VISUAL AND SPATIAL ANALYSIS:
Advances in Data Mining,
Reasoning and Problem Solving

Editors

Boris Kovalerchuk
Jim Schwing

The foundations and applications of visual problem solving and decision making are many and varied. To organize these topics, the book has been divided into five parts: (1) visual problem solving and decision making, (2) visual and heterogeneous reasoning, (3) visual correlation, (4) visual and spatial data mining, and (5) visual and spatial problem solving in geospatial domains.

As noted, Part 1 addresses visual decision making and is divided into two chapters. Chapter 1 provides a broad overview of current trends in visual decision making and problem solving. This overview includes: further differentiating the visualization of a solution and the generation of a solution visually. The chapter describes general, hierarchical, visual decision-making models using structural information and ontologies.
Chapter 2 provides an extensive discussion of the efficiency of information visualization techniques. It suggests an informal model (called information visualization value stack model) that predicts a problem area called “sweet spot”, where information visualization will most likely achieve utilization. This model is based on a set of qualitative problem parameters identified in the chapter.
Visual and heterogeneous reasoning is the focus of Part 2 and consists of Chapters 3-7. Reasoning plays a critical role in decision making and problem solving. Chapter 3 provides a comparative analysis of visual and verbal (sentential) reasoning approaches and their combination called heterogeneous reasoning. It is augmented with a description of application domains of visual reasoning. One of the conclusions of this chapter is that the fundamental iconic reasoning approach introduced by Charles Peirce is the most comprehensive heterogeneous reasoning approach.
Chapter 4 describes a computational architecture for applications that support heterogeneous reasoning. Heterogeneous reasoning is, in its most general form, reasoning that employs representations drawn from multiple representational forms. Of particular importance, and the principal focus of this architecture, is heterogeneous reasoning that employs one or more forms of graphical representation, perhaps in combination with sentences (of English or another language, whether natural or scientific). The architecture is based on the model of natural deduction in formal logic. This chapter describes and motivates modifications to the standard logical model necessary to capture a wide range of heterogeneous reasoning tasks.
Chapter 5 provides a discussion of mathematical visual symbolism for problem solving based on an algebraic approach. It is formulated as lessons that can be learned from history. Visual formalism is contrasted with text through the history of algebra beginning with Diophantus’ contribution to algebraic symbolism nearly 2000 years ago. Along the same lines, it is shown that the history of art provides valuable lessons. The evident historical success provides a positive indication that similar success can be repeated for modern decision-making and analysis tasks. Thus, this chapter presents the lessons from history tuned to new formalizations in the form of iconic equations and iconic linear programming.

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