Theoretical Foundations of Information Visualization - Information Visualization: Human-Centered Issues and Perspectives - page 51

• whether distances exist between the elements. Any continuous set such as

time, space, and values of temperature has distances, but there may be dis-
tances also in discrete sets such as a set of integer values denoting numbers of
some items. The discrete set of substances has no distances.

• whether and how the elements are ordered. Thus, time moments are linearly

ordered and may also be cyclically ordered, depending on the time span of
observations.

It should be noted that a set consisting of combinations of values of several compo-
nents does not inherit the properties of the individual components. Thus, a set of
combinations of values of melting temperature and atomic weight is only partly or-
dered although the value sets of the original attributes are fully ordered. This data
characterization framework is presented in more detail in [3].

2.2 Patterns

Definition: Pattern is an artifact that represents some arrangement of characteristics
corresponding to a (sub)set of references in a holistic way, i.e. abstracted from the
individual references and characteristics.

This is a more generic definition than is given in data mining: “a pattern is an ex-
pression E in some language L describing facts in a subset F E of a set of facts F [i.e.
a dataset, in our terms] so that E is simpler than the enumeration of all facts in F E ” [4].
In our definition, we mean any kind of representation, for example, graphical or
mental.
We posit that all existing and imaginable patterns may be considered as instan-
tiations of certain archetypes (or, simply, types). It is quite reasonable to assume
that such archetypes may exist in the mind of a data analyst and drive the process of
visual data analysis, which is commonly believed to be based on pattern recogni-
tion: the analyst looks for constructs that can be regarded as instances of the exist-
ing archetypes.
A pattern-instance may be characterized by referring to its type and specifying its
individual properties, in particular, the reference (sub)set on which the pattern is
based. Properties may be type-specific (for example, amount and rate of increase).

2.3 Pattern-by-Data Typology

The following table defines the basic types of patterns in relation to the characteristics
of data for which such pattern types are relevant. We cannot guarantee at the present
moment that this typology is complete; further work is obviously needed. Note that
neither the columns nor the rows of the table are mutually exclusive. Thus, when the
characteristic set is ordered and has distances, the pattern types from all columns are
relevant. Similarly, when the reference set is linearly and cyclically ordered, the pat-
terns from all rows are possible.
These basic pattern types may be included in composite patterns. The types of
composite patterns depend on the properties of the reference set: