Scientific Visualization, 2019, volume 11, number 1, pages 139 - 176, DOI: 10.26583/sv.11.1.11
Data abstraction models: sampling (parallel coordinates), filtering, clustering
Author: D.V. Manakov1
N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
1 ORCID: 0000-0001-6852-8096 , manakov@imm.uran.ru
Abstract
When considering computer visualization as an independent discipline, it is necessary to build its mental space with its semantics, pragmatics and basis. Thus any two visualization specialists will be able to speak the same language. This basis is chosen from a sufficiently wide interdisciplinary field of knowledge. Verification of visualization in the spirit of fuzzy sets is defined in terms of the ratio of two basis functions of accuracy and completeness of visualization, it must ensure that the end user is offered a formally correct model of visualization or in other words that the developers of visualization systems have solved the task.
At the present stage of the development of computer visualization, the criterion of completeness is more important. First, it is necessary to form a mental space, and then, by clarifying the semantics, the pragmatics and the basis, replacing the mental space with a logical space, go to the verification of visualization. The construction of monotonically increasing basic functions, for example, the accuracy of visualization: statement of the problem, prototype, application, service, allows to view the classification as a continuous process. Possible statements of problems are considered as challenges and determine not only prospective directions of visualization development, but also their set produces a completeness function.
In the computer visualization sector of IMM UrB RAS, the possibility of developing on-line parallel computing services is considered. Based on the web-visualization constructor, one can implement stand-alone support for standard data abstraction models, in particular, filtering, clustering, and sampling. The main part of this paper contains an overview of these models. In order to identify common approaches, we develop a fuzzy verified classification that takes into account both the frequency of occurrence of models, structural units, informative features, and the mathematical level of data abstraction.
Since visualization becomes the environment of an automated analytical process, the directions related to self-organization, for example, dissipative systems, are of interest for visual analytics. From these positions, it is possible to clarify the notion of a structural unit of visual analysis, including data abstraction models. The structural units of the visual process include the visual paradigm, sensitivity analysis, refactoring, calibration, limited uncertainty, web-visualization. Building a logical space provides automatic verification. We propose considering the structural unit as a continuous mapping of the class of subsets of data to a logical space.
Keywords: verification of visualization, logical space, dissipative systems, limited uncertainty, filtering, clustering, sampling, parallel coordinates..
