Remapping Switzerland with t-SNE

Below, each municipality is represented by a dot in the plot on the right-hand side. On the left, the geographical map of Switzerland depicts the municipalities with a colour that is chosen based on the position in the plot.

Share this page Share on Facebook Share on Twitter Share on Google+


On the right part above, each municipality is shown by a dot. This representation is obtained directly from all the results to national-level issue votes, using a dimensionality reduction technique called t-SNE (for t-distributed stochastic neighbor embedding).

In contrast to principal component analysis as used in the voting patterns, t-SNE enables to capture non-linear relationships present in the voting data. Informally, it captures the relative similarity between municipalities in the data and it tries to keep these similarities in a two-dimensional space. Hence, it is potentially able to reveal more insights in two dimensions and generate the visualization above. However, it lacks the easy interpretability of individual axes.

In line with the principal component analysis, we observe a clustering in voting behavior by the language spoken in each municipality. However, even more remarkable, a finer sub-clustering by canton is also obtained. For example, spot the cluster corresponding to the canton of Bern: the German-speaking municipalities are located on right hand side of the plot and the French-speaking municipalities are located on the left hand side of the plot. First, municipalities of Bern are split by the language spoken and then grouped together within their cantonal sub-cluster. As also apparent in the principal component analysis, the canton of Wallis exhibits a unique voting behavior. It is isolated at the top of the plot, but it is still split according to the two spoken languages.

The drop-down menu allows you to choose the data used to color the dots that represent the municipalities. The most interesting data to look at are the canton a municipality belongs to. To reduce the number of elements in the legend, it is possible to choose only cantons that speak a specific language.

On the left hand side above, the color of each municipality is directly determined by its position in the two-dimensional space on the right side.