Voting patterns similarities

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I'm interested in any research materials on voting patterns.

I have a data set of how PMs (members of parliament) voted in my country during last couple of years. Each PM has 3 buttons: Yes, No, Abstain. There are also two special situations: PM can be absent during the voting and he/she can be present but not vote (it's wrong but they do it sometimes). So any particular voting result is represented as a huge vector whose values are yes/no/abstain/present_not_voted/absent.

I'd like to find some similarities in PMs' voting patterns and cluster them in groups based on these similarities. There are some interesting questions like coalition stability and party loyalty which (in theory) could be answered with the data described above. Unfortunately i deeply lack any references.

While googling i've come across some site which formed an undirected graph based on American senators voting. It looked cool but i didn't find any explanation on how such graph can be formed. Intuitively "similar" is a symmetric binary relation so undirected graph representation sounds quite natural. But how can one define "similarity" for my data? Probably there are some standard ways of doing this. Any help will be highly appreciated.

Answers

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The politicians and Political parties follow a set of principles and characteristics. They always follow these things during voting on legislations and bills. you can use T-distributed Stochastic Neighbor Embedding (t-SNE), machine learning algorithm for visualization developed by Laurens van der Maaten and Geoffrey Hinton. This method helps us to visualize the clusters and similarities of the observations.

Like-minded MP's and political parties with similar principles cluster together(neighbors).

The t-SNE 1algorithm comprises two main stages. First, t-SNE constructs a probability distribution over pairs of high-dimensional objects in such a way that similar objects have a high probability of being picked, whilst dissimilar points have an extremely small probability of being picked. Second, t-SNE defines a similar probability distribution over the points in the low-dimensional map, and it minimizes the Kullback–Leibler divergence between the two distributions with respect to the locations of the points in the map. Note that whilst the original algorithm uses the Euclidean distance between objects as the base of its similarity metric, this should be changed as appropriate.