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I have a corpus {text1, text2, text3, text4, ..., etc.}. I have no prior knowledge about the text. Lets say we extract all the n-grams (unigrams, bigrams, trigrams, 4-gram, 5-gram, ...) along with their frequency from the text.

My question is how can we merge the best N n-grams form the unigrams, bigrams, trigrams, 4-gram, 5-gram to one variable n-gram dictionary (that contains different n-gram lengths) with a simple "statistical" action?

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  • $\begingroup$ Do you mean How do I program it? If so this is off-topic here so perhaps you can clarify. $\endgroup$ – mdewey May 22 '17 at 11:34
  • $\begingroup$ No I didn't mean how I program it. how to program I know excellent. I ask from the conceptual side. How I merge N different ngrams to one dictionary and take only the top K . (merge by frequency) $\endgroup$ – MAK May 22 '17 at 14:18
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What you are looking for is statistical means for identifying collocations (that is, non-compositional phrases). Have a look at Foundations of Statistical Natural Language Processing, Manning & Schütze 1999, Chapter 5. A collocation is an expression consisting of two or more words that correspond to some conventional way of saying things. Collocations are non-compositional phrases because their meaning cannot be understood [viz., composed] from its parts. E.g., strong tea, weapons of mass destruction, to make up, the rich and powerful, stiff breeze, broad daylight, white wine, ...

While a whole bunch of collocation detection strategies exist, from "normal" t-tests to calculating your n-grams' point-wise mutual information (PMI, see Church & Hanks (1990)) or via the Dice (1945) coefficient (see Smadja & McKeown (1994)), I prefer the likelihood ratio test by Dunning (1993) and as applied to non-compositional phrases by Lin (1993), because it is fairly robust for both excluding frequently co-occurring words and including infrequent collocations that are hard to detect. E.g., for bi-grams of a two word sequence $[1, 2]$ with counts $c$ for either word or the bi-gram, and a total number of words $N$ in your corpus, you get:

$$ \lambda = {-2}\ log \frac{B(c_{12}, c_1, p_2) B(c_2-c_{12},N-c_1,p_2)}{B(c_{12},c_1,p_{2|1})B(c_2-c_{12},N-c_1,p_{2|\neg1})} $$

Where $B(k, n, p) = \binom{n}{k} p^k (1-p)^{n -k}$ (note that the binomial term $n$ over $k$ can be dropped), $p_2 = \frac{c_2}{N}$, $p_{2|1} = \frac{c_{12}}{c_1}$, and $p_{2|\neg1} = \frac{c_2-c_{12}}{N-c_1}$. The $-2$ multiplier is in there to make $\lambda$ asymptotically $\chi^2$ distributed. As cutoff, I'd recommend $\lambda > 10.83$, which is the critical value for $\chi^2$ with 99.9% confidence at 1 d.f., but you might use lower cutoffs for better recall, depending on what you want to do with those collocations.

To extend this to higher n-grams, just re-run the test on the merged bi-grams to get tri-grams, a.s.f. (see Mikolov et. al. (2013), where they applied this strategy to a discounted PMI collocation detection approach). For more details, and an in-depth discussion, please refer to Manning & Schütze's excellent book chapter.

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