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Pattern Recognition of Strings With Substitutions, Insertions, Deletions and Generalized Transpositions
 Pattern Recognition
"... 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. Altho ..."
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Cited by 12 (2 self)
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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 chaincoded 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 rec...
A Formal Theory for Optimal and Information Theoretic Syntactic Pattern Recognition
"... 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 ..."
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Cited by 4 (2 self)
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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[YU], 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 involv...
String Taxonomy Using Learning Automata
 IEEE Transactions on Systems, Man and Cybernetics
, 1997
"... A typical syntactic pattern recognition (PR) problem involves comparing a noisy string with every element of a dictionary, H. The problem of classification can be greatly simplified if the dictionary is partitioned into a set of subdictionaries. In this case, the classification can be hierarchical ..."
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Cited by 4 (0 self)
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A typical syntactic pattern recognition (PR) problem involves comparing a noisy string with every element of a dictionary, H. The problem of classification can be greatly simplified if the dictionary is partitioned into a set of subdictionaries. In this case, the classification can be hierarchical  the noisy string is first compared to a representative element of each subdictionary and the closest match within the subdictionary is subsequently located. Indeed, the entire problem of subdividing a set of strings into subsets where each subset contains "similar" strings has been referred to as the "String Taxonomy Problem". To our knowledge there is no reported solution to this problem (see footnote on Page 2). In this paper we shall present a learningautomaton based solution to string taxonomy. The solution utilizes the Object Migrating Automaton (OMA) whose power in clustering objects and images [33,35] has been reported. The power of the scheme for string taxonomy has been demons...
Optimal and Information Theoretic Syntactic Pattern Recognition for Traditional Errors
 In Advances in Structural and Syntactic Pattern Recognition
, 1996
"... 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 ..."
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Cited by 1 (0 self)
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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[YU], the probability of receiving Y given that U was transmitted, can be computed in cubic time using dynamic programming. Experimental results which involve dictionaries with strings of lengths between 7 and 14 with an overall average noise of 39.75 % demons...
Pattern Recognition of Strings Containing Traditional and Generalized Transposition Errors
"... 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 ..."
Abstract
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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 [LW75] 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 chaincoded 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 reco...
NORTH HOLLAND String Alignment With Substitution, Insertion, Deletion, Squashing, and Expansion Operations*
"... Let X and Y be any two strings of finite length. The problem of transforming X to Y using the edit operations of substitution, deletion, and insertion has been extensively studied in the literature. The problem can be solved in quadratic time if the edit operations are extended to include the operat ..."
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Let X and Y be any two strings of finite length. The problem of transforming X to Y using the edit operations of substitution, deletion, and insertion has been extensively studied in the literature. The problem can be solved in quadratic time if the edit operations are extended to include the operation of transposition of adjacent characters, and is NPcomplete if the characters can be edited repeatedly. In this paper we consider the problem of transforming X to Y when the set of edit operations is extended to include the squashing and expansion operations. Whereas in the squashing operation two (or more) contiguous characters of X can be transformed into a single character of Y, in the expansion operation a single character in X may be expanded into two or more contiguous characters of Y. These operations are typically found in the recognition of cursive script. A quadratic time solution to the problem has been presented. This solution is optimal for the infinitealphabet case. The strategy to compute the sequence of edit operations is also presented. 1.