Normal force

A bigram or digram is every sequence of two adjacent elements in a string of tokens, which are typically letters, syllables, or words; they are n-grams for n=2. The frequency distribution of bigrams in a string are commonly used for simple statistical analysis of text in many applications, including in computational linguistics, cryptography, speech recognition, and so on.

Gappy bigrams or skipping bigrams are word pairs which allow gaps (perhaps avoiding connecting words, or allowing some simulation of dependencies, as in a dependency grammar).

Head word bigrams are gappy bigrams with an explicit dependency relationship.

Bigrams help provide the conditional probability of a token given the preceding token, when the relation of the conditional probability is applied:

$P(W_{n}|W_{n-1})={P(W_{n-1},W_{n}) \over P(W_{n-1})}$

That is, the probability $P()$ of a token $W_{n}$ given the preceding token $W_{n-1}$ is equal to the probability of their bigram, or the co-occurrence of the two tokens $P(W_{n-1},W_{n})$, divided by the probability of the preceding token.

Applications

Bigrams are used in one of the most successful language models for speech recognition. They are a special case of N-gram.

Bigram frequency attacks can be used in cryptography to solve cryptograms. See frequency analysis.

Bigram frequency is one approach to statistical language identification.

Bigram Frequency in the English language

The frequency of the most common letter bigrams in a small English corpus is:

th 1.52       en 0.55       ng 0.18
he 1.28       ed 0.53       of 0.16
in 0.94       to 0.52       al 0.09
er 0.94       it 0.50       de 0.09
an 0.82       ou 0.50       se 0.08
re 0.68       ea 0.47       le 0.08
nd 0.63       hi 0.46       sa 0.06
at 0.59       is 0.46       si 0.05
on 0.57       or 0.43       ar 0.04
nt 0.56       ti 0.34       ve 0.04
ha 0.56       as 0.33       ra 0.04
es 0.56       te 0.27       ld 0.02
st 0.55       et 0.19       ur 0.02

Complete bigram frequencies for a larger corpus are available.

See also

• Digraph (orthography)
• N-gram
• Letter frequency