When one thinks of a perceptual map, the image of brands laid on a grid of quadrants usually springs to mind. Only in a bizarre dream might the chart instead contain a dozen axes, varying in length, radiating in seemingly random directions from the origin. But this is not a dream, these are the perceptual maps of modern market research.

The traditional four quadrant perceptual map is, admittedly, intuitive to understand and easy to plot. It contains such simple information I could draw an accurate one by hand knowing only the values of each brand’s attributes. The advent of “Big Data” (a buzzword I use reluctantly) has created more information to process than ever before. New tools and methods are being adopted to refine this wealth of data into useful insights. Multidimensional perceptual maps are one such method. These charts are dense with information and reveal insights a traditional perceptual map would miss. The list below details the additional types of information a multidimensional perceptual map can display.

The deck is clearly stacked in the multidimensional perceptual map’s favor in terms of information density. By “information density” I mean the amount of data the chart can show relative to its complexity. Here, an increase in complexity has brought exponential returns on the amount of data shown. It won’t do us any favors if the chart remains indecipherable to its intended audience, but fortunately reading a multidimensional perceptual map is no secret. The major hurtle is deviating from the traditional Cartesian plane which many believe is a natural law of the visualization world. The five basic principles to interpreting a multidimensional plot are listed below:

  • Arrows extending from the origin represent the positive direction of an attribute’s axis
  • The direction opposite an arrow represents the negative direction of an attribute’s axis
  • A brand’s relationship to any attribute can be found by imagining a line extending perpendicularly from that axis to the brand, including the axis space beyond the arrow and before the origin in the opposite direction (illustrated below)
  • The length of an attributes arrow indicates the strength it has to differentiate brands from each other
  • Brand attribute positioning is relative to other brands and not representative of their actual attribute rating

If you’ve made it this far then I hope you take my argument for using multidimensional perceptual maps into consideration. This next part is more technical and if you don’t plan on building your own multidimensional perceptual maps I suggest you end here. Data scientists and research analysts interested in building these information dense plots please read on.

The type of plot used to represent points and vectors is called a biplot. These are created on normal Cartesian planes, but for our purposes the arrows will represent axes instead of the normal x and y. I usually hide the x and y axes in the plot so people don’t focus on them. Several methods can be used to calculate the position of the brand points and attribute arrow endpoints in the plot. I prefer one called Linear Discriminant Analysis (LDA) since I believe it creates an evenly distributed visualization of brands. I like to run the analysis on standardized data to generate the endpoints of the attribute arrows and on the original data for brand point positions. The analysis outputs columns of data called Linear Discriminants assigning a value each attribute and brand, usually labelled as LD1 and so on. LD1 represents the line through multidimensional space at which differentiation has been maximized between the brands, LD2 represents the next most differentiating line. These first two LD lines together represent the x and y axes of a 2 dimensional plane which optimally visualizes the higher dimensional space containing all of the brands along the several attribute axes. It’s not a perfect representation, but this will be more than enough information. Biplots can be difficult to graph. I use a custom-built script to rapidly generate the plot as an image file. The simplest method would be to create a scatterplot with labels of the brands and attribute arrow endpoints in PowerPoint, then manually draw the attribute arrows from the origin to each endpoint. For all of this I use R with the packages MASS and ggplot2, and I believe SPSS also has an LDA analysis feature. For even more advanced challenges, try incorporating LD3 to visualize a z axis or include a new set of brands without influencing the position of the attribute axes.

By: Anders Bergren