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The bag-of-words model (BoW) is a model of text which uses a representation of text that is based on an unordered collection (a "bag") of words. It is used in natural language processing and information retrieval (IR). It disregards word order (and thus most of syntax or grammar) but captures multiplicity.
If we convert strings (with only letters in the English alphabet) into character 3-grams, we get a -dimensional space (the first dimension measures the number of occurrences of "aaa", the second "aab", and so forth for all possible combinations of three letters). Using this representation, we lose information about the string.
A plot of the frequency of each word as a function of its frequency rank for two English language texts: Culpeper's Complete Herbal (1652) and H. G. Wells's The War of the Worlds (1898) in a log-log scale. The dotted line is the ideal law y ∝ 1 / x
In the formula, A is the supplied m by n weighted matrix of term frequencies in a collection of text where m is the number of unique terms, and n is the number of documents. T is a computed m by r matrix of term vectors where r is the rank of A—a measure of its unique dimensions ≤ min(m,n).
The output of this program is an alphabetical listing, by frequency of occurrence, of all word types which appeared in the text. Certain function words such as and, the, at, a, etc., were placed in a "forbidden word list" table, and the frequency of these words was recorded in a separate listing...
The equation for Katz's back-off model is: [2] (+) = {+ (+) (+) (+) > + (+)where C(x) = number of times x appears in training w i = ith word in the given context. Essentially, this means that if the n-gram has been seen more than k times in training, the conditional probability of a word given its history is proportional to the maximum likelihood estimate of that n-gram.
Heaps' law: It describes the number of distinct words in a document (or set of documents) as a function of the document length. Brevity law or Zipf's law of abbreviation: It qualitatively states that the more frequently a word is used, the 'shorter' that word tends to be. [8]
Word frequency is known to have various effects (Brysbaert et al. 2011; Rudell 1993). Memorization is positively affected by higher word frequency, likely because the learner is subject to more exposures (Laufer 1997). Lexical access is positively influenced by high word frequency, a phenomenon called word frequency effect (Segui et al.).