From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> The goal of the research described in this paper is to develop an application-independent presentation tool that automatically designs effective graphical presentations (such as bar charts, scatter plots, and connected graphs) of relational information. Two problems are raised by this goal: The codification of graphic design criteria in a form that can be used by the presentation tool, and the generation of a wide variety of designs so that the presentation tool can accommodate a wide variety of information. The approach described in this paper is based on the view that graphical presentations are sentences of graphical languages. The graphic design issues are codified as expressiveness and effectiveness criteria for graphical languages. Expressiveness criteria determine whether a graphical language can express the desired information. Effectiveness criteria determine whether a graphical language exploits the capabilities of the output medium and the human visual system. A wide variety of designs can be systematically generated by using a composition algebra that composes a small set of primitive graphical languages. Artificial intelligence techniques are used to implement a prototype presentation tool called APT (A Presentation Tool), which is based on the composition algebra and the graphic design criteria. <s> BIB001 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> An automatic presentation system is an intelligent interface component which receives information from a user or application program and designs a combination of graphics and text that effectively conveys it. It is a facility that assumes the presentation responsibilities for other programs. An important research question has been how information should be specified or described by an application program for it to be presented by an automatic presenter. This paper proposes a taxonomy of information characteristics which would need to be provided to either human or computer designers for them to create presentations reflecting the individual needs of a diverse group of users. The proposed taxonomy of characteristics defines the representational goals for intelligent interfaces which reason about graphical displays. <s> BIB002 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> An extension to the n-Vision visualization system, which provides users with a 3D virtual world within which they can visualize and manipulate representations of multivariate relations is discussed. The extension, AutoVisual, is rule based system that eliminates the difficulty in choosing among the many alternative when designing visualizations. AutoVisual designs interactive virtual worlds for visualizing and exploring multivariate relations. It is guided by user-specified visualization tasks and a rule base of design principles. AutoVisual's visualization techniques and the visualization tasks it handles are described. Example visualizations AutoVisual has generated for two problem domains are discussed. > <s> BIB003 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> Vista is a knowledge-based system that helps scientists design visualization techniques. It generates a technique for a given data set and lets users modify the design interactively using a compositional design methodology. To ensure the effectiveness of its designs, Vista uses many rules, mostly heuristic in nature, that were acquired through literature surveys and discussions with visualization experts. In general, Vista's design was based on research in graphical perception. It extends the design methodology of Automatic Presentation Tool (APT) (J.D. Mckinlay, 1986), a presentation tool for 2D graphics, to three dimensions. While Vista's primary function is to automatically generate an effective visualization technique design for a given data set, it also allows users to interactively modify this design and renders the resulting image using a variety of rendering algorithms. > <s> BIB004 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> In order to develop a foundation for visualization, we develop lattice models for data objects and displays that focus on the fact that data objects are approximations to mathematical objects and real displays are approximations to ideal displays. These lattice models give us a way to quantize the information content of data and displays and to define conditions on the visualization mappings from data to displays. Mappings satisfy these conditions if and only if they are lattice isomorphisms. We show how to apply this result to scientific data and display models, and discuss how it might be applied to recursively defined data types appropriate for complex information processing. > <s> BIB005 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> We focus on the research required to establish a foundation for the evolving needs of visualization systems. Three main topics underpin these needs: models, the need for abstractions to describe the core components of the visualization process and the interfaces between them, including users and their behavior; validation, the problem of determining whether visualizations meet consistency and effectiveness criteria on test data or measures; and systems, the design, realization, and operational problems of systems integrating a range of functionalities to give scientists a working environment for visualization. We outline key aspects of each topic, commenting on the current status of work and isolating areas that require significant research. We conclude by suggesting strategies to initiate this research. > <s> BIB006 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> Visage is a prototype user interface environment for exploring and analyzing information. It represents an approach to coordinating multiple visualizations, analysis and presentation tools in data-intensive domains. Visage is based on an information-centric approach to user interface design which strives to eliminate impediments to direct user access to information objects across applications and visualizations. Visage consists of a set of data manipulation operations, an intelligent system for generating a wide variety of data visualizations (SAGE) and a briefing tool that supports the conversion of visual displays used during exploration into interactive presentation slides. This paper presents the user interface components and styles of interaction that are central to Visage's information-centric approach. <s> BIB007 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> In this paper , we describe a novel technique for visualizing large amounts of high-dimensio nal data, called ‘circle segments’. The technique uses one colored pixel per data value and can therefore be classified as a pixel-per-value technique [Kei 96]. The basic idea of the ‘circle segments’ visualization technique is to display the data dimensions as segments of a circle. If the data consists of k dimensions, the circle is partitioned into k segments, each representing one data dimension. Inside the segments, the data values belonging to one dimension are arranged from the center of the circle to the outside in a back and forth manner orthogonal to the line that halves the segment. Our first results show that the ‘circle segment’ technique is very powerful for visualizing large amounts of data, providing more expressive visualizations than other wellknown techniques such as the ‘recursive pattern’ technique and traditional ‘line graphs’. <s> BIB008 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> Information visualization encounters a wide variety of different data domains. The visualization community has developed representation methods and interactive techniques. As a community, we have realized that the requirements in each domain are often dramatically different. In order to easily apply existing methods, researchers have developed a semiology of graphic representations. We have extended this research into a framework that includes operators and interactions in visualization systems, such as a visualization spreadsheet. We discuss properties of this framework and use it to characterize operations spanning a variety of different visualization techniques. The framework developed in the paper enables a new way of exploring and evaluating the design space of visualization operators, and helps end users in their analysis tasks. <s> BIB009 </s> From visual data exploration to visual data mining: a survey <s> Formal Models of Visualization <s> Originally published in French in 1967, "Semiology of Graphics" holds a significant place in the theory of information design. Founded on Jacques Bertin's practical experience as a cartographer, Part One of this work is an unprecedented attempt to synthesize principles of graphic communication with the logic of standard rules applied to writing and topography. Part Two brings Bertin's theory to life, presenting a close study of graphic techniques including shape, orientation, color, texture, volume, and size in an array of more than 1,000 maps and diagrams. <s> BIB010
Creating visualizations has been dealt with hitherto essentially as an ad hoc process, without any formal design methods, engineering, or evaluation, although some previous attempts at formalizing the visualization process have been made. The usefulness of such formal models is threefold. First, they can offer consistent user guidance on how to tackle the process of creating visualizations from data. Second, to some extent they can help in fully or partially automating the process of creating visualizations. Third, they can provide an objective basis for comparison of the effectiveness of different visualizations of the same data to achieve a certain task and also offer insight for the creation of new techniques. Most of the previous work on formal models has been targeted either at presentation graphics BIB010 , BIB001 or scientific visualization BIB003 ,  , BIB004 , 42], BIB002 , BIB007 5 ,  . Many research efforts on deriving systematic approaches for generating scientific visualizations have been conducted as part of attempts to automate the process and have been strongly influenced by the early work on APT-A Presentation Tool BIB001 . Albeit a starting point, they do not offer much help in analyzing visualizations of high-dimensional Table Data as the nature of both data sets and visual data exploration tasks differ considerably from those of scientific data. A notable exception is the Data State Reference Model by Chi and Riedl BIB009 , which uses an operator framework to characterize different visualization techniques (both scientific and information visualizations). Chi  argues that, although taxonomies of visualization techniques based on the data domains are useful to end users, they do not help implementers to understand the design options and the potential applicability of such techniques. The Data State Model, depicted in Chi's operator-centric framework provides a conceptual model that extracts all the crucial visualization operations (meaning user interactions) along the visualization pipeline, enabling the identification of the important artifacts for design. As such, it can help both end-users and designers to get better insight into the whole visualization process, creating an understanding of the situations in which operators can be applied, how they can be applied, and what they do. End users can predict the results of their interaction actions and choose the appropriate operators to achieve a desired result. Designers can classify and understand the relationships between operators and the composition of interactions and also identify similarities among different techniques, with the potential to encourage system modularization and standardization. The framework provides an alternative basis for categorization of visualization techniques and environments as compared to the approaches discussed in Sections 3.1 and 3.2. A table is provided in BIB009 showing how 36 different techniques and systems fit into this taxonomy. Hoffman  proposes a formal model of Table Visualiza tions based on an abstraction named Dimensional Anchor (DA). The DA is an attempt to provide a unified model for some table visualization techniques (Parallel Coordinates, Survey Plot, RadViz, and Scatter Plots). It is a construction with an associated geometry, typically a straight line, and a set of graphical parameters. In his particular implementation of the model, Hoffman defines nine meaningful parameters, such as size of scatter plot points, width of the rectangle in a survey plot, and so on. The arrangement of a number of DAs determines the basic layout of the visualization for different techniques. Hoffman defines a generalized visualization BIB008 . Homepage for the SAGE Project: http://www.cs.cmu.edu/Web/ Groups/sage/sage.html. space and a visualization function for generating a specific visualization display, which allows a mathematical treatment of the visualizations. His work is a preliminary attempt at a generalized treatment of visualization techniques whose major contribution is to point out the desirability and feasibility of such a generalization and the creation of "families" of techniques with shared characteristics. Further research is required to take it to an appropriate formalization level as the current formalization is not sufficiently general to encompass all visualizations or even all visualizations in the category it addresses. Although both this and the Data Space Model by Chi and Riedl are not formal as compared to the formal model proposed in BIB005 or the general reference model aimed at in BIB006 , they illustrate interesting attempts toward explaining and systemizing the process of producing visualizations.