# Low-Level Components of Analytic Activity in Information Visualization

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4 4. Find Extremum General Description: Find data cases possessing an extreme value of an attribute over its range within the data set. Pro Forma Abstract: What are the top/bottom N data cases with respect to attribute A? - What is the car with the highest MPG? - What director/film has won the most awards? - What Robin Williams film has the most recent release date? Finding high or low values of an attribute was a very common operation across the student questions. Note that this task differs from Sort (task 5) since a complete sort is not always necessary to find an extreme value, and also differs from Find Anomalies (task 8) since anomalies are not always extreme values. 5. Sort General Description: Given a set of data cases, rank them according to some ordinal metric. Pro Forma Abstract: What is the sorted order of a set S of data cases according to their value of attribute A? - Order the cars by weight. - Rank the cereals by calories. Although this task is fairly self-explanatory, it appeared only infrequently as a task unto itself. Sorting is generally a substrate for extreme value finding, especially when searching for a number of values at the extreme and not just the most extreme value. 6. Determine Range General Description: Given a set of data cases and an attribute of interest, find the span of values within the set. Pro Forma Abstract: What is the range of values of attribute A in a set S of data cases? - What is the range of film lengths? - What is the range of car horsepowers? - What actresses are in the data set? The range task is an important task for understanding the dynamics of data within a data set. Users can use range data to help decide the suitability of the data set for a particular analysis, or understand something about the general types of values found for a particular attribute. The range of a categorical attribute can be thought of as an enumeration of all its unique values in a set. 7. Characterize Distribution General Description: Given a set of data cases and a quantitative attribute of interest, characterize the distribution of that attribute s values over the set. Pro Forma Abstract: What is the distribution of values of attribute A in a set S of data cases? - What is the distribution of carbohydrates in cereals? - What is the age distribution of shoppers? Distribution, like range, is another important task for characterizing data. Users can get a general sense of distribution to understand normalcy in data as opposed to anomaly (see task 8, Find Anomalies ). Sometimes the distribution task is hidden; for example, Compare Frosted Flakes calories per serving to those of all other cereals is really a question of location within a distribution. 8. Find Anomalies General Description: Identify any anomalies within a given set of data cases with respect to a given relationship or expectation, e.g. statistical outliers. Pro Forma Abstract: Which data cases in a set S of data cases have unexpected/exceptional values? - Are there exceptions to the relationship between horsepower and acceleration? - Are there any outliers in protein? Anomalous values in a data set often provide a basis for further exploration. This task can be thought of as a complementary task to distribution, although it is not always framed as such (e.g. sometimes a distribution is assumed, as in the case of a standard box-and-whisker plot). 9. Cluster General Description: Given a set of data cases, find clusters of similar attribute values. Pro Forma Abstract: Which data cases in a set S of data cases are similar in value for attributes {X, Y, Z, }? - Are there groups of cereals w/ similar fat/calories/sugar? - Is there a cluster of typical film lengths? Users naturally group similar items together. This proximity can have a number of connotations depending on the clustering attributes; for example, similar products may be market competitors, members of a family of products, or simply represent the normal or expected case as opposed to outliers. 10. Correlate General Description: Given a set of data cases and two attributes, determine useful relationships between the values of those attributes. Pro Forma Abstract: What is the correlation between attributes X and Y over a given set S of data cases? - Is there a correlation between carbohydrates and fat? - Is there a correlation between country of origin and MPG? - Do different genders have a preferred payment method? - Is there a trend of increasing film length over the years?

5 One of the most interesting observations about the corpus of student questions as a whole was how frequently students desired to correlate one or more non-numeric attributes. The semantics of such questions, in our interpretation, leaned more towards isolating coincidences of interest. Membership in a category may be predictive of certain attribute values, but does not predict those same attribute values in a different category; for example, a comparison of American, German, and Japanese cars gas mileage does not allow you to predict the gas mileage of Korean cars. The semantics of true quantitative correlation questions deal with purely numeric variables and the ability to generate a mathematical predictive model relating the values of attributes within a data set. Questions such as the fourth example question above involving trends over time were quite common in the corpus of questions. We interpret such questions simply as correlations with temporal variables. 5 DISCUSSION It is difficult to construct a taxonomy that perfectly characterizes a domain so open to interpretation. In this section we discuss internal and external issues with the taxonomy and analysis methods. 5.1 Compound Tasks Considering the set of tasks in the taxonomy to be analytic primitives allows us to examine some questions that do not cleanly fit into one category but rather appear to be compositions of primitive tasks. For instance, the task Sort the cereal manufacturers by average fat content involves a Compute Derived Value (average fat) primitive followed by a Sort primitive. Further, users may simply be interested in particular attribute values from a set smaller than the entire data set; for example, on the movies data set, one might ask, Which actors have co-starred with Julia Roberts? One can complete this task by first finding all movies with Julia Roberts (Filter) and then enumerating the set of actors within those movies (Retrieve Value). As another example, consider the question, Who starred in the most films in 1978? This task differs from the basic extremum task in that the domain of the extremum operation is no longer data cases, but aggregate relationships of those data cases; in specific, a user must enumerate each actor and actress in the relevant portion of the data set (Retrieve Value), assign each one a count of the number of data cases in which each actor/actress was present (Compute Derived Value), and finally determine which actor/actress has the highest count (Find Extremum). 5.2 Omissions from the Taxonomy Even outside the context of combining analytic primitives, there were a number of questions that still did not fit cleanly into the taxonomy. Such questions are marked either by a fundamentally mathematical or computational nature rather than an analytic one, or by uncertainty, either in the analytic process necessary to answer the question or user criteria employed during the knowledge-making process Low-level Mathematical and Cognitive Actions In constructing the taxonomy, we abstracted away as low-level, and thus beyond the scope of the present work, some basic mathematical and cognitive operations, such as determining that a data case mathematically satisfies filtering criteria or conditions and computing aggregate values from a mathematical perspective. In particular, we explicitly acknowledge the existence of a lowlevel mathematical comparison operation, one in which a value is evaluated for being less than, greater than, or equal to another value or values. This leads to the notion of questions whose overall goal is too low-level for our analytic task taxonomy. For instance, the following questions involve the aforementioned mathematical comparison operation: Which cereal has more sugar, Cheerios or Special K? Compare the average MPG of American and Japanese cars. These questions utilize Retrieve Value and Compute Derived Value primitives, respectively, followed by a mathematical comparison operation. We view this very low-level comparison as being a fundamental cognitive action taken by the person using a visualization tool, rather than as a primitive in our analytic task taxonomy Higher-level Questions We have found that the proposed ten tasks cover the vast majority of the corpus of analytic questions we studied. Some questions, however, imply tasks not explicitly covered by our task set, but instead they can be thought of as guiding higher-level exploration in the data set. For example: Do any variables correlate with fat? How do mutual funds get rated? Are there car aspects that Toyota has concentrated on? Much learning of a domain can occur in the use of a properly structured visualization, and discovering interesting relationships between domain parameters is one part of that learning. While the corpus of questions mainly limited such exploration to correlation (another factor to be discussed in the next section), a lessstructured exploration is definitely possible Uncertain Criteria Other questions in the corpus contained uncertain criteria, for example: Do cereals (X, Y, Z ) sound tasty? What are the characteristics of the most valued customers? Are there any particular funds that are better than others? While these questions may be answered by supposing the existence of some black-box aggregation function, there may be other ways to answer the question, such as use of a distribution or clustering method. Fundamentally, each of these questions involves a value judgment that is beyond the proposed primitives. Another style of question common in the set involves a comparison operation that is much higher in level and more abstract than the fundamental mathematical comparison operation discussed earlier in the section. For instance, consider the questions: What other cereals are most similar to Trix? How does the Toyota RAV4 compare to the Honda CRV? Compare the distributions of values for sugar and fat in the cereals. Each of these questions involves a more subjective evaluation of a data case, attribute, or derived value in comparison to others. We felt that the fundamental operation being performed in each of

7 support for the operation. For example, how does the visualization presented by a system support characterizing distributions or finding anomalies? Does a system adequately facilitate the computation of derived values? Furthermore, by identifying and enumerating these primitive analysis task types, we hope to foster a continued emphasis on the importance of analytic measures of information visualization systems. It is vital that information visualization system designers both develop innovative, new visualization techniques and clearly articulate the analytic qualities of those techniques. These primitive analysis task types also can serve as an informal checklist along which to assess and evaluate new systems and techniques. REFERENCES [1] Robert A. Amar and John T. Stasko, Knowledge Precepts for Design and Evaluation of Information Visualizations, IEEE Transactions on Visualization and Computer Graphics, 11(4): , July/August [2] Jacques Bertin. Graphics and Graphic Information Processing. Walter de Gruyter, New York, [3] Stuart Card. "Information visualization." In Human-Computer Interaction Handbook: Fundamentals, Evolving Technologies and Emerging Applications. pp , Lawrence Erlbaum Associates, Inc., Mahwah, NJ, [4] Stuart Card and Peter Pirolli. The Sensemaking Process and Leverage Points for Analyst Technology as Identified through Cognitive Task Analysis, Proc. International Conference on Intelligence Analysis [5] Ed H. Chi and John T. Riedl, An Operator Interaction Framework for Visualization Systems, Proc. InfoVis 98, pp [6] Ed H. Chi, A Taxonomy of Visualization Techniques using the Data State Reference Model, Proc. InfoVis 00, pp [7] IN-SPIRE, [8] Alfred Kobsa, An Empirical Comparison of Three Commercial Information Visualization Systems, Proc. InfoVis 01, pp [9] William M. Newman, A Preliminary Analysis of the Products of HCI Research, Based on Pro Forma Abstracts, Proc. CHI 94, pp [10] Steven F. Roth and Joe Mattis, Data characterization for intelligent graphics presentation, Proc. CHI 90, pp [11] Purvi Saraiya, Chris North and Karen Duca, An Evaluation of Microarray Visualization Tools for Biological Insight, Proc InfoVis 04, pp [12] Ben Shneiderman, The Eyes Have It: A Task by Data Type Taxonomy for Information Visualizations, Proc. IEEE Symposium on Visual Languages 96, p [13] John Tukey. Exploratory Data Analysis. Addison-Wesley, Reading, MA, [14] Stephen Wehrend and Clayton Lewis, A Problem-Oriented Classification of Visualization Techniques, Proc. Vis 90, pp [15] Michelle X. Zhou and Stephen K. Feiner, Visual task characterization for automated visual discourse synthesis, Proc. CHI 1998, pp

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