d, g (ordered) set ↦→ continuous range
Discretise the range of available target values into x steps, where x is the number of source values. If discreteStepCount set
Discretise the range of available target values into discreteStepCount steps.
e ordered set ↦→ ordered set/list
If |source set| ≤ |target set|
Stretch the available range of ordered target values to the whole range of source values (similar to mapping intervals of continuous data).
If |source set| > |target set|
Issue a warning and ask if cycling should be used (will be ambiguous except in special cases, where the context helps to distinguish the values).
f, h, i (ordered) set ↦→ (ordered) set/list
If |target set| = 1
Use the same target value for all source values. Else if |source set| ≤ |target set|
Use a random subset of target values. Else if |source set| > |target set| Issue an error.
For each mapping case shown in Fig. 7.6, we indicate by the background colour whether the mapping case leads to information loss (white), the target graphic attribute is not fully exploited with respect to its ability to express the scale (grey) or whether the scale of source and target values exactly match (green)8. Information may also be lost when discretisation happens during the calculation, e. g., in case a2, we have to accept some information loss, which may be tolerable for the sake of achieving clear distinct values that can more easily be distinguished.
7.4
Defining Scale of Measurement
When calculating Value Mappings, RVL engines must act differently depending on the scale of measurement of source data and target graphic attributes, as we described in the last section. In the following, we introduce the options that the RVL and VISO vocabularies offer for specifying these scales. Furthermore, we describe how RVL engines should proceed in order to derive scales from explicit settings, implicit settings and the data itself.
For globally defining the scale of measurement of a property, vocabulary from the VISO/data module can be used. Making ex:size a subproperty of viso-data:has_quantitative_value tells RVL engines that values of the property size are quantitative, for instance:
ex:size rdfs:subPropertyOf viso-data:has_quantitative_value .
8 Although this is similar to the definition the two expressiveness criteria by Mackinlay [Mac86a], we do not
consider the expressiveness of graphic relations directly in the RVL specification, but, here, we only refer to the relation between the two involved scale of measurements (the scale of the source and the scale of the target values). Statements, as defined by Mackinlay, such as »saturation can only express ordinal and quantitative values« are not considered at the language specification level, but should be loaded from a VISO/facts-based knowledge base by visualisation systems.
CHAPTER 7. A LANGUAGE FOR RDFS/OWL VISUALISATION – RVL
In some cases, setting the scale of measurement globally may not be desired, but needs to be done locally, for the context of a Value Mapping. In other cases, global settings may not be possible, e. g., if no numeric values at all are attached to the resources. Multiple options exist for locally defining the scale of measurement. The first is to define a property to order or quantify the source values, e. g.:
ex:PersonA ex:receivedAward ex:Silver ; ex:Bronce ex:ranked "3"^^xsd:float ;
4 ex:Silver ex:ranked "2"^^xsd:float ; ex:Gold ex:ranked "1"^^xsd:float ; [] a rvl:ValueMapping ;
rvl:orderSourceValuesBy ex:ranked ;
9
... other settings of the Value Mapping ...
Here, rvl:orderSourceValuesBy is used to select the relation ex:ranked for ordering the resources Bronce, Gold, Silver. This allows for ranking these resources differently in different situations. Setting rvl:orderSourceValuesBy resp. rvl:quantifySourceValuesBy can be omitted, if values are assigned via VISO/data properties such as viso-data:has_quantitative_value, as these properties will be evaluated by default. For assigning order, two other options exist: First, an (RDF) list of the resources may be used. Using a list allows for selecting certain values while omitting others. Lists may be created ad hoc and anonymously in a mapping or given a name for reuse.
ex:CityA ex:size ex:Medium ; ex:CityB ex:size ex:Big ; [] a rvl:ValueMapping ; 5 rvl:sourceValueOrderedSet ( ex:Big ex:Medium ex:Small ) ; 10
... other settings of the Value Mapping ...
Second, a property relating the various resources may be selected. In the example below, the scale of measurement for ex:size is given by defining the property ex:gt (greaterThan) as an order relation. This way, the order of the size values Small, Medium, Big is defined.
ex:Big ex:gt ex:Medium . ex:Medium ex:gt ex:Small .
4 [] a rvl:ValueMapping ;
rvl:orderSourceValuesBy ex:gt ;
... other settings of the Value Mapping ...
7.4.1
Determining the Scale of Measurement
The decision diagram in Fig. 7.7 describes how to calculate the scale of measurement of source values from statements defined with the RVL and VISO-data vocabularies. The scale of measurement can be derived from explicitly and implicitly stated global or local settings or – if no other information is available – also be guessed from the source values’ data type. Advanced guessing of the scale of measurement is beyond the scope of this work. However, we specify two domain-agnostic cases based on the type of source literals that are used: For xsd:int, we assume an ordinal scale of measurement and for xsd:float, we assume a quantitative scale of measurement. In all remaining cases, we can only assume a nominal scale.
The calculation of the scale of measurement for the target values (not shown here) could be done analogous to the calculation of the scale of measurement for the source values in Fig. 7.7, but, since we require every graphic relation to explicitly define its scale of measurement, no such calculation is necessary.
7.4. DEFINING SCALE OF MEASUREMENT Scale of measurement explicitly (globally) defined? rvl:orderSourceValuesBy defined? rvl:quan�fySourceValuesBy defined? no
yes,
quan�ta�ve
rvl:sourceValueInterval defined?yes,
ordinal
yes,
nominal
QUANTITATIVE ORDINAL NOMINAL rvl:sourceValueOrderedSet defined? Guess Scale of Measurement depending on the type of literal that is used no yes no yes no xsd:float xsd:int other yes yes noCHAPTER 7. A LANGUAGE FOR RDFS/OWL VISUALISATION – RVL