## Data Representations, Transformations, and Statistics for Visual ReasoningAnalytical reasoning techniques are methods by which users explore their data to obtain insight and knowledge that can directly support situational awareness and decision making. Recently, the analytical reasoning process has been augmented through the use of interactive visual representations and tools which utilize cognitive, design and perceptual principles. These tools are commonly referred to as visual analytics tools, and the underlying methods and principles have roots in a variety of disciplines. This chapter provides an introduction to young researchers as an overview of common visual representations and statistical analysis methods utilized in a variety of visual analytics systems. The application and design of visualization and analytical algorithms are subject to design decisions, parameter choices, and many conflicting requirements. As such, this chapter attempts to provide an initial set of guidelines for the creation of the visual representation, including pitfalls and areas where the graphics can be enhanced through interactive exploration. Basic analytical methods are explored as a means of enhancing the visual analysis process, moving from visual analysis to visual analytics. Table of Contents: Data Types / Color Schemes / Data Preconditioning / Visual Representations and Analysis / Summary |

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### Contents

Data Types | 1 |

Color Schemes | 5 |

Data Preconditioning | 11 |

Visual Representations and Analysis | 17 |

Summary | 61 |

Bibliography | 63 |

Authors Biography | 75 |

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aggregate algorithm AMOEBA analytical process Andrienko animation anomalies applied appropriate power batting average bivariate calculated calendar view centroid Chernoff faces choice choropleth maps color map color scale color schemes Computer control charts correlation created dasymetric map data distribution data set data types data values defined dimensional reduction eigenvectors example exploration Figure geographical given Graphics high-dimensional histogram IEEE inter-annual interactive techniques k-means clustering kernel density estimation line graph means methods Moran’s multi-dimensional scaling multivariate data nearest neighbor node nominal data normal distribution number of bins ofthe data ofvariables parallel coordinate plot parameter player points power transformation principal component analysis relationship represent result Runs Batted sample scanning window scatterplot matrix Self-organizing maps smoothing spatial autocorrelation spatial scan statistic standard deviation star glyph temporal data trends typically underlying analysis underlying data univariate users utilize variance vector visual representation visualization and analysis visualization techniques width