Tasks

Abstract

In this chapter, we use the metaphor of a mathematical function to identify the types of tasks (questions) involved in exploratory data analysis. A task is viewed as consisting of two parts: the target, i.e. what information needs to be obtained, and the constraints, i.e. what conditions this information needs to fulfil. The target and constraints can be understood as unknown and known (specified) information, respectively; the goal is to find the initially unknown information corresponding to the specified information.

Our task typology has its origin in the ideas expressed by Jacques Bertin in his Semiology of Graphics (Bertin 1967/1983). Like Bertin, we distinguish tasks according to the level of data analysis (“reading level”, in Bertin’s terms) but additionally take into account the division of data components into referrers and attributes:

• Elementary tasks refer to individual elements of the reference set; for example, “what is the proportion of children in the enumeration district X?”

• Synoptic tasks involve the whole reference set or its subsets; for example, “describe the variation of the proportions of children over the whole country” (or “over the southern part of the country”).

The tasks are further divided according to the target (“question type”, in Bertin’s terms), i.e. what is the unknown information that needs to be found. At the elementary level, the target may be one or more characteristics (attribute values) or one or more references (referrer values). For example:

• What is the proportion of children in the enumeration district X? (That is, find the characteristic corresponding to the reference “district X”.)

• In what enumeration districts are the proportions of children 20% or more? (That is, find the references corresponding to the characteristics “20% and more”.)

It is important that, when a task involves several references, each of them is dealt with individually.

We have extended Bertin’s ideas by explicitly considering the possible relations between references and between characteristics. Relations may also appear in a task target or may be used in task constraints. For example:

• Compare the proportions of children in district X and district Y (i.e. find the relation between the characteristics corresponding to the references “district X” and “district Y”).

• Find districts where the proportion of children is higher than in district X (i.e. find references such that the corresponding characteristics are linked by the relation “higher than” to the characteristic of “district X”).

At the synoptic level of analysis, we introduce the notion of a “behaviour” — the set of all characteristics corresponding to a given reference (sub)set, considered in its entirety and its particular organisation with respect to the reference sub(set). The behaviour is a generalisation of such notions as distributions, variations, and trends; for example, the variation of the proportions of children over the whole country or the trend in a stock price over a week.

Synoptic tasks involve reference (sub)sets, behaviours, and relations between (sub)sets or between behaviours. Here are a few examples:

• Describe the variation of the proportion of children over the whole country (target: the behaviour of the proportion of children; constraint: the whole country as the reference set).

• Find spatial clusters of districts with a high proportion of children (target: the reference subset(s); constraint: the behaviour specified as “spatial cluster of high values”).

• Compare the distributions of the proportion of children in the north and in the south of the country (target: two behaviours and the relation between them; constraint: two reference subsets, the north and the south of the country).

Elementary tasks play a marginal role in exploratory data analysis, as compared with synoptic tasks. Among synoptic tasks, the most challenging are tasks of finding significant connections between phenomena, such as cause-effect relations or structural links, and of finding the principles of the internal organisation, functioning, and development of a single phenomenon. We call such tasks “connectional”.

The main purpose of our task typology is to evaluate the existing tools and techniques for EDA in terms of their suitability for different tasks and to try to derive operational general principles for tool selection and tool design.