Viterbi algorithm: Difference between revisions

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The '''Viterbi algorithm''', named after its developer [[Andrew Viterbi]], is a [[dynamic programming]] [[algorithm]] for finding the most [[likelihood function|likely]] sequence of hidden states – known as the '''Viterbi path''' – that result in a sequence of observed events, especially in the context of [[hidden Markov model]]s. The '''forward algorithm''' is a closely related algorithm for computing the probability of a sequence of observed events. Its a subset of a wider topic known as [[information theory]].

The Viterbi algorithm was originally conceived as an [[error-correction]] scheme for noisy digital communication links, finding universal application in decoding the [[convolutional code]]s used in both [[CDMA]] and [[GSM]] digital cellular, [[dial-up]] modems, satellite, deep-space communications, and [[802.11]] wireless LANs. It is now also commonly used in , [[speech recognition]], [[keyword spotting]], [[computational linguistics]], and [[bioinformatics]]. For example, in speech-to-text speech recognition, the acoustic signal is treated as the observed sequence of events, and a string of text is considered to be the "hidden cause" of the acoustic signal. The Viterbi algorithm finds the most likely string of text given the acoustic signal.

The algorithm is not general; it makes a number of assumptions. First, both the observed events and hidden events must be in a sequence. This sequence often corresponds to time. Second, these two sequences need to be aligned, and an observed event needs to correspond to exactly one hidden event. Third, computing the most likely hidden sequence up to a certain point ''t'' must depend only on the observed event at point ''t'', and the most likely sequence at point ''t'' − 1. These assumptions are all satisfied in a first-order hidden Markov model.