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This chapter has presented the Clutter-reduction Taxonomy for information visualisation. Its construction is novel in several ways. First, it is based on a thorough survey of the literature, both to select a set of clutter reduction techniques that

represent the wide range of methods used in current visualisations and perhaps more importantly, to generate a set of criteria, expressed as benefits, with which to assess each technique. Second, evidence from the literature and the author’s personal experience has assessed each technique whether it satisfies each criterion. Some special cases have been identified together with those which are only met or partially met in certain situations. Discussion of these cases and other comments are logically organised, which makes browsing particularly easy.

The task of selecting a set of clutter reduction techniques is not easy. After the initial survey of the literature resulted in fifteen techniques that were subsequently reduced to eleven which were distinct and represented a wide range in common use. Other techniques such as aggregation and dimensional reduction could well have been included, but on balance they are not used interactively and hence do not feature in the final list. Colour mapping should have perhaps been included, especially as this is referred to in the taxonomy as a method for discriminating between points and lines. However, as a clutter reduction technique, colour mapping is difficult to define.

The differences between point/line displacement and topological distortion were deliberated over. Although it may appear on the display that those techniques which move points should be classified as displacement, it is important to differentiate between moving a point relative to its original position within the frame of reference, and distorting the frame of reference. It can be argued that the difference from the users point of view is influenced by the Gestalt Law of Common Fate9_{. Therefore an}

action, which essentially stretches or distorts the background on which the points are set (the frame of reference), is perceived as moving the points collectively rather than individually and hence is easier to comprehend. One only has to watch a user apply a fisheye distortion to a scatterplot or map to realise that this is viewed by the majority as a collective displacement due to a topological distortion of the background on which the points sit.

Following the presentation of the taxonomy, a case was made for its validity and utility. The validity is based on a sound systematic and inductive approach to its creation, whilst the utility was demonstrated by several examples of its use in developing new visualisations and the prospect of gaining a better insight into the use of techniques.

A comparison was then made between the Clutter-reduction Taxonomy and two other classification schemes related to clutter reduction for information visualisation. Ward [Ward 02] and Bertini’s [Bertini 07] work are both useful in summarising available

9 _{"The law of common fate states that when objects move in the same direction, we tend to see them as} a unit.". http://infovis-wiki.net/index.php?title=Gestalt_Laws

methods or classes and grouping these helps the user consider similarities and differences. However, searching the accompanying text for examples and explanations limits their use and it is unfortunate that that neither author has extended their tables, as in Tables 3-9, 3-11 and 3-12, to provide a more useful overview and incidentally expose omissions. Their usefulness to a visualisation designer is also limited, especially when it comes to combining more than one technique, as there is no clear method of comparing techniques.

We finally looked at why the use of criteria is important in providing a way to compare techniques. A criteria-based classification often leads to a more accessible overview of the data. The act of choosing the criteria and being forced to think about each technique in relation to each criterion is very beneficial in devising the classification in the first place. The Fisheye Menu example demonstrated the benefit of using a criteria- based classification to think about an existing visualisation.

One of the driving forces behind the development of this taxonomy was to assess where sampling fits into the gamut of clutter reduction techniques. This is addressed in the next chapter. However, the process of its construction has prompted a thorough examination of clutter reduction and has produced a tool that can act as a guide to match techniques to problems where different criteria may have different importance. More importantly, this taxonomy provides a means for information visualisation designers to suggest new techniques and critique existing ones.

Chapter 4

Clutter reduction: random sampling

and lenses

In Chapter 3 we considered a proposal for a random sampling-based application, the Astral Visualiser, which raised a number of issues relating to sampling, such as display continuity and suggested the Reality Check function to reassure users. The proposed z-index method looked well placed to address many of these issues and in addition, we saw that sampling showed much promise as a clutter reduction technique.

In this chapter, we will describe the implementation of these features through the development of some sampling visualisations, applying the z-index method to generate the necessary data samples. We uncover the strengths and weaknesses of sampling by comparing it with some other clutter reduction techniques and show the viability of combining techniques. Furthermore, the possibility of localised sampling in the form of a lens, is investigated.

We will also encounter some lens re-sampling animations, enabled by the improved interactive performance and describe two novel lenses, one of which demonstrates the effective use of sampling to enhance a standard feature of parallel coordinate applications.

Section 4.1 describing sampling-based scatterplot and parallel coordinate visualisations. The implementation of the Reality Check is also described together with an illustration of its use.

Section 4.2 compares some clutter reduction techniques including change opacity, change point size, filtering and now sampling using the same dataset to assess their effectiveness.

Section 4.3 considers the problem of sampling datasets with a wide range of overlap densities across the plot. A possible solution of a moveable lens with its own sampling control is proposed. The features of this Sampling Lens application are described, together with some implementation details, including the extension of the z-index method to generate the lens samples.

Section 4.4 illustrates some additions to the visualisation, including two special purpose lenses for parallel coordinates (the inter-axis and axis lenses), a related data visualiser and several experimental Reality Check transitions.

Figure 4-1

Figure 4-2

Sampling-based scatterplot visualisation showing age (horizontal axis) versus monthly income (vertical axis) for a sample of 9432 people [SIPP 2004 dataset]. The point colour represents their highest educational achievement. The key was added later.

Finally, in Section 4.5, we reflect on the main issues that arise from the development of the sampling-based applications, including the Sampling Lens and summarise the benefits and disadvantages of sampling.