# Plot Latent Dirichlet Allocation output using t-SNE?

I found this blog where the author trains an Latent Dirichlet Allocation (LDA) model on 20 Newsgroups. The output is then an $N\times K$ matrix where $N$ is the number of articles (row wise) and $K$ is the number of topics (column wise) i.e. each row is a discrete topic distribution.

The author then uses t-SNE to reduce the dimensionality of the matrix from $K$ dimensions to 2 dimensions to be able visualize the document groupings by topic. The document groupings of the t-SNE output even seem to make sense.

My question is, is it reasonable to do this? LDA outputs a discrete distribution over topics for every document. t-SNE reduces the dimensionality of vectors / points in a high dimensional space to visualize local structure. As the output of LDA is a distribution, I thought it would be somehow incorrect to do this? I understand that the distribution, being discrete, can be thought of as a point in the $K$ dimensional space. But using t-SNE to visualize a discrete output somehow seems incorrect. Am I missing something here?

EDIT: The metric the author uses in t-SNE is euclidean distance - that is why I am confused, because the author is using the euclidean distance to compare distributions.

So what does euclidean distance between topic probabilities measure? Let's say we have topic probabilities of two documents $$p = (p_1, ..., p_K),$$ $$q = (q_1, ..., q_K).$$ If the distance between $p$ and $q$ is $0$ then documents have exactly the same topic distributions. If the distance between $p$ and $q$ increases, topic distributions become more separated. Extreme case is when $p$ and $q$ are in the form (0,...,0,1,0,...,0), and $1$ occurs on different coordinate, so the documents have completely different topics. Then the distance is maximal and equal to $1$. So the distance between t-SNE coordinates should represent how similar are the subjects of two documents.