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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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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...
The Normalized String Editing Problem Revisited
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... Marzal and Vidal [8] recently considered the problem of computing the normalized edit distance between two strings, and reported experimental results which demonstrated the use of the measure to recognize handwritten characters. Their paper formulated the theoretical properties of the measure and de ..."
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Marzal and Vidal [8] recently considered the problem of computing the normalized edit distance between two strings, and reported experimental results which demonstrated the use of the measure to recognize handwritten characters. Their paper formulated the theoretical properties of the measure and developed two algorithms to compute it. In this short communication we shall demonstrate how this measure is related to an auxiliary measure already defined in the literature  the interstring constrained edit distance [10,11,15]. Since the normalized edit distance can be computed efficiently using the latter, the analytic and experimental results reported in [8] can be obtained just as accurately, but more efficiently, using the strategies presented here. I. PROBLEM STATEMENT In the comparison of text patterns, phonemes and biological macromolecules a question that has attracted much interest is that of quantifying the dissimilarity between strings. A review of such distance measures and ...
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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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...
Symbolic Channel Modelling For Noisy Channels Which Permit Arbitrary Noise Distributions
 Proc. of the 1993 Int. Symp. on Comp. and Inform. Sci
, 1993
"... In this paper we present a new model for noisy channels which permit arbitrarily distributed substitution, deletion and insertion errors. Apart from its straightforward applications in string generation and recognition, the model also has potential applications in speech and unidimensional signal pr ..."
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In this paper we present a new model for noisy channels which permit arbitrarily distributed substitution, deletion and insertion errors. Apart from its straightforward applications in string generation and recognition, the model also has potential applications in speech and unidimensional signal processing. The model is specified in terms of a noisy string generation technique. Let A be any finite alphabet and A* be the set of words over A. Given any arbitrary string U A*, we specify a stochastically consistent scheme by which this word can be transformed into any Y A*. This is achieved by specifying the process by which U is transformed by performing substitution, deletion and insertion operations. The scheme is shown to be Functionally Complete and stochastically consistent. The probability distributions for these respective operations can be completely arbitrary. Apart from presenting the channel in which all the possible strings in A* can be potentially generated, we also specify ...
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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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...
Noisy Subsequence Recognition Using Constrained String Editing Involving Substitutions, Insertions, Deletions and Generalized Transpositions
 In ICSC
, 1994
"... . We consider a problem which can greatly enhance the areas of cursive script recognition and the recognition of printed character sequences. This problem involves recognizing words/strings by processing their noisy subsequences. Let X * be any unknown word from a finite dictionary H. Let U be a ..."
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. We consider a problem which can greatly enhance the areas of cursive script recognition and the recognition of printed character sequences. This problem involves recognizing words/strings by processing their noisy subsequences. Let X * be any unknown word from a finite dictionary H. Let U be any arbitrary subsequence of X * . We study the problem of estimating X * by processing Y, a noisy version of U. Y contains substitution, insertion, deletion and generalized transposition errors  the latter occurring when transposed characters are themselves subsequently substituted. We solve the noisy subsequence recognition problem by defining and using the constrained edit distance between X H and Y subject to any arbitrary edit constraint involving the number and type of edit operations to be performed. An algorithm to compute this constrained edit distance has been presented. Using these algorithms we present a syntactic Pattern Recognition (PR) scheme which corrects noisy tex...
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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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...
String editing under a combination of constraints, Inform. Sci
, 1993
"... Let X and Y be any two strings of finite lengths N and M, respectively, over a finite alphabet. An edit distance between X and Y is defined as the minimum sum of elementary edit distances associated with edit operations of substitutions, deletions, and insertions needed to transform X to Y. In this ..."
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Let X and Y be any two strings of finite lengths N and M, respectively, over a finite alphabet. An edit distance between X and Y is defined as the minimum sum of elementary edit distances associated with edit operations of substitutions, deletions, and insertions needed to transform X to Y. In this paper, the problem of efficient computation of such a distance is considered under the assumption that the numbers of edit operations are limited and that the maximum lengths, F and G, of runs of deletions and insertions are given, respectively. Besides, the edit sequence is ordered in a sense that between every two successive runs of substitutions there can be either at most one run of deletions followed by at most one run of insertions or just one run of deletions or insertions. An algorithm is derived that computes the minimum edit distance associated with editing X to Y subject to the specified constraints. The algorithm requires O(NM min{N, M}) time and O(NM) space. Possible applications for the synchronization errorcorrecting codes and for the cryptanalysis of certain stream ciphers are also discussed. 1.
INFORMATION SCIENCES 77,253273 (1994) 253 Constrained Tree Editing
"... The distance between two ordered labeled trees is considered to be the minimum sum of the weights associated with the edit operations (insertion, deletion, and substitution) required to transform one tree to another. The problem of computing this distance and the optimal transformation using no edi ..."
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The distance between two ordered labeled trees is considered to be the minimum sum of the weights associated with the edit operations (insertion, deletion, and substitution) required to transform one tree to another. The problem of computing this distance and the optimal transformation using no edit constraints has been studied in the literature [3,4,79, 111. In this paper, we consider the problem of transforming one tree T1 to another tree T2 using any arbitrary edit constraint involving the number and type of edit operations to be performed. An algorithm to compute this constrained distance is presented. If for a tree T, Span(T) is defined as the Min(Depth(T),Leaves(T)), the time and space complexities of this algorithm are:
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.