There are a number of reasons for why we visually represent the data. At the data exploration stage, we can gain an immediate understanding of data properties. Visual representation serves to highlight patterns in data and suggest modeling strategies. Exploratory graphs are usually made quickly and in large numbers. We are not so much concerned with aesthetic or stylistic issues, but we simply want to see what the data looks like.

Beyond using graphs to explore data, they are a primary means of communicating information about our data. Visual representation helps clarify data properties and stimulate viewer engagement. The human visual system is the highest bandwidth channel to the brain, and visualization is the most efficient way to present a large amount of information. By creating a visualization, we can immediately get a sense of important parameters, such as the maximum, minimum, and trends that may be present in the data. Of course, this information can be extracted from data through statistical analysis, however, analysis may not reveal specific patterns in the data that visualization will. The human visual pattern recognition system is, at the moment, significantly superior to that of a machine. Unless we have clues as to what we are looking for, algorithms may not pick out important patterns that a human visual system will.

The central problem for data visualization is mapping data elements to visual attributes. We do this by first classifying the data types as nominal, ordinal, or quantitative, and then determining which visual attributes represent each data type most effectively. Nominal or categorical data refers to a name, such as the species, male or female, and so on. Nominal data does not have a specific order or numeric value. Ordinal data has an intrinsic order, such as house numbers in a street, but is different from quantitative data in that it does not imply a mathematical interval. For example, it does not make much sense to multiply or divide house numbers. Quantitative data has a numeric value such as size or volume. Clearly, certain visual attributes are inappropriate for nominal data, such as size or position; they imply ordinal or quantitative information.

Sometimes, it is not immediately clear what each data type in a particular dataset is. One way to disambiguate this is to find what operations are applicable for each data type. For example, when we are comparing nominal data, we can use equals, for instance, the species Whitefly is not equal to the species Thrip. However, we cannot use operations such as greater than or less than. It does not make sense to say, in an ordinal sense, that one species is greater than another. With ordinal data, we can apply operations such as greater than or less than. Ordinal data has an implicit order that we can map on a number line. For quantitative data, this consists of an interval, such as a date range, to which we can apply additional operations such as subtractions. For example, we can not only say that a particular date occurs after another date, but we can also calculate the difference between the two dates. With quantitative data that has a fixed axis, that is a ratio of some fixed amount as opposed to an interval, we can use operations such as division. We can say that a particular object weighs twice as much or is twice as long as another object.

Once we are clear on our data types, we can start mapping them to attributes. Here, we will consider six visual attributes. They are position, size, texture, color, orientation, and shape. Of these, only position and size can accurately represent all three types of data. Texture, color, orientation, and shape, on the other hand, can only accurately represent nominal data. We cannot say that one shape or color is greater than another. However, we can associate a particular color or texture with a name.

Another thing to consider is the perceptual properties of these visual attributes. Research in psychology and psycho physics have established that visual attributes can be ranked in terms of how accurately they are perceived. Position is perceived most accurately, followed by length, angle, slope, area, volume, and finally, color and density, which are perceived with the least accuracy. It makes sense, therefore, to assign position and then length to the most important quantitative data. Finally, it should also be mentioned that we can encode, to some extent, ordinal data in a colors value (from dark to light) or continuous data in a color gradient. We cannot generally encode this data in a colors hue. For instance, there is no reason to perceive the color blue as somehow greater than the color red, unless you are making a reference to its frequency.

The color gradient to represent ordinal data

The next thing to consider is the number of dimensions that we need to display. For uni-variate data, that is, where we only need to display one variable, we have many choices such as dots, lines, or box plots. For bi-variate data, where we need to display two dimensions, the most common is with a scatter plot. For tri-variate data, it is possible to use a 3D plot, and this can be useful for plotting geometric functions such as manifolds. However, 3D plots have some drawbacks for many data types. It can be a problem to work out relative distances on a 3D plot. For instance, in the following figure, it is difficult to gauge the exact positions of each element. However, if we encode the z dimension as size, the relative values become more apparent:

Encoding Three Dimensions

There is a large design space for encoding data into visual attributes. The challenge is to find the best mapping for our particular dataset and purpose. The starting point should be to encode the most important information in the most perceptually accurate way. Effective visual coding will depict all the data and not imply anything that is not in the data. For example, length implies quantitative data, so encoding non-quantitative data into length is incorrect. Another aspect to consider is consistency. We should choose attributes that make the most sense for each data type and use consistent and well-defined visual styles.