. This recognition allows qualitative assessment of complex relationships that in turn are used to drive further mining explorations.

Our progress toward integrating KDD and GVis [MacEachren, Wachowicz et al. 1999] has, thus far, included drawing analogies between the conceptual goals of the two processes, such as the identification of features or patterns in data or the prediction of future states, and the development of a complementary set of operations and methods extracted from the two processes which may be used as a guide for the design of interface tools in an environment which brings these methods together. In addition, we have reported on a prototypical set of implementations to facilitate operations like category extraction and classification. With these approaches and tools, a domain expert will be able to interact with the visual displays and drive the iterative KDD process. It is this human-centered knowledge-driven approach which the tools reported in this paper will facilitate and which defines the primary links between KDD and GVis.

The statistical graphics tool introduced below, the dynamic parallel coordinate plot, was developed for the particular task of representing multidimensional information in a coherent, concise, and interactive manner. As such, it extends the capabilities of the GVis applications and is particularly effective as a tool for the visualization of results of a multivariate classification algorithm. It serves as one of several linked tools in the visualization "toolkit" which is included in the prototype system developed at Penn State (Figure 1).

Figure 2. Parallel coordinate geometry.

Parallel coordinate geometry

The dynamic parallel coordinate plot employs a novel methodology to visualize beyond three dimensions by representing each observation not as a point in a scatter plot but as a series of unbroken line segments connecting parallel axes, each of which represents a different variable. The approach was first considered formally by in 1981[Inselberg 1981] . Since then, task-specific variations of the graphic device have been put forth by other statisticians and computer scientists [Wegman 1990, Miller and Wegman, 1991]. A dynamic version of the PCP has recently been introduced by Chang and Yang [1996]. It has been used in the context of data mining by Keim and Kriegel [1996], and has appeared as a spatial statistical display in interfaces including that of the ARGUS project [Dykes 1997]. By representing variables as parallel – as opposed to orthogonal – axes, the representation breaks the bonds of two or three-dimensional representations such as scatter plots.

The line segments are constructed so that they intersect the axes at a point representative of the relative observed value of that variable. As an example, consider an hourly meteorological reading. The observation would be represented by a series of points, one on each axis, positioned near the top of the axis if that variable's observed value were relatively high, near the middle if the value were near the median, and near the bottom if the value were relatively low. These points would then be connected by line segments, resulting in a distinct (perhaps unique) signature of observed values for that observation (see Figure 2a). The implications for multivariate classification are obvious; the signatures of representations in a PCP correspond directly to those signatures described as part of the automated classification algorithm in data mining.

Using the PCP, interactions among variables can be quickly identified. Observations with similar data values across all variables will share similar signatures; clusters of like observations can thus be discerned. Two variables which are directly related to one another would appear on the PCP as two axes connected by a series of parallel (or at the least non-crossing) line segments (see Figure 2b). Temperature and dewpoint, for example, tend to be directly related to one another; a low temperature is accompanied by a low dewpoint, and a parallel coordinate representation of these two variables would clearly show this pattern. Conversely, an inverse relationship between two variables would be displayed as a series of line segments which cross each other between the axes. Gas mileage and vehicle weight is shown (in Wegman [1990]) to exhibit this relationship, and the PCP representation resembles, vaguely, a "bow tie" of intersecting line segments (see Figure 2c). In fact, the number of crossings of line segments is directly related to the correlation coefficient r [Wegman 1990].

Though able to represent n-dimensional information in one diagram, parallel coordinate plots have obvious drawbacks. First, the sheer number of observations in a large geographic database quickly overloads the representation to the point where very little information can be perceived and extracted [Gahegan 1998]. The plot becomes a confusing jumble of lines resembling a haystack or an overworked telephone switchboard. In addition, the order in which the axes are lined up clearly would influence the amount and quality of the insight gained from the representation. An additional problem particular to geographic databases is the necessary reduction of space to one dimension (to fit on one axis), or, better but not ideal, the imposition of a north-south / east-west structure on data so that the location can be represented as a line connecting two axes representing latitude and longitude, respectively.

The dynamic PCP described here incorporates strategies for effectively visualizing large multidimensional structure in data while avoiding the drawbacks outlined above. The implementation facilitates the exploration of relationships among variables and among observations in a variety of novel ways described below. It can be effectively used in particular for multivariate classification; features described in the next section can be used in tandem to understand and to drive the classification resulting from data mining. The dynamic PCP has been designed not only as a stand-alone representation for statistical visualization but also as a primary interface tool for an environment for GVis and KDD, driving such operations as data selection, color and class manipulation, data mining weight adjustment, and representation parameterization for other forms of statistical graphics in the toolbox.

Figure 3. Axis variable reassignment.

The following sections outline the unique interactions afforded by the dynamic parallel coordinate plot, and describe how these features address some of the limitations of less interactive forms of this representation.

Even to the statisticians who originally proposed this methodology, reordering of the axes was considered a vital feature for the exploratory types of analysis best supported by this type of representation [Wegman 1990]. Relationships among a small number of variables would be difficult to discern if those variables were distant from one another on the representation. One of the key features of the dynamic parallel coordinate plot is the ability to adjust which variable is assigned to each axis. By selecting different variables on different axes, relationships between pairs or among groups of variables can be interactively explored (see Figure 3). Rather than assigning the variables to arbitrary axes, a user might wish to order the axes according to data mining weight or some expert knowledge of associations among the variables. It is quite conceivable that two variables not adjacent to each other in one ordering may prove to have a surprising or unexpected association which, using the PCP, would be discerned only when the variables are moved to adjacent axes.

Figure 4. Focusing.

Focusing.

The density of lines in the PCP can be reduced dramatically using a focusing tool. Using this feature, a researcher may isolate observations which share a value or a range of values of a particular variable. Focusing the PCP removes the lines of all other observations from the display to reduce the visual clutter and draws the focused observations in yellow (see Figure 4). Questions that might be answered easily using this technique might be "are the outliers of the barometric pressure variable also extreme values of other variables, like precipitation?" or "how similar are the traces of all of the observations at this latitude?" or, in a data mining context, "what variable dominates the classification of the observations in class 6?"

Figure 5. Brushing.

Another method of reducing the complexity of lines in the plot is through the use of the brushing feature of the dynamic PCP. Multiple line segments in the PCP may be selected simultaneously by click-dragging a box around the bundle. Upon release of the mouse button, the observations of which the boxed line segments are a part are highlighted. This can be a very effective method of drawing attention to the signatures of a group of observations that share similar values of one attribute. In addition, brushing can be used to highlight a subgroup of observations which have an inverse relationship between two variables (see Figure 5).

Figure 6. Strumming

Individual observations may be highlighted on the parallel coordinate plot by moving the mouse over the line segment, termed "strumming" because the action resembles using a pick on guitar strings (see Figure 6). This highlights the PCP trace across the whole plot, allowing users to identify interesting relationships in individual observation between a pair of variables (for example, an outlier observation with low surface humidity but significant rainfall) or a series of variables (like a single observation that is higher than average "across the board"). Additionally, because this strumming action occurs in real time, users may be able to identify critical attribute values where significant multivariate relationship changes occur. For example, strumming along the temperature variable axis in a plot of a climate data set may reveal a point where there is be a binary switch in the precipitation type variable from rain to snow. This abrupt switch would be best visualized by animating each observation in sequence according to temperature while watching the locations of the observations on another (precipitation type) axis.

Observations may be classified according to one variable and represented using this classification with an appropriate color scheme. This also serves to reduce the representation's complexity by varying the color of the lines in a logical way. The dynamic PCP system allows the adjustment of the color scheme of the display with the click of a button, and the user is able to customize colors by right-clicking the color bar and using a standard color picker to adjust individual colors. Ten built-in color schemes are presently included in the tool, derived from the taxonomy described in Brewer [1994]. Additionally, the number of classes is manipulable: the present implementation allows anywhere from three to seven classes. Also fully interactive are the class breaks: the default is a quantiles scheme, but, since the distribution of the variable is part of the representation, a "natural breaks" classification (or any other customized classification) is easily implemented.

As part of the larger visualization system described in MacEachren, Wachowicz et al. [1999], the PCP serves as a tool for adjusting the display parameters of other representation forms. In its present state, the PCP is linked with a 3-dimensional scatter plot, and the pull-down menus above each axis correspond to the position of the variable on the 3D scatter plot. The variable represented by the color bar in the scatter plot (see Figure 1) is also adjustable on the PCP, as is that which is represented by the size of the points (or glyphs) in the plot. Future versions of the dynamic PCP may also drive a data mining algorithm by allowing users to specify which variable should be weighted most heavily in the automated classification, perhaps using a left-to-right ordering of the variables from maximum to minimum weight.

Figure 7. The future dynamic PCP.

At the time of the writing of this paper, many features of the dynamic PCP are "on the drawing board," but have yet to be programmed into the system. First among these future plans is the implementation of an embedded spatial representation: a two-dimensional map of the region being analyzed, the plane of which is orthogonal to the plane of the parallel axes (see Figure 7). In addition, the representation of time in the PCP may be reconsidered to better reflect the fundamental differences between time and other attribute or spatial variables. Some adaptation of the temporal legend devices described and tested in in Kraak, Edsall et al. [1997] and Edsall and Peuquet [1997] might be implemented in future versions of the tool. An interactive method of rescaling or transforming the axes, for example from linear to logarithmic scale, might be a useful addition to the dynamic PCP, as would a zooming feature so that a higher number of variables might be visible in one window at once.

In this section, the use of the dynamic PCP as a multivariate exploration tool will be demonstrated. The exploration of climate data provides a likely scenario for the type of tasks facilitated by the dynamic PCP. Though a climatologist may be able to use the dynamic PCP as a tool for the confirmation of existing hypotheses, he or she may also take advantage of the interactive features of the tool described above to reveal surprises about the data and the phenomenon represented and subsequently generate new hypotheses.

The data set used in this example come from a synoptic-scale gridded model of wintertime climate in Texas and northern Mexico from 1985 to 1993, selected because it is nearly exempt from noisy, incomplete, or contradictory information [Cavazos-Perez 1998]. The data has been by a public domain software package called AutoClass, which, in addition to distributing observations into classes, returns the likelihood that each observation truly belongs in the class to which it is assigned (for more information on the detail of AutoClass, refer to Cheeseman and Stutz [1996]). For this example, a subset of the classed data has been selected which includes all of those observations classified with a very high probability of belonging in the class to which it was assigned. By selecting this subset, a researcher is able to answer questions about the prototype, or most typical, observation in the class, and, in so doing, might uncover information about the behavior of the classification algorithms which might drive further classification runs.

In Figure 8, the user has focused on a specific class to explore which variables appear to bear the most weight for that class, and whether the observations share a common, prototypical multidimensional signature. This class, number 6 of 27, shows that all observations in that class are characterized by above-median surface humidity, high mid-level humidity, a negative barometric pressure change, and eastern location (over the Gulf of Mexico). It seems that these are moist days; indeed, all of these observations represent days of moderate to heavy rain totals (see Figure 8, second axis from right). The axes can be assigned according to the amount of "spread" of the focused observations, thereby giving an idea of the most influential variables used in the creation of that class.

The dynamic PCP can be used to detect spurious classification. Below, the user has focused on a class (24) created in the data mining run with an unusually scattered set of observations: no obvious "typical" multidimensional signature is detectable (see Figure 10). Close inspection reveals, however, that many of the observations share two characteristics: they occur on the same day, and they all have the same sea level barometric pressure change – zero. An expert intimate with this data set would recognize that these are the observations from the first day of the entire data set (highlighted in red by brushing the top of the SeqDate axis), and, as such, the pressure change from the previous day is undefined (not necessarily zero). Yet the database registers an undefined pressure change as zero, and therefore these observations should be cropped from the data set before the next classification attempt, since a group of observations all occurring on the same day and all with exactly zero pressure change would (and do) create or at least heavily influence a class of their own based on misleading information.

Figure 10. Focus on class 24, heavily influenced by spurious data.

Apart from the efficacy of the dynamic PCP for visualizing automated classification results, the technique is well-suited to examine univariate and bivariate characteristics of the data. It can be observed by selecting color breaks carefully that the precipitation variable is (not surprisingly) distributed logarithmically, with many observations at or near zero and few (with decreasing frequency) higher in the range. The humidity variables (see Figure 1, third and fourth axes from left) are perhaps surprising by their lack of correlation: high humidity at the surface does not (nor should it) necessarily imply high humidity in the mid-levels of the atmosphere. For more information about the efficacy of the PCP for examining general statistical characteristics of data sets, see Wegman [1990], Inselberg [1997], and Brundson, Fotheringham et al. [1998].

These are a limited set of examples of insight generation using these tools. Judging a visual analysis tool is most effectively done by applying it to a number of other sorts of data sets, since, as Inselberg correctly points out, each data set has its own "personality" and its exploration calls for considerable ingenuity [Inselberg 1997, p. 107]. Yet the application of this technology to the general types of problems and tasks described above for other data sets is certainly within reason. The tools and methods discussed in this paper afford users the interaction necessary to supplement human understanding and perception to "black-box" classification algorithms. The interactivity provided in the dynamic parallel coordinate plot is designed to facilitate the discovery of the most appropriate classification scheme(s) for complex spatiotemporal phenomena. The methods for multivariate classification and its visualization presented here are designed to reduce the complexity of complex multivariate data and provide an informative and vital connection between the data and the analyst.

The research reported in this paper is funded by a grant from the U.S. Environmental Protection Agency, High Performance Computing and Communications Program (Grant # R825195 - 01 - 0).

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