A new Family of Time-Plots

Perception of multidimensional data is a very tricky thing. Usually two dimensional data (e.g. a scatter plot of body height versus body weight) can be easily inspected by eye, whereas tree dimensions are often difficult to analyze. The focus of interest in analysis of such data lies on the interactions between the variables. The complexity of interactions between the variables does not increase in a linear way, but in the order of n!. This problem often urges researchers to abandon visual inspection and interpretation of their data and to start the analysis by statistical means, applying models offered by their statistical packages rather than the researcher's knowledge about the data.

Geographical data which change over time have by definition at least four to five and often more dimensions: two or three dimensions representing space, one dimension for time, and one or several dimensions for the attributes of interest.

In the past several methods were developed to deal with the problem of higher dimensional data. One common approach is to use color (hue, saturation, value), texture and symbols additionally to the two dimensions available on a sheet of paper or a computer monitor to ``squeeze'' all the dimensions into one graphical representation (Healey, 1997; Winfree, 1980; Bertin, 1977). Basically this effort assumes that by depicting all information into one graphic, one should be able to recognize the patterns hidden in the data. An example of such a plot is given in figure 5.1 for an ant walking on a petri dish.

Figure 5.1: Example 3-D plot with two spatial (x, y) and one temporal axis of an ant walking on a petri dish. It illustrates how difficult it is to interpret higher dimensional representations.

This method works fine for presenting results at a final stage as it is often done in cartographic representations. For the exploratory and analytical steps it disregards the fact that the human perception is seldom capable of making use of multiple aspects for pattern detection at once. Most of the time overlaying several attributes onto the same graphic is hiding more than it is revealing. Receiving a complex picture we often try to extract partial information out of it to identify the information needed as we do for example in the tests for red/green blindness.

In this section I will present a novel approach for analyzing the patterns in concern here, the movements of animals. The basic idea is to reduce the dimensionality of the data to a level of complexity that does not over-burden our perception. This is performed by reducing the spatial aspects to one dimension (e.g. distance, angle, parallelity) and introducing one or two time axes. Using this technique new analytical plots are created to help identify regularities in the data. By introducing time axes into these plots, an overview of the spatio-temporal changes in the movement data can be obtained.

In the following sections the so-called Family of Time-Plots (figure 5.2) is presented. The name comes from the Time axis used. The following discussion is divided into three parts. The first part introduces the T-plots (sections 5.1- 5.4). These are relatively simple plots with one time axis, where the Concept of Temporal Data Frames (Chapter 4) is applied. They visualize the change of one spatial aspect. The next section introduces the TT-Plots, which contain two time axes (sections 5.5- 5.9). They are used to analyze intra-dataset parameters, i.e. characteristics originating from a single dataset. Then the TT2-Plots will finish the section (section 5.10). They also contain two time axes, but they are intended for use with 2 datasets to describe inter-dataset characteristics).

Figure 5.2: Classification of the Time-Plot Family.

If someone tries to identify geometrical shapes in snow patterns, he or she needs to be able to name a set of shapes such as squares, circles, lines and ellipses or more concrete ones such as a house, a bird, or a sheep as it is done in the Japanese yukigata (snow pattern descriptions, Yamada (1996)). The same is the case when someone tries to identify patterns in point arrangements or movement patterns. Hence the plots are first illustrated using artificial data, starting with simple patterns followed by more complex data (figure 5.3). Then a first approach to an identification catalogue is presented. In chapter 6 applications of these analysis methods to real biological data are presented.

The artificial movement patterns used for demonstration purposes are shown in figure 5.3. Beginning with the most simple form, the first pattern represents a point walking forth and back on a diagonal line (5.3a). The second movement is an object walking on a circle, whereas the third describes a 8-shaped movement. The last and most complicated artificial movement pattern introduced here is a star shape, where the object passes several times through a center in the middle of its activity (5.3d).

Figure 5.3: Artificial movement patterns used for demonstration purposes (from left to right): a: line, b: circle, c: 8-shaped, d: star.

a

b

c

d

These four movement patterns will serve as introductory examples in the next sections.