I have been experimenting with word2vec recently. Word2vec trains a neural network to guess which word is likely to appear given the context of the surrounding words. The result is a vector representation of each word in the trained vocabulary with some amazing properties (the canonical example is king - man + woman = queen). You can also find similar words by looking at cosine distance - words that are close in meaning have vectors that are close in orientation.
This sounds like it should work well for finding related posts. Spoiler alert: it does!
My old system listed posts with similar tags. This worked reasonably well, but it depended on me remembering to add enough tags to each post and a lot of the time it really just listed a few recent posts that were loosely related. The new system (live now) does a much better job which should be helpful to visitors and is likely to help with SEO as well.
I don't have a full implementation to share as it's reasonably tightly coupled to my custom CMS but here is a code snippet which should be enough to get this up and running anywhere:
The first step is getting a vector representation of a post. Word2vec just gives you a vector for a word (or short phrase depending on how the model is trained). A related technology, doc2vec, adds the document to the vector. This could be useful but isn't really what I needed here (i.e. I could solve my forgetfulness around adding tags by training a model to suggest them for me - might be a good project for another day). I ended up using a pre-trained model and then averaging together the vectors for each word. This paper (PDF) suggests that this isn't too crazy.
For the model I used word2vec-slim which condenses the Google News model down from 3 million words to 300k. This is because my blog runs on a very modest EC2 instance and a multi-gigabyte model might kill it. I load the model into Word2vec.Tools (available via NuGet) and then just get the word vectors (GetRepresentationFor(...).NumericVector) and average them together.
I haven't included code to build the word list but I just took every word from the post, title, meta description and tag list, removed stop words (the, and, etc) and converted to lower case.
Now that each post has a vector representation it's easy to compute the most related posts. For a given post compute the cosine distance between the post vector and every other post. Sort the list in ascending order and pick however many you want from the top (the distance between the post and itself would be 1, a totally unrelated post would be 0). The last line in the code sample shows this comparison for one post pair using Accord.Math, also on Nuget.
I'm really happy with the results. This was a fast implementation and a huge improvement over tag based related posts.