The paper presents development of the authors' approach to visualization of graph models of various types based on the use of visualization metaphors and aimed at increasing cognitive clarity of these models. One of the key problems of this approach is investigated - namely, formalization of the process of constructing representation metaphors for graph models. Features of graph models that allow formalizing the process of their visualization are considered, the necessary terminology is introduced. A number of principles have been formulated that must be considered when forming metaphors for representing graph models. On the basis of the introduced principles, a general approach to the construction of representation metaphors for visualization of arbitrary graph models is proposed. The main ideas for applying the proposed approach are demonstrated by the example of a fuzzy cognitive map when constructing a metaphor for representing the results of its structure and target analysis. The directions of advanced research have been determined, within the framework of which it is planned to further formalize the approach in order to ensure the possibility of its software implementation. In the future, the presented approach can become an important component of an integrated approach to building a visualization mechanism for an arbitrary graph model, which provides support for efficient visual analysis throughout all stages of modeling.
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In modern theory and practice of knowledge engineering and decision making, it is often required to deal with models that can be represented in the form of graphs. Examples of graph models include
models that is usually the most natural and intuitive for user perception. Indeed, each of these models can be easily associated with a graph with vertices corresponding to the main elements of the object, system or situation under consideration (for example, these can be elements of a decision-making problem or a model of knowledge about a certain subject area), and the edges between the vertices
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correspond to relations between the respective elements. Depending on the type of a model, the vertices
of a graph can be either homogeneous (i.e., represent “equal” elements of the same nature) or
heterogeneous (for example, there are qualitatively different types of nodes in decision trees). A similar
statement is true for the edges of a graph. Semantic interpretations of vertices and edges determine
characteristics of a graph. So, it can be direcred or undirected, be or not be weighted, allow cycles or
be acyclic, etc. Also, a mathematical apparatus, used within the framework of a specific type of graph
model, plays an important role: for example, probabilistic models [
The presence in the discussed models of the graph form of representation naturally leads to the
problem of their visualization. It is characterized by the availability of many possible ways to solve it,
among which, as a rule, there is no predominantly correct way. Taking this into account, an approach
can be used to describe the visualization problem in general which is based on the concept of a
visualization metaphor [
An important aspect of working with any graph model that affects the efficiency of its application
is the simplicity of perception of the model by the researcher. To describe this aspect, a concept of
cognitive clarity is often used [
In [
Accordingly, each of constituents of a visualization metaphor must contribute to enhancing
cognitive clarity of a graph model. At the same time, the spatial metaphor provides an increase in
cognitive clarity mainly due to optimization of a number of formal indicators characterizing graph
tiling, which are taken as criteria for cognitive clarity at this stage. The authors proposed [
Graph model
Spatial metaphor Representation metaphor
Thus, at the moment, the task of constructing spatial metaphors of graph models has a general solution, which is later to be elaborated and adapted for various types of models considering their specific features. At the same time, we are also interested in formalization and automation of the process of constructing qualitative metaphors for representing graph models which provide a high level of cognitive clarity of these models in their visual analysis. Next, we will consider some ways to solve this problem.
significant in the context of their visualization.
First, each specific type of graph models is characterized by a certain structure which can be formally described. So, in the general case, the main elements of the model (i.e., graph vertices) can belong to one of several types, the conceptual meaning and internal structure of which, as a rule, are specified and described in advance. The same applies to relations between elements (graph edges) – the acceptable types of such relations and the corresponding conceptual interpretations are usually known in advance. Further, to simplify the terminology used, we will call structural components of the corresponding graph – both vertices and edges – model elements.
Secondly, as a rule, model elements are assigned some attributes (i.e. properties, characteristics of these elements) that have certain tolerance ranges and interpretations and can also have an internal structure, i.e. contain a number of simpler attributes. Elementary attributes that have no internal structure, from the point of view of tolerance ranges, usually correspond to elementary data types: text strings, integers or real numbers (often from certain ranges), elements of discrete sets, binary yes/no values, etc. In fact, attributes make up the parametric space of a graph model and can reflect both its initial data (that is, specified when building the model) and the results of its analysis.
attribute of the element is rendered by assigning some visual feature corresponding to the visual image.
of model elements, the visual features of which reflect the attributes of these elements.
Thus, a type of tolerance range of the attribute must be considered, in particular, whether it is discrete or continuous. It should also be taken into account whether it is important to know the exact value of the attribute from the point of view of the visual analysis of the model, or whether some “approximate picture” which provides a qualitative insight into the situation is sufficient. Otherwise, the choice of visualization methods is predominantly subjective. In addition, in some cases it can be dictated by already established traditions. Such a situation often arises in cases of widespread use of software tools for supporting a certain type of model (for example, it is characteristic of Bayesian networks). In any case, possible ways to visualize various types of attributes can be represented in a certain formalized form, thus forming a knowledge base suitable for use in developing representation metaphors for any graph models.
Also, when building representation metaphors, it is important to consider that various attributes of model elements become relevant at different stages of modeling. For example, at the stage of building a model, attributes representing the results of its analysis will be irrelevant (since at this stage they do not yet have definite values). In addition, if the process of model analysis includes a number of logically separate stages (as, for example, in the case of cognitive maps where it is customary to distinguish structure and target and scenario stages of analysis), then such a model is characterized by the presence of several separate groups of element attributes. In turn, each of the stages can be logically divided into sub-stages, which leads to emergence of subgroups of attributes, etc. All this allows us to introduce the concept of a graph model representation, by which we mean a special relation between elements and their attributes. The representation selects from the set of all element attributes a subset of those that are to be visualized. Thus, when constructing metaphors for visualizing graph models, the representation can be used as a named template that makes it easier for the analyst to select model elements and attributes for solving a specific visual analysis problem.
Let us formulate a number of principles that determine the rules of forming representation metaphors for graph models. These principles should be considered when developing approaches to constructing such metaphors. The semantic content of these principles is schematically illustrated in Fig. 2. 1. The principle of partial visualization. As a rule, only some subset of elements and their attributes available in the model are visualized “at one point in time” (or, based on the terminology introduced above, one representation is visualized). This is due both to the high structural and parametric complexity of graph models, which, as a rule, exceeds the analyst’s cognitive capabilities, and to the multi-stage process of studying models, when at a certain stage there is a possibility and need to visualize only a part of the information related to the model. 2. The principle of injective visualization. Different attributes of model elements within the same representation metaphor must be visualized in different ways. In other words, mixing of two or more attributes within one visual feature is not allowed, since this will entail mixing of the corresponding properties of the model in the analyst's perception. 3. The principle of surjective visualization. Each separate visual feature must reflect a specific attribute that is significant in the context of the problem being solved. In other words, the researcher's perception of the model must not be cluttered with information that is irrelevant in the context of the problem, since this can lead to a slowdown in visual analysis. 4. The principle of subordination. Each subordinate element of the model must be visualized in such a way that its visual image makes it possible to unambiguously establish which particular element it is subordinate to. A special case of subordination is logical nesting of one element of the model in another, which should be displayed, respectively, as nesting of visual images. 5. The principle of restructuring. In some cases, it is possible to merge two discrete attributes into one attribute based on the Cartesian product of their tolerance ranges. So, in the example considered below (Table 1), it is allowed to merge the “Type” and “Target” attributes (the resulting attribute takes on the values “unmanaged target”, etc.). The reverse variant of application of this principle is s teu ed ittrb lizua fa is to ve e b sub to S
Model element А1 А2 А3 VF1 VF2 VF1 VF2
VF3 also possible: the original attribute is split into two attributes of different types. For example, the attribute “Influence magnitude” can be divided into “Influence sign” and “Influence intensity” (Table 2). In general, application of this principle allows optimizing a representation metaphor due to a more rational use of the space of available visual features.
Partial visualization principle Space of model input data
Space of visual model
to be visualized
and/or expanding the space of visual features
visualized within one representation metaphor. This stage can be performed in an accelerated version, by choosing a specific representation from a set of possible representations (if there is a similar set which can be formed, for example, on the basis of previous experience with graph models of this type).
In fact, at this stage, an attempt is made to establish a correspondence between the specified attributes and the available visual features taking into account the known methods of visualizing attributes of various types. Available visual features are formalized by means of a basic template of a visual image – a pre-compiled structure that stores a hierarchy of visual features with indications of their types. At this stage, compliance with the principles of injective and surjective visualization as well as the principle of subordination is ensured. If necessary, it is possible to use the restructuring principle, while the decision to merge or split attributes is made by the analyst. 3. If it is impossible to establish at least one correspondence option, the analyst can be offered to narrow down the subset of visualized attributes. The excluded attributes can be visualized in the future using a different representation metaphor. Another way to achieve the desired correspondence is to expand the space of available visual features by modifying the visual image template, which is also performed by the analyst. In each of the two methods, it is possible and advisable to formulate recommendations for the analyst on the choice of an optimal course of action to achieve the required result. 4. Generating possible options for representation metaphor implementation, which is carried out according to the principle of enumerating visualization methods (i.e., combining acceptable correspondences between attributes and visual features), considering the given preference of these methods.
metaphor for V.B. Sylov’s fuzzy cognitive map (FCM) [
and have a single set of attributes, thus being “homogeneous”, i.e. belonging to the same type. All relations between elements (relations between concepts) existing in the model define cause-and-effect influences between them, have common sets of attributes and, thus, also belong to the same type.
a small sample of attributes is given), for which tolerance ranges and examples of visualization methods
that provide sufficient cognitive clarity are indicated. When listing the attributes, the authors relied
on the implementation of Sylov’s FCM apparatus within the framework of IGLA decision support
system [
and is going to visualize the following concept attributes at the same time: name, type, influence on the system, as well as all available attributes of relations between concepts. Meanwhile, suppose that the basic template of the concept visual image contains only two visual features: the text displayed on it and the background color (which corresponds to the quest for creating the simplest metaphors with high cognitive clarity).
correspondence between attributes and visual features under the indicated conditions. According to known visualization methods (which could be obtained by formalizing knowledge from Table 1), the displayed text is matched to the concept name, but the background color of the concept cannot simultaneously reflect its two other attributes (type and influence on the system). Accordingly, a violation of the principle of injective visualization has occurred.
Customer requirement volume
Value of SP from users’ point of view
Requirement specification complexity Software product quality
Level of utilized
technology
Number of improvements at the implementation stage
Expected workload Volume of attracted resources
The key difference between these representation metaphors is the way of visualizing the influences of concepts on the system: the colors of the graph vertices (Fig. 4) and the elements of the bar graph distributed over the set of vertices (Fig. 5) are used as visual features. This allowed, in the second metaphor, to “release” the vertex color for visualization of the concept type (thus, in this cognitive model, the concepts “Customer requirement volume” and “Requirement specification complexity” are managed, i.e. direct control actions can be exerted on the corresponding parameters of the system, the other concepts are unmanaged). Thus, the advantage of the second metaphor is the simultaneous visualization of the concept type and its influence on the system. Due to this, the analyst can obtain a larger amount of information of interest to him in the course of one act of visual perception of the cognitive model. The “trade-off” for this is the speed of the very act of perception, which slows down due to the complication of the visual image, which, however, in the given example is insignificant.
concepts) can demonstrate flexibility of the proposed approach and consideration of the subjective component within its framework: the choice of the final version of the representation metaphor from a number of acceptable ones as well as adjustment of preferable color schemes remain with the analyst.
mechanism can be the performance of all necessary actions with the graph model predominantly (or even exclusively) in a visual form. In other words, the visualization mechanism can be considered the more successfully constructed, the more work can be done with its use without involving alternative means and forms of information display.
A number of specific directions can be also indicated for the development of the proposed approach in the near future. They are focused primarily on ensuring the possibility of software implementation of the algorithm that underlies it: Formalization of the terminological apparatus introduced within the framework of the approach, in particular, the concepts of a graph model element, an attribute, a representation, a visual image and a visual feature. Development of a language (languages) for a formal description of the composition of the graph model and the structure of its visual image or adaptation to this task of any of the existing markup languages (for example, XML or JSON). Providing automated generation of a set of graph model representations based on a formal description of its composition. Development of a language for formal description of representation metaphors for graph models resulting from the application of this approach.
In the context of the indicated directions, a software tool for supporting visual analysis of various graph models of knowledge representation and decision making can become a promising applied result of the research carried out by the authors. This tool can be implemented in the form of a library for building visual analysis mechanisms, which can be used in the development or modernization of decision support systems and other software systems the work of which is closely related to information representation in the form of graphs.