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The work of Wong and Bergeron in 1997 [212] provided a historical overview of the vi- sualization field focusing on high-dimensional visualization. They have traced the field’s origin back to a period before 1976 when most of the visualization work was done by

mathematicians, physicists, and statisticians, supported by psychologists. Then they de- scribe three periods of intense development of the field leading to the present day.

The major focus of the paper, however, is on the last two periods of the development, which started in 1987 with the publication of the seminal paper by McCormick et al. [136]. During those periods several techniques, and systems were developed. They noted that the main objectives of the high-dimensional visualization methods are: to visually summarize the data, and to find key trends and relationship among variates.

The authors recognize the difficulty in finding a suitable set of criteria to properly categorize high-dimensional visualization techniques. They suggest, however, possible candidates such as the goal of the visualization, the type and/or dimensionality of the data, and the visual dimensionality of the technique.

They group techniques in three major categories, techniques based on 2-variate dis- plays, multivariate displays, and animation. Because the characterizing feature of these categories is based on the visual nature of a technique we may conclude that the au- thors introduced a display-based classification scheme. The three categories are briefly described next.

2.2.4.1 Techniques based on 2-variate displays

As the name suggests this category encompasses the techniques whose visual represen- tation is essentially two-dimensional. Techniques in this category were designed to deal with just a few hundred data items, and they rarely use colour to depict information.

The origin of techniques that fall into this category is closely related to the field of Statistics, and they have hugely been influenced by work done by Tukey [69, 197], Tufte [195, 196], Cleveland [47–49], and Chambers [39]. Consequently, it is noticeable that the main concern of techniques in this category is to show correlation between variates and provide an exploratory tool that affords the identification of models that better describe the data.

Most of the methods here are made of points and lines and the technique most rep- resentative for this category is unquestionably the scatterplot matrix. They also classify in this category a list of auxiliary tools and concepts that the techniques in this category normally use or follow, such as: using a reference grid to help locating data items; display- ing a fitting curve in an attempt to describe a data model; and employing the banking10 principle to improve the visual perception of the plot.

10_{A principle that requires the adjustment of the aspect ratio to improve the perception of the orientation}

2.2.4.2 Multivariate displays techniques

This is the group where the majority of methods belong. The determining features of this category are: the output of coloured and relatively complex images (which usually means a steep learning curve for the users); a high-speed generation of display to support a considerable degree of interaction; and finally, the ability to deal with datasets more complex than the ones tackled by techniques in the previous category.

This category is further divided into sub-categories11, namely brushing, panel matrix, iconography, hierarchical displays, and non-Cartesian displays.

Brushing This sub-category has only one element:brushingapplied to ascatterplot ma- trix. Brushing is a mechanism that affords direct manipulation of thescatterplot matrix’s visual display. According to the authors brushing can be of two kinds, either labeling or enhanced linking. The former happens when one causes information label(s) to pop- up once an item has been ‘brushed’ by an interactive device, such as a mouse pointer; whereas the latter works in a way similar to that described earlier in Section 2.2.2.2.

Panel matrix This sub-category describes techniques that represent high-dimensional visualization as an array of 2D plots, generated by pairwise combination of variables.

Iconography The defining criterion for techniques in this sub-category is to use graph- ical objects such as glyphs or icons to represent data. The data attributes or variables are mapped to geometric features of these graphic objects. Normally the number of graphical objects is equal to the cardinality of the high-dimensional dataset and they are arranged on the display in such a way as to reveal visual patterns recognizable by humans. It is expected that these patterns represent interesting behaviour of the data.

Hierarchical displays The common characteristic of techniques in this sub-category is to impose a hierarchical organization upon the visual space. Then subsets of the variables are assigned to different levels of that hierarchy, until all the dimensions have been used. Commonly the dimensionality of each hierarchical level is≤ 3.

Non-Cartesian displays In this sub-category the techniques rearrange the axes to be non-orthogonal and the data is displayed along the modified axes.

11_{We have adopted the term sub-category instead of the original sub-group to keep a consistent terminol-}

2.2.4.3 Animation based techniques

This is the third category of the taxonomy and comprises the methods that use animation to enhance the presentation of the data. The authors did not introduce any sub-category for this group.

2.2.4.4 Critique

Firstly we present Table 2.4 that summarizes the Wong and Bergeron classification of concepts, tools, techniques, and software systems.

Group 1: Techniques Based on 2-variate Displays Reference grid, fitted curve, banking, scatterplot matrix

Group 2: Multivariate Based Techniques

Brushing Panel matrix Iconography Non-Cartesian displays Hierarchical display

Brushing technique Hyperslice; Stick figure; Parallel coordinates; Hierarchical axis;

hyperbox autoglyph; VisDB dimension stacking;

color icon worlds within worlds

XmdvTool12

Group 3: Animation Based Techniques

Grand tour, Exvis, scalar visualization animation model

Table 2.4: Listing the techniques and methods classified according to the three categories of Wong and Bergeron’s taxonomy.

The three major contributions made by the authors are the following:-

1. They have contributed to the clarification of terms such as multivariate and multi- dimensional, providing a more formal definition for those terms. They have also presented a historic overview, contextualizing the evolution of the field over a 30 year period (1977-1997).

2. They have compiled a concise and useful description of several representative tech- niques, concepts, and software systems related to the multivariate multidimensional visualization field.

a welcome contribution to the field, although we believe that their classification presents some shortcomings we discuss below.

The first shortcoming is that they do not distinguish interaction techniques (e.g.brush- ing), concepts (e.g. banking), tools (e.g. reference grid), visual techniques (e.g. scatter- plot matrix), or software systems (e.g. XmdvTool). As a consequence one could argue, for instance, that the Exvis fits into the Iconography sub-category, and the animation is just an interaction feature, rather than a defining one. The second point is the creation of the brushing sub-category that describes only one technique. The third drawback is that the definition of the category for techniques based on 2-variate displays may overlap with the definition of the sub-category non-Cartesian displays because theparallel coor- dinates technique, for example, fits into both definitions. Finally, the categories of their classification do not account for data analysis tasks.

The authors recognize, however, that finding a convincing set of criteria that clearly differentiate the visualization techniques is a difficult task.