A Method for the Correction of Garbled Words Based on the Levenshtein Metric

Okuda, Teruo; Tanaka, Eiichi; Kasai, Tamotsu

doi:10.1109/tc.1976.5009232

Cited by 178 publications

(55 citation statements)

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“…Thus, in both string processing and string recognition it is not uncommon to represent the dictionary as a finite set of words, and using this model, string correction can be achieved using a suitable similarity metric [3,4,5,6,9,18,19,20,21,22,23,24,25,26].…”

Section: I1 Alphabet and Dictionary Representationsmentioning

confidence: 99%

“…In the literature, these operations are the most popular, because the general string editing problem has been studied using these operations [3,4,5,6,7,8,9,18,19,20,21,22,23,24,25,26,27,35,36,37,38,39,40,41,42,43], and furthermore, these operations can also be used to study problems involving subsequences and supersequences [6,27,37,38,39].…”

Section: I2 Stochastic Channel Versus Dictionary Representationsmentioning

confidence: 99%

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A formal theory for optimal and information theoretic syntactic pattern recognition

Oommen

Kashyap

1998

Pattern Recognition

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In this paper we present a foundational basis for optimal and information theoretic syntactic pattern recognition. We do this by developing a rigorous model, M * , for channels which permit arbitrarily distributed substitution, deletion and insertion syntactic errors. More explicitly, if A is any finite alphabet and A * the set of words over A, we specify a stochastically consistent scheme by which a string U ∈ A * can be transformed into any Y ∈ A * by means of arbitrarily distributed substitution, deletion and insertion operations. The scheme is shown to be Functionally Complete and stochastically consistent. Apart from the synthesis aspects, we also deal with the analysis of such a model and derive a technique by which Pr[Y|U], the probability of receiving Y given that U was transmitted, can be computed in cubic time using dynamic programming. One of the salient features of this scheme is that it demonstrates how dynamic programming can be applied to evaluate quantities involving complex combinatorial expressions and which also maintain rigid probability consistency constraints. Experimental results which involve dictionaries with strings of lengths between 7 and 14 with an overall average noise of 39.75 % demonstrate the superiority of our system over existing methods. Apart from its straightforward applications in string generation and recognition, we believe that the model also has extensive potential applications in speech, uni-dimensional signal processing, and computational molecular biology.

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Section: I1 Alphabet and Dictionary Representationsmentioning

confidence: 99%

Section: I2 Stochastic Channel Versus Dictionary Representationsmentioning

confidence: 99%

A formal theory for optimal and information theoretic syntactic pattern recognition

Oommen

Kashyap

1998

Pattern Recognition

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“…This trellis is 2-dimensional in the case of the GLD [2,8,15,19,21,23], the Length of the LCS [3,4,21] and the Length of the Shortest Common Supersequence [8]. Indeed, the same trellis can be traversed using various set operators to yield the Set of the LCSs and the Set of the Shortest Common Supersequences [8].…”

Section: Iii1 Graphical Representation Of the Algorithm And An Examplementioning

confidence: 99%

“…al. [19] extended this concept by weighting the edit operations, and many other researchers among whom are Wagner and Fisher [23] generalized it by using edit distances which are symbol dependent. The latter distance is termed as the Generalized Levenshtein Distance (GLD).…”

Section: Introductionmentioning

confidence: 99%

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Pattern recognition of strings with substitutions, insertions, deletions and generalized transpositions

Oommen

Loke

1997

Pattern Recognition

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We study the problem of recognizing a string Y which is the noisy version of some unknown string X * chosen from a finite dictionary, H. The traditional case which has been extensively studied in the literature is the one in which Y contains substitution, insertion and deletion (SID) errors. Although some work has been done to extend the traditional set of edit operations to include the straightforward transposition of adjacent characters 2[14] the problem is unsolved when the transposed characters are themselves subsequently substituted, as is typical in cursive and typewritten script, in molecular biology and in noisy chain-coded boundaries. In this paper we present the first reported solution to the analytic problem of editing one string X to another, Y using these four edit operations. A scheme for obtaining the optimal edit operations has also been given. Both these solutions are optimal for the infinite alphabet case. Using these algorithms we present a syntactic pattern recognition scheme which corrects noisy text containing all these types of errors. The paper includes experimental results involving sub-dictionaries of the most common English words which demonstrate the superiority of our system over existing methods.1 Partially supported by the Natural Sciences and Engineering Research Council of Canada. A preliminary version of this paper can be found in the Proceedings of the 1995 IEEE International Conference on Systems, Man and Cybernetics, Vancouver, October 1995, pp. 1154-1159 There has been some recent work done [Oo93] to consider the squashing and expansion operations too, where in the squashing operation two (or more) contiguous characters of X can be transformed into a single character of Y, and in the expansion operation a single character in X may be expanded into two or more contiguous characters of Y.Pat. Recog. with Subst., Insert., Delet.and Gen. Transpos. Errors. Page 2

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Near‐Capacity Variable‐Length Coding

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A Method for the Correction of Garbled Words Based on the Levenshtein Metric

Cited by 178 publications

References 10 publications

A formal theory for optimal and information theoretic syntactic pattern recognition

A formal theory for optimal and information theoretic syntactic pattern recognition

Pattern recognition of strings with substitutions, insertions, deletions and generalized transpositions

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