7 – Solution Picking Topics

So let’s think. In the distribution on the left, we’re very likely to pick a point, say, here close to a corner or the edges. Let’s say, for example, close to politics. That means our article is 80 percent about politics, 10 percent about sports, and 10 percent about science. On the distribution in the middle, we can pick any point with equal probability. Say, this document, which is 40 percent about science, 40 percent about politics, and 20 percent about sports. On the distribution on the right, we’re very likely to pick points in the middle like this document, which is almost an equal probability science, sports, and politics. That would happen for all the articles we would pick. They would be points in these probability distributions. So let’s think. If we have a bunch of articles, would the articles be more likely to be about one topic or three topics at the same time? Well, most articles are about only one thing; either science, sports or politics. Some few articles are about two topics, and almost no article will be about the three topics at the same time. Therefore, the most likely distribution for topics is the one in the left. So, this is what we’ll do. For our LDA model, we’ll pick a Dirichlet distribution with small parameters Alpha such as 0.7, 0.7, and 0.7. From here, we’ll sample a few points to be our documents. Each point gives us a vector of mixture probabilities, Theta, then we’ll characterize the distribution of topics for that particular document. This is how Dirichlet distributions look like in 3D. The probability of picking a point on the triangle depends on the height of the probability distribution at that point. Therefore, we want to pick our topics from the model on the left.

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