Exploring the temporal dimension enables understanding and explaining past events, analysing actions in the present and predicting future outcomes. Time has been thor- oughly explored across many areas, with different ways of perceiving and representing time. For instance, chronobiology (Halberg, 1969) is concerned with the temporal characteristics of biologic phenomena, including sub-topics such as chronophysiology,
chronotoxicology and chronopathology. In artificial intelligence, formalising the notion of
time enables computational reasoning about time and relating non-temporal assertions to temporal assertions (Pani and Bhattacharjee, 2001). Yet another area of study is geography, where understanding spatiotemporal processes necessarily includes time in order to derive cause and effect relationships and represent change (Peuquet, 1994). In some of these areas, time is conceptualised according to their specific needs; higher level concepts and characteristics of time, however, can be used across multiple disciplines.
For example, describing the multiple units of time as granularities is relevant to both geography and artificial intelligence.
As temporal data visualisation is closely related to the lower level aspects of representa- tion of temporal information, some areas of study are more relevant than others. Aigner et al. (2011) highlighted in particular the works of Goralwalla et al. (1998), in databases, and Frank (1998), in geographic information systems. Goralwalla et al. described an object-oriented model of time based on four aspects of temporal data: the structure of time, the representation of time, the order of time and the history of time. The following sections introduce these four aspects and relate them to data visualisation.
Temporal structure
The temporal structure contains the basic temporal features of a model of time. Three components are defined by the author: the type of time primitive, the type of time
domain and the determinacy of time. The time primitives represent the different ways
that observed time can be described: anchored primitives can have a temporal location (e.g. November 23rd), while unanchored primitives refer to quantities of time (e.g. 3 days). Anchored primitives are divided into instants, which are single anchored times, and intervals, which are pairs of anchored times. The only unanchored primitive is a
span or duration.
The domain refers to the mathematical structure that is used to describe the primitives: in discrete domains, time primitives are modelled after integers: 0 second is always followed by 1 second ands this applies to every unit of time. In continuous domains, time can be infinitely divided: 0 second can be 0.1 second, 0.2 second and so on. Bettini et al. (1998) also introduced the idea of lower and upper bounds of a time domain; as, in practice, very often data is collected over a certain period of time instead of
infinitely, the bounds define the starting and ending times of the collection period.
Finally, determinacy refers to the uncertainty that is inherent to the relationship between the different time units and the non-temporal observations: an event that occurred on November 23rd is indeterminate in relation to the hours of that day.
Structure and visualisation: visualising temporal data requires deciding through
which visual channels the temporal dimension will be displayed. The structure of time directly influences this decision; many times it is directly related to the data and thus not always under control of the visualisation designer. Most visual channels
are appropriate for representing instants. Intervals, on the other hand, require the representation of both its starting and ending times; durations can also be derived from intervals. This leads to the following design choices, illustrated in fig. 2.1:
• Anchored visual mark: the length property of visual marks can be used to display the temporal interval by mapping time to one positional visual channel and anchoring the visual mark at the appropriate starting and ending times;
• Unanchored duration: when there is no need to display time in a positional visual channels, the interval duration can be calculated instead. In this case, the
duration ceases to be a reference and becomes a non-reference attribute;
• Mixed approach: a cartesian representation called triangular model (Qiang et al., 2012) uses both methods to display interval data. In this type of visualisation, the temporal domain is mapped to the horizontal axis, while a scale of duration is mapped to the vertical axis. In this case, point-based visual marks are used to represent intervals and anchored in the calculated midpoint of the interval. Vertically, the point is positioned in the corresponding value of the duration. This combination severely limits the choices of visual encodings for non-temporal attributes and is discussed again in later chapters. Another mixed approach is the representation of set of possible occurrences (SOPO) proposed by Rit (1986) which emphasises the uncertainty of events happening during an interval.
Temporal representation
This aspect is concerned with human readability and usability with regard to time; it relates to the multiple units of time (or granularities) that humans use to represent the passage of time and the temporal scales that result from the organisation of these units, primarily in the form of calendars. The relationship between different granularities and how to manage them has also been explored in areas such as databases; Bettini et al. (1998) introduced the formal concept of a calendar, while Dyreson et al. (2000) described a model to efficiently support granularities in databases based on these concepts. Goralwalla et al.’s concept of calendar is a set of granularities, with definitions of labels and number of time points in each granularity, and conversion functions between the granularities.
Representation and visualisation: granularities determine the number of time
t t1 t2 t t1 t2 I1 I1 (a) (b) (c) | {z } I1 d d
Fig. 2.1 Visual representations of intervals. In (a), an anchored visual mark is used to represent interval I1 in a temporal horizontal axis. In (b), the duration of the interval
is derived and displayed as the length of an unanchored bar; in this case, the horizontal axis may contain a distribution of intervals, for example, for comparing their duration. In (c), the mixed approach is used; the point corresponding to I1 is placed on the midpoint of the interval in the horizontal axis and on the corresponding duration in
the vertical axis.
used to visualise the data, which must be configured to facilitate addressing the tasks that are related to the granularity. In interactive visualisations, the support for multiple granularities must also be considered; this is further discussed in this chapter and is one of the direct motivations for this research.
Temporal order and history
Temporal order refers to the flowing of time in relation to the number observers. Goral- walla et al. define two types of order: linear and branching. In a linear domain, time flows from past to future in a single viewpoint. Branching domains contain points in
time where viewpoints on the data diverge. One example is a measurement that is consistent up to a certain date; from that date on, different measurements are taken and share the same temporal reference. Order is also closely related to the characteris- tics of granularities such as the cyclical nature of months, days, etc. In fact, Frank (1998) provided an alternative classification of time in which he considered linear and
cyclic time separately from branching time: in this case, branching is considered as a
characteristic of all attributes of the dataset instead of only the temporal domain.
Order and visualisation: the order is an informing characteristic of time that guides
the design of visualisations. Visualisation can emphasise linear, cyclic or both aspects of time (see fig. 2.2). For instance, circular arrangements can be used with cyclical time, such as months of the year, where January and December are contiguous in the visualisation; months of the year can also be visualised through charts from left to
right, where the cyclical aspect of months is not emphasised. Lastly, spirals are an
example of visualisation that emphasise both aspects, as the spiral grows linearly and yet time points are visually aligned in cycles.
t
t
t
(a) (b) (c)
t
Fig. 2.2 Schematic representation of temporal order. In (a), linearity is emphasised. In (b), cyclicity is emphasised. In (c), the visualisation emphasises both linear (blue arrow) and cyclic (red arrow) aspects.
The history aspect refers to data management issues, such as deciding how non-temporal variables are related to temporal variables in observed records. As such, it does not have particular effects on the visualisations.
Summary
This section described the basic concepts of time primarily informed by Frank (1998); Goralwalla et al. (1998): how it can be modelled as temporal data and what are the primary characteristics that relate to temporal data visualisation. The following section
describes how frameworks and theories in the visualisation literature employ these concepts to facilitate visualisation design.