Correct me if I am wrong, but I do not think that DBPedia includes the full Wikipedia articles (only extended abstracts). So I believe that json dumps of DBPedia and Wikipedia dumps produced using this tool are two different things.
Sparse fast Fourier transform is even more "magical" than fast Fourier transform (FFT). If you assume that the discrete Fourier transform (DFT) has only k non zero coefficients, then, there exists an algorithm to compute it in O(k log(n)). That's right, you do not have to see the entire signal to compute the DFT, which is pretty awesome.
The Elements of Statistical Learning, by T. Hastie, R. Tibshirani and J. Friedman [1] is also a very good one. Plus, the book is freely available on the authors' website.
From what I have understood by watching his TED talk, the algorithm he designed seems very similar to papers published in the NLP field recently [1] [2] [3]. I find it quite elegant, and I agree that the kid is really smart.
The idea behind those algorithms is to build a graph on words, using WordNet, or a corpus such as Wikipedia. Edges are added between words which are semantically close, or which often appear in the same documents. Then, to compare two words (or two bags of words), you compute the limiting distributions of the two random walks starting at each of the words. Those random walks will more explore nodes which are close to the starting nodes, and so, similar words will have similar random walks.