Swiss Voting Patterns: Nonlinear Projection with t-SNE

On the Swiss map below, each municipality is shown with a color that represents its voting habits as obtained by a linear project through "t-distributed stochastic neighbour embedding" (t-SNE), from 1981 until today. Two municipalities with similar colors have similar voting habits, i.e., they are close to each other in the scatter plot. Observe for instance the differences between urban centers and rural areas, or between the different linguistic regions.

Explanation

On the scatter plot above, each municipality is shown by a dot. This representation is obtained directly from all the results to national-level referendum votes, using a dimensionality reduction technique called t-distributed stochastic neighbor embedding (t-SNE). On the Swiss map, the color of each municipality is directly determined by its position in the two-dimensional scatter plot.

In contrast to principal component analysis as used in the linear projection, t-SNE enables to capture nonlinear 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.