A bigram or digram is a sequence of two adjacent elements from a
string of
tokens, which are typically letters, syllables, or words. A bigram is an
''n''-gram for ''n''=2. The frequency distribution of every bigram in a string is 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.
Details
Bigrams help provide the conditional probability of a token given the preceding token, when the relation of the
conditional probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occu ...
is applied:
That is, the probability
of a token
given the preceding token
is equal to the probability of their bigram, or the co-occurrence of the two tokens
, divided by the probability of the preceding token.
Applications
Bigrams are used in most successful
language models for
speech recognition
Speech recognition is an interdisciplinary subfield of computer science and computational linguistics that develops methodologies and technologies that enable the recognition and translation of spoken language into text by computers with the ...
. They are a special case of
N-gram.
Bigram frequency attacks can be used in
cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...
to solve
cryptograms
A cryptogram is a type of puzzle that consists of a short piece of encrypted text. Generally the cipher used to encrypt the text is simple enough that the cryptogram can be solved by hand. Substitution ciphers where each letter is replaced by ...
. See
frequency analysis.
Bigram frequency is one approach to
statistical language identification.
Some activities in
logology or recreational linguistics involve bigrams. These include attempts to find English words beginning with every possible bigram, or words containing a string of repeated bigrams, such as ''logogogue''.
Bigram frequency in the English language
The frequency of the most common letter bigrams, rounded to the closest centesimal, in a large English corpus is:
th 3.56% of 1.17% io 0.83%
he 3.07% ed 1.17% le 0.83%
in 2.43% is 1.13% ve 0.83%
er 2.05% it 1.12% co 0.79%
an 1.99% al 1.09% me 0.79%
re 1.85% ar 1.07% de 0.76%
on 1.76% st 1.05% hi 0.76%
at 1.49% to 1.05% ri 0.73%
en 1.45% nt 1.04% ro 0.73%
nd 1.35% ng 0.95% ic 0.70%
ti 1.34% se 0.93% ne 0.69%
es 1.34% ha 0.93% ea 0.69%
or 1.28% as 0.87% ra 0.69%
te 1.20% ou 0.87% ce 0.65%
Bigram frequencies for a different corpus is available.
See also
*
Digraph (orthography)
A digraph or digram (from the grc, δίς , "double" and , "to write") is a pair of characters used in the orthography of a language to write either a single phoneme (distinct sound), or a sequence of phonemes that does not correspond to ...
*
N-gram
*
Letter frequency
*
Sørensen–Dice coefficient The Sørensen–Dice coefficient (see below for other names) is a statistic used to gauge the similarity of two samples. It was independently developed by the botanists Thorvald Sørensen and Lee Raymond Dice, who published in 1948 and 1945 respec ...
References
{{Natural Language Processing
Formal languages
Classical cryptography
Natural language processing