Thus when a cross-lingual topic picks up words that cooccur in mono-lingual text, it would prefer picking up word pairs whose translations in other languages also co-occur with each other, giving us a coherent multilingual word distribution that characterizes well the content of text in different languages.
let Θ = {θ j } (j = 1, ..., k) be a set of k cross-lingual topic models to be discovered from a multilingual text data set with s languages such that p(w|θ i ) is the probability of word w according to the topic model θ i .