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For a Random Forest, we can construct a N x N (where N is the number of data points) proximity matrix P where P[i,j] is how "close" the i-th data point is from the j-th data point. In Gilles Loupes' PhD dissertation, he shows an example of a very beautiful proximity visualization using the MNIST dataset:

My question is - how are these proximity plots made? Is there any intuitive difference between that and your traditional distance/similarity matrices? For example, if I have N = 500 data points, should I run the proximity matrix through some sort of dimensionality reduction technique like PCA / SVD / t-SNE so it is of form 500 x 2, and the visualize it?

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  • $\begingroup$ Is there no description of how the plot was constructed in the text of the dissertation that you cite? $\endgroup$ – Sycorax says Reinstate Monica May 20 at 18:10
  • $\begingroup$ There is not.@Sycorax $\endgroup$ – Yu Chen May 20 at 18:10
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A few lines later in the dissertation, the author writes

Figure 4.6 represents the proximity matrix learned for a 10-class handwritten digit classification task, as projected on a plane using Multidimensional Scaling [Kruskal, 1964].

In addition to the citation the author provides, you can find more information about by searching for posts bearing the tag.

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  • $\begingroup$ Thank you, I guess I did not see this when I was perusing the paper. $\endgroup$ – Yu Chen May 20 at 19:36

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