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Levenshtein distance

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	Levenshtein distance - Wikipedia, the free encyclopedia
		In information theory, the Levenshtein distance or edit distance between two strings is given by the minimum number of operations needed to transform one string into the other, where an operation is an insertion, deletion, or substitution.
		It can be considered a generalization of the Hamming distance, which is used for strings of the same length and only considers substitution edits.
		The Levenshtein distance has several simple upper and lower bounds that are useful in applications which compute many of them and compare them.
	en.wikipedia.org /wiki/Levenshtein_distance (600 words)

	Example: Edit Distance (Site not responding. Last check: 2007-10-15)
		One of the classic problems solvable by dynamic programming is computing the “edit distance” between two strings: the minimum number of single-character insertions, deletions, or replacements required to convert one string into another.
		The edit distance between “good” and “goodbye” is 3.
		Like that function, an edit distance function would be useful to our spell checker program as a way of determining words from the dictionary that are “similar to” a misspelled word and that could therefore be suggested as possible replacements.
	www.cs.odu.edu /~zeil/cs361/Lectures-f02/08styles/styles/editdistance.html (122 words)

	CodeGuru: CEditDist Abstract Template Class for Edit Distance Calculation on Generic Data Types (Site not responding. Last check: 2007-10-15)
		The edit distance is defined as the minimum cost required to convert one string into another, where the conversion can include changing one character to another, deleting characters and inserting characters, with user-defined costs for each basic operation.
		Edit distance calculations are useful for finding the degree of similarity between strings, e.g.
		This is because the least expensive edit replaces the second character in a from 1 to 2, replaces the sixth character from 2 to 1, and deletes the last character in a, for a total of two changes and one deletion, with a cost of 3+3+5=11.
	www.codeguru.com /cpp_mfc/EditDist.shtml (584 words)

	Humdrum Toolkit Command Reference -- simil (Site not responding. Last check: 2007-10-15)
		In describing the edit operations, String 1 is the source string and String 2 is the template string.
		In the case where all edit operations are assigned a penalty of +1, the minimum quantitative similarity between two strings is 0.37.
		Edit penalties are defined by specifying the operation, followed by some spaces or tabs, followed by some real number.
	www.musiccog.ohio-state.edu /Humdrum/commands/simil.html (2019 words)

	Long-distance track event - Wikipedia, the free encyclopedia
		The 3,000 meter Steeplechase is a distance event requiring greater strength, stamina and agility than the flat 3,000 meter event.
		Longer races are rarely contested on the track, although records do exist for distances up to 1600 kilometers (see marathons and ultramarathons).
		3,000 meters is considered a middle distance track event.
	en.wikipedia.org /wiki/Long-distance_track_event (214 words)

	Global and Local Alignment Via Dynamic Algorithm (Site not responding. Last check: 2007-10-15)
		The permitted edit operations are insertion (I) of a character into the first string, deletion (D) of a character from the first string and substitution or replacement (R) of a character in the first string with a character in the second string.
		String edit problem is to compute the edit distance between two given strings, along with an optimal edit transcript that describes the transformation.
		The edit transcript is recovered from the path by interpreting each horizontal edge in the path, as an insertion of character, interpreting each vertical edge as a deletion and interpreting each diagonal edge as a match or as a substitution.
	www.msci.memphis.edu /~giri/compbio/f99/ningxu/NOTE10.html (1477 words)

	Nearest words (Site not responding. Last check: 2007-10-15)
		Edit distance is a way of calculating the distance ("nearness") of two words.
		The edit distance counts how many operations (delete, insert, substitution) that is needed for transforming one word to another.
		the edit distance between the word hakan and the word håkan is 1, since we need one substitution ("å" is substituted for "a").
	www.hakank.org /nearest_words (189 words)

	Functions and CALL Routines : COMPGED Function
		Generalized edit distance is a generalization of Levenshtein edit distance, which is a measure of dissimilarity between two strings.
		The Levenshtein edit distance is the number of deletions, insertions, or replacements of single characters that are required to transform string-1 into string-2.
		The generalized edit distance is the minimum-cost sequence of operations for constructing string-1 from string-2.
	support.sas.com /91doc/getDoc/lrdict.hlp/a002206133.htm (1067 words)

	CS514 Lab 5
		As mentioned in the tutorial, consider each line to be a character in the string and have the edit distance be measured in per-line operations rather than per-character operations.
		For the purposes of this lab, the normalized edit distance is the edit distance calculated by the dynamic programming algorithm divided by the number of lines in the largest of the two files.
		Your edit distances will be smaller, but you should still calculate the renormalized edit distance as the edit distance divided by the number of lines in the largest file.
	www.cs.wustl.edu /~raa4/CS514_SP02/labs/lab5 (1509 words)

	Dynamic Programming Algorithm, Edit Distance
		The edit distance of two strings, s1 and s2, is defined as the minimum number of point mutations required to change s1 into s2, where a point mutation is one of:
		If only the value of the edit distance is needed, only two rows of the matrix need be allocated; they can be "recycled", and the space complexity is then O(s1), i.e.
		Modify the edit distance DPA to that it treats a transposition as a single point-mutation.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Dynamic/Edit (1216 words)

	Levenshtein distance
		We can adapt the algorithm to use less space, O(m) instead of O(mn), since it only requires that the previous row and current row be stored at any one time.
		If the strings are the same size, the Hamming distance is an upper bound on the Levenshtein distance; otherwise the Hamming distance plus the difference in sizes is an upper bound.
		CSE 590BI, Winter 1996 Algorithms in Molecular Biology (http://www.cs.washington.edu/education/courses/590bi/96wi/) The algorithms from lectures 2, 3 and 4 are based on the Levenshtein distance but implement a different scoring function.
	www.arikah.net /encyclopedia/Levenshtein_distance (747 words)

	Levenshtein
		The edit distance is defined as the number of deletions, insertions, or substitutions required to transform the source into the target.
		Edit distance can be (and has been) used for spell checking and speech recognition purposes.
		They are both straightforward implementations of Levenshtein's algorithm - a dynamic programming algorithm capable of calculating the edit distance in time proportional to the length of the source times the length of the target.
	www.mozart-oz.org /mogul/doc/lager/levenshtein (333 words)

	Theory Group @ PENN (Site not responding. Last check: 2007-10-15)
		A sublinear algorithm for weakly approximating the edit distance
		We show how to determine whether the edit distance between two strings is small in sublinear time.
		Our algorithm for testing the distance works by recursively subdividing the strings into smaller substrings and looking for pairs of substrings in $A$, $B$ with small edit distance.
	www.cis.upenn.edu /~algorithms/seminar/20030214.html (178 words)

	6 Edit Distance Two (weighted) (Site not responding. Last check: 2007-10-15)
		Edit distance Two diversity is based on the depth-weighted edit distance between individuals used by Ekárt and Németh (2000).
		inter-population diversity method is developed based on pair-wise distance by counting the frequencies of symbols for each position in the genome.
		Both edit distance One and Two are vulnerable to outliers, especially when the best fit individual is the outlier.
	www.cs.nott.ac.uk /~smg/thesis_html/node60.html (292 words)

	SURVO MM Help System (web edition) (Site not responding. Last check: 2007-10-15)
		www.merriampark.com/ld.htm Levenshtein (edit) distance is a measure of the similarity between two strings s and t.
		The distance is the number of deletions, insertions, or substitutions required to transform s into t.
		In Survo, Levenshtein distance is used for detecting typos in command and specification words (see ERROR?) and in heuristic searches by the FIND command (see HFIND?).
	www.survo.fi /help/q0c_04.html (150 words)

	What is Translation Memory? (Site not responding. Last check: 2007-10-15)
		Edit distance is the number of "edits," or changes, that need to be made to convert one string into another.
		There are many descriptions of edit distance online, including this one.
		The translator can then choose to retrieve the translation for the similar segment, editing the parts that are different if need be, or ignoring the suggestion and typing in his own translation.
	ginstrom.com /translation/translation_memory.html (1509 words)

	Learning String Edit Distance Costs
		Stochastic edit distance is defined in chapter 2 as the negative logarithm of the probability that two strings are simultaneously grown using left-insertion, right-insertion, and joint-insertion operations.
		It is then identical to conventional edit distance where the edit costs are the negative logarithms of the corresponding generative insertion probabilities.
		As we anticipated the Viterbi and stochastic edit distance behave similarly.
	www.pnylab.com /pny/papers/PhD/PhD/node3.html (3007 words)

	String edit distance matrices - Research Group on Computer Vision and Artificial Intelligence (Site not responding. Last check: 2007-10-15)
		The edit distance is a distance measure that reflects the structural dissimilarity of strings, such that low distance corresponds to similar strings and high distance to dissimilar strings.
		The edit distance data we provide can be used for evaluating new classification methods and clustering procedures in structural pattern recognition.
		The string datasets and the edit distance matrices have been prepared and computed in 2004-2005 at the Research group on Computer Vision and Artificial Intelligence, University of Bern.
	iamwww.unibe.ch /~fki/varia/distancematrix (193 words)

	ECE551 (Site not responding. Last check: 2007-10-15)
		The option is first entered through the DIP switches to select one of the three modes namely Edit Distance mode, Sub String mode and the String Reverse mode.
		The main module collect the input characters and sends the characters to the comparing module which compares directly the two strings and the edit distance or the match values are calculated and sent to the main module.
		In this case, the two eight character input strings are compared and the edit distance is calculated by determining the number of deletions/insertions required to transform one string into another.
	microsys6.engr.utk.edu /~agothan1/report.html (1562 words)

	IEEE Transactions on Pattern Analysis and Machine Intelligence,March 2004 (Vol. 26, No. 3) (Site not responding. Last check: 2007-10-15)
		Edit distance was originally developed by Levenstein several decades ago to measure the distance between two strings.
		The edit distance has played important roles in a wide array of applications due to its representational efficacy and computational efficiency.
		Within this framework, two specialized distance measures are developed: The reshuffling MED to handle cases where a subpattern in the target pattern is the reshuffles of that in the source pattern, and the coherence MED which is able to incur local content based substitution, insertion, and deletion.
	csdl.computer.org /comp/trans/tp/2004/03/i0311abs.htm (876 words)

	Calculating Edit Distance Between Sequences
		The task is to calculate the "edit distance" between two sequences.
		At the end, the total distance is in the cell at (m,n).
		Martin Jansche adds:: there is also the connection between string edit distance and weighted automata.
	www.ling.ohio-state.edu /~cbrew/795M/string-distance.html (866 words)

	Re: 2-D edit distance calculation (Site not responding. Last check: 2007-10-15)
		An edit distance is the minimum number of editing operations to turn one string into another, where an editing operation is something like insert, delete or change a characer.
		For example to change "cat" into "bart" you could: change c into b insert r between a and t 2 operations, so edit distance is 2.
		You could also get more fancy with additional edit operations and by assigining different costs to the edit operations.
	documents.cfar.umd.edu /newsgroups/ocrarchive/msg00781.html (94 words)

	focs,45th Annual IEEE Symposium on Foundations of Computer Science (FOCS'04) (Site not responding. Last check: 2007-10-15)
		Edit distance has been extensively studied for the past several years.
		Nevertheless, no linear-time algorithm is known to compute the edit distance between two strings, or even to approximate it to within a modest factor.
		We develop algorithms that solve gap versions of the edit distance problem: given two strings of length n with the promise that their edit distance is either at most k or greater than \ell, decide which of the two holds.
	csdl.computer.org /comp/proceedings/focs/2004/2228/00/22280550abs.htm (316 words)

	How Hard is to Compute the Edit Distance (Site not responding. Last check: 2007-10-15)
		The edit distance between an input string and a language L is the minimum cost of a sequence of edit operations (substitution of a symbol in another incorrect symbol, insertion of an extraneous symbol, deletion of a symbol) needed to change the input string into a sentence of L.
		In this paper we study the complexity of computing the edit distance, discovering sharp boundaries between classes of languages for which this function can be efficiently evaluated and classes of languages for which it seems to be difficult to compute.
		Our main result is a parallel algorithm for computing the edit distance for the class of languages accepted by one--way nondeterministic auxiliary pushdown automata working in polynomial time, a class that strictly contains context--free languages.
	homes.dico.unimi.it /~pighizzi/pubbl/fct95 (188 words)

	Software I - Spring semester 1997/8 Exercise 1: Edit Distance
		Intuitively, the editing distance is the cost (or ``number'') of operations that one need to apply to text to receive text1.
		Then, the editing distance is the price of matching of those two characters (0 if the two characters are equal, and 15 otherwise), plus
		The required editing distance is the minimum of this three options, so your function should try those three options (using recursion), and return the cheapest value computed (which is the editing distance).
	valis.cs.uiuc.edu /~sariel/teach/1997/soft98b/ex1/exercise.html (562 words)

	5 Discussion of a Causal Model (Site not responding. Last check: 2007-10-15)
		Figures 6.7 and 6.8 show the evolution of the Spearman correlation coefficient between the average size of a population and its best fitness (raw fitness, where lower is better), entropy and diversity, respectively.
		Generally, size is negatively correlated with fitness (low fitness with large size), negatively correlated with edit distance diversity (low edit distance with large size) and positively correlated with entropy (high entropy with large size).
		The 7-degree polynomial is the exception with erratic correlation between edit distance and size, and appears to contain aspects of both the 3-degree polynomial and the 11-degree polynomial.
	www.cs.nott.ac.uk /~smg/thesis_html/node96.html (371 words)

	Text::WagnerFischer - An implementation of the Wagner-Fischer edit distance
		The edit distance is a measure of the degree of proximity between two strings, based on ``edits'': the operations of substitutions, deletions or insertions needed to transform the string into the other one (and vice versa).
		This particular distance is the exact number of edit needed to transform the string into the other one (and vice versa).
		Note that the distance is calculated to reach the _minimum_ cost, i.e.
	cpan.uwinnipeg.ca /htdocs/Text-WagnerFischer/Text/WagnerFischer.html (400 words)

	1 Population Measures: Entropy and Edit Distance Diversity (Site not responding. Last check: 2007-10-15)
		To better understand the distribution of fitness values that a selection method is presented with, and the ability of the population to represent solutions for each problem instance, we use the measure of entropy based on fitness, described in detail in Chapter 4.
		Measuring the genetic diversity of populations is difficult, as there are many aspects of tree shapes and contents that could be measured.
		In this study, a measure is used based on the edit distance between two trees, introduced and used in Chapter 4 as edit distance One, and in Chapter 5 as the non-weighted edit distance.
	www.cs.nott.ac.uk /~smg/thesis_html/node90.html (274 words)

	Levenshtein distance (Site not responding. Last check: 2007-10-15)
		(2) A Θ(m × n) algorithm to compute the distance between strings, where m and n are the lengths of the strings.
		Levenshtein distance (Java, C++, Visual Basic), includes a great explanation and links to code in Perl, C, JavaScript, Python, and many more languages.
		AUTHOR(S), "Levenshtein distance", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/Levenshtein.html (199 words)

	Evaluating RIL as basis for evaluating Automated Speech Recognition devices and the consequences of using probabilistic ... (Site not responding. Last check: 2007-10-15)
		The stochastic Edit Distance can be applied as an input into the RIL, which is then called the RILstochastic.
		Similarly, the RIL using the Viterbi Edit Distance is called RILviterbi.
		A technique, generally used in ASR device training, is used to derive the Stochastic Edit Distance.
	www.dcs.shef.ac.uk /teaching/eproj/ug2002/abs/u9vm.htm (362 words)

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