What are the differences between multivariate data visualizations and multidimensional visualizations?

Question

I believe this should be the correct place for this topic since it did not seem to fit naturally on the math Stack Exchange.

I am writing an essay about data visualization, but am having trouble nailing down some terminology. I used data from the OECD to investigate trends in the data about OECD member countries. I created a graph in Tableau using data from the OECD that depicts the GDP per capita, average # of years spent in education system, satisfaction score as reported by the member country citizens, and a "Feel Safe" score as reported by the member country citizens (a percentage of the surveyed population who said they would feel safe walking home alone at night). Click the following link to download the full OECD data set I used.

I am confused about whether to label my graph as a multivariate visualization or a multidimensional visualization.

The core of my confusion comes from someone claiming that my graph is only two-dimensional since it can be displayed on a page. However, "dimensions" usually refers to the number of independent variables in a data set and the data displayed in my graph contains four independent variables.

• Could someone please tell me what my graphic should be categorized as, and possibly explain some of the differences between multivariate and multidimensional data/visualizations (if any)?

Answer 1

I don't think there is a well-defined (or well enough defined) terminology for that.

Multi-variate means that it involves multiple (dependent or independent) variables. Which is pretty clear.

Multi-dimensional in mathematical sense means that the data points are from a multi-dimensional space (typically vector space). This is exactly the same as multi-variate. In this sense, your visualization is both multi-variate and multi-dimensional. And both the size of the markers and the color represent individual dimensions or variables, which is then equivalent. Also, time would be an individual dimension. Personally, I would go with this interpretation of the term multi-dimensional.

If you want to restrict the term multi-dimensional to spatial dimensions of the plot, then size and color of markers would not be dimensions in that sense. I personally find this interpretation confusing. Time then also would not be a dimension in this sense, unless you represent it by a 3rd axis in the graph. This, again, is confusing as many people actually often put time into the same category as spatial dimensions.

So, all in all I would stick to the mathematical interpretation of dimensions here so that multi-variate and multi-dimensional will be equivalent.

Answer 2

I think that it is quite the opposite of what @Konstantin says. The differences between multidimensional and multivariate are easier to understand through an example:

Consider you are recording wind speed at different places, say $P_1, P_2, P_3, ... P_n$. You will have $n$ time series, right? But only one variate, which is the wind speed. So this is your $n$-dimensional, one-variate data.

Now, imagine that at the same points, you start recording different variables, like wind $v_1$, pressure $v_2$, ozone concentration $v_3$, so each location recording is a function $ f(v_1, v_2, v_3)$. So you will have to deal with a $n$_dimensional, $3$-variate process.

I your specific case, you have a diagram, that is neither multidimensional nor multivariate.

It is the data to have this properties not the diagram.

If you explain better the data, we can further discuss about it.