Visualization is the science and art of creating representations of numerical data that we can interpret using our senses. Most often, the experience is visual, but there are interfaces to data involving touch and hearing as well. The data is generally not in a form that is immediately viewable, such as MRI measurements of the inside of a body, numerical models of water flow in the ocean, or sales and inventory information across several stores. The data must be transformed into a representation that we can see. There are two steps to the visualization process:

• the act of converting data into something we can experience with our senses, and
• the act of viewing/touching/hearing the result and interpreting it.

It is the combination of these two steps that we refer to as Visualization. The process of Visualization is iterative; we set up algorithms to convert the data into visual form, interact with and interpret the data, and then we make modifications to the data or algorithms and do it all again until we have found what we are looking for. A web search for definitions of the word “Visualization” will lead to three major categories, namely

• Information Visualization – the visualization of abstract data (e.g. measurements of packet traffic through a network, business sales, inventory, customer churn)
• Scientific Visualization – the visualization of three dimensional data (e.g. MRI, CAT, weather measurements)
• Visual Analytics – analysis and visualization of any data, this includes Information and Scientific Visualization, but extends to data analysis with statistical and predictive techniques. (E.g. click-stream data, social media content)

The boundaries between Information and Scientific Visualization have never been particularly clear, and similar techniques are useful in both. Visual Analytics is a new area which is finding value in techniques from both Information and Scientific Visualization. The broader definition also contains new data sources that are now appearing under the heading “Big Data” along with computational techniques such as machine learning. These techniques extract information from that data running on large scale computational systems possibly designed around Hadoop. There doesn’t seem to be much value in trying to maintain a distinction between areas of visualization anymore, so we won’t try. We will simply use the word Visualization to mean the act of creating visual forms from data for the purpose of human interpretation.

Figure 1 shows a table of numbers. The numbers themselves tell us little without some context. This is what data in a computer system look like – many numbers. We need to know more about these numbers before we have some understanding of them. Mathematical models can be constructed – a set of equations that can recreate the data that we have, and perhaps allow us to make testable predictions of some sort. In this case, a set of equations that reproduce this data are: $$\begin{eqnarray}x = \left[R+r cos(\phi)\right] cos(\theta) \\ y = \left[R+r cos(\phi)\right] sin(\theta)\end{eqnarray} \\ z = r sin(\phi)$$ If you are comfortable with the language of the equations, you can use them to recreate the table of numbers and much more. They need to be worked with to be understood.

To help reach understanding, we can provide a visual representation of the table or equations, as shown in Figure 2. The data in the table are a small portion of the values required to describe a torus. The equations are a mathematical model, a description of the torus, which can be used to generate this particular torus, but also any torus that we may wish to create.

Our brains grasp the relationships in complex data much more easily when we can see the data. This method of creating a view of the data to speed the “time to insight”, as Bill Gates put it in a talk in 2005, has become a stated goal of many data analysis and visualization systems that are now commercially available.