2008 LanguageIndependentTextCorrecti

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Subject Headings: Text Error Correction (TEC) System; Finite State Automata; FSA-based TEC System, Levenshtein-Transducer, Edit Distance.

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Abstract

Many natural language applications, like machine translation and information extraction, are required to operate on text with spelling errors. Those spelling mistakes have to be corrected automatically to avoid deteriorating the performance of such applications. In this work, we introduce a novel approach for automatic correction of spelling mistakes by deploying finite state automata to propose candidates corrections within a specified edit distance from the misspelled word. After choosing candidate corrections, a language model is used to assign scores the candidate corrections and choose best correction in the given context. The proposed approach is language-independent and requires only a dictionary and text data for building a language model. The approach have been tested on both Arabic and English text and achieved accuracy of 89%.

1 Introduction

The problem of detecting and correcting misspelled words in text has received great attention due to its importance in several applications like text editing systems, optical character recognition systems, and morphological analysis and tagging (Roche and Schabes, 1995). Other applications, like machine translation and information extraction, operate on text that might have spelling errors. The automatic detection, and correction of spelling errors should be of great help to those applications.

The problem of detecting and correcting misspelled words in text is usually solved by checking whether a word already exists in the dictionary or not. If not, we try to extract words from the dictionary that are most similar to the word in question. Those words are reported as candidate corrections for the misspelled word.

 Similarity between the misspelled word and dictionary words is measured by the Levenshtein edit distance (Levenshtein, 1966; Wagner and M.Fisher, 1974). The Levenshtein edit distance is usually calculated using a dynamic programming technique with quadratic time complexity (Wagner and M.Fisher, 1974). Hence, it is not reasonable to compare the misspelled word to each word in the dictionary while trying to find candidate corrections.

 The proposed approach uses techniques from finite state theory to detect misspelled words and to generate a set of candidate corrections for each misspelled word. It also uses a language model to select the best correction from the set of candidate corrections using the context of the misspelled word. Using techniques from finite state theory, and avoiding calculating edit distances makes the approach very fast and efficient. The approach is completely language independent, and can be used with any language that has a dictionary and text data to building a language model.

The rest of this paper will proceed as follows. Section 2 will present an overview of related work. Section 3 will discuss the different aspects of the proposed approach. Section 4 presents a performance evaluation of the system. Finally, a conclusion is presented in section 5.

2 Related Work

Several solutions were suggested to avoid computing the Levenshtein edit distance while finding candidate corrections. Most of those solutions select a number of dictionary words that are supposed to contain the correction, and then measure the distance between the misspelled word and all selected words. The most popular of those methods are the [[similarity keys methods (Kukich, 1992; Zobel and Dart, 1995; De Beuvron and Trigano, 1995). In those methods, the dictionary words are divided into classes according to some word features. The input word is compared to words in classes that have similar features only.

In addition to the techniques discussed above, other techniques from finite state automata have been recently proposed. (Oflazer, 1996) suggested a method where all words in a dictionary are treated as a regular language over an alphabet of letters. All the words are represented by a finite state machine automaton. For each garbled input word, an exhaustive traversal of the dictionary automaton is initiated using a variant of the Wagner-Fisher algorithm (Wagner and M.Fisher, 1974) to control the traversal of the dictionary. In this approach Levenshtein distance is calculated several times during the traversal. The method carefully traverses the dictionary such that the inspection of most of the dictionary states is avoided. (Schulz and Mihov, 2002) presents a variant of Oflazers’s approach where the dictionary is also represented as deterministic finite state automaton. However, they avoid the computation of Levenshtein distance during the traversal of the dictionary automaton. In this technique, a finite state acceptor is constructed for each input word. This acceptor accepts all words that are within an edit distance k from the input word. The dictionary automaton and the Levenshtein-automaton are then traversed in parallel to extract candidate corrections for the misspelled word. The authors present an algorithm that can construct a deterministic Levenshtein-automaton for an arbitrary word of degrees 1, and 2 which corresponds to 1 or 2 errors only. They suggest another algorithm that can construct a non-deterministic Levenshtein-automaton for any other degree. They report results using a Levenshtein-automaton of degree 1 (i.e. words having a single insertion, substitution, or deletion) only.

The method we propose in this work also assumes that the dictionary is represented as a deterministic finite state automaton. However, we completely avoid computing the Levenshtein-distance at any step. We also avoid reconstructing a Levenshtein-automaton for each input word. The proposed method does not impose any constraints on the bound k, where k is the edit distance between the input word and the candidate corrections. The approach can adopt several constraints on which characters can substitute certain other characters. Those constraints are obtained from a phonetic and spatial confusion matrix of characters.

The purpose of context-dependent error correction is to rank a set of candidate corrections taking the misspelled word context into account. A number of approaches have been proposed to tackle this problem that use insights from statistical machine learning (Golding and Roth, 1999), lexical semantics (Hirst and Budanitsky, 2005), and web crawls (Ringlstetter et al., 2007).

3 Error Detection And Correction In Text Using FSMs

The approach consists of three main phases: detecting misspelled words, generating candidate corrections for them, and ranking corrections. A detailed description of each phase is given in the following subsections.

3.1 Detecting Misspelled Words

The most direct way for detecting misspelled words is to search the dictionary for each word, and report words not found in the dictionary. However, we can make use of the finite state automaton representation of the dictionary to make this step more efficient. In the proposed method, we build a finite state machine (FSM) that contains a path for each word in the input string. This FSM is then composed with the dictionary FSM. The result of the composition is merely the intersection of the word]]s that exist in both the input string and the dictionary. If we calculated the difference between the FSM containing all words and this FSM, we get an FSM with a path for each misspelled word. Figure 1 illustrates an FSM that contains all words in an input string.

Figure 1: An FSM representation of a word list.

3.2 Generating Candidate Corrections

The task of generating candidate corrections for misspelled words can be divided into two sub-tasks: Generating a list of words that have edit distance less than or equal k to the input word, and selecting a subset of those words that also exist in the dictionary. To accomplish those tasks, we create a single transducer (Levenshtein-transducer) that is when composed with an FSM representing a word, generates all words withing any edit distance k from the input word. After composing the misspelled word with Levenshtein-transducer, we compose the resulting FSM with the dictionary FSM to filter out words that do not exist in the dictionary.

3.2.1 Levenshtein-Transducers For Primitive Edit Distances

To generate a finite state automaton that contain all words within some edit distance to the input word, we use a finite state transducer that allows editing its input according to the standard Levenshtein-distance primitive operations: substitution, deletion, and insertion.

A finite-state transducers (FST) is a 6-tuple [math]\displaystyle{ (Q,\Sigma_1,\Sigma_2,\sigma,i,F) }[/math], where [math]\displaystyle{ Q }[/math] is a set of states, [math]\displaystyle{ \Sigma_1 }[/math] is the input alphabet, [math]\displaystyle{ \Sigma_2 }[/math] is the output alphabet, [math]\displaystyle{ i }[/math] is the initial state, [math]\displaystyle{ F \subseteq Q }[/math] is a set of final states, and a is a transition function (Hopcroft and Ullman, 1979; Roche and Shabes, 1997). A finite-state acceptor is a special case of an FST that has the same input/output at each arc.

 Figure 2 illustrates the Levenshtein-transducer for edit distance 1 over a limited set of vocabulary (a,b , and c). We can notice that we will stay in state zero as long as the output is identical to the input. On the other hand we can move from state zero, which corresponds to edit distance zero, to state one, which corresponds to edit distance one, with three different ways:

* input is mapped to a different output (input is consumed and a different symbol is emitted) which corresponds to a substitution,

3.2.2 Adding Transposition

Another non-primitive edit distance operation that is frequently seen in misspelled words is transposition. Transposition is the operation of exchanging the order of two consecutive symbols ([math]\displaystyle{ ab \to ba }[/math]). Transposition is not a primitive operation because it can be represented by other primitive operations. However, this makes it a second degree operation. As transposition occurs frequently in misspelled words, adding it to the Levenshtein-transducer as a single editing operation would be of great help.

To add transposition, as a single editing operation, to the Levenshtein-transducer we add arcs between states zero and one that can map any symbol sequence [math]\displaystyle{ xy }[/math] to the symbol sequence [math]\displaystyle{ yx }[/math], where [math]\displaystyle{ x }[/math], and [math]\displaystyle{ y }[/math] are any two symbols in the vocabulary. Figure 3 shows the Levenshtein-transducer with degree 1 with transposition over a limited vocabulary ([math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math]).

Figure 3: A Levenshtein-transducer for edit distance 1 with transposition.
3.2.3 Adding Symbol Confusion Matrices

Adding a symbol confusion matrix can help reduce the number of candidate corrections. The confusion matrix determines for each symbol a set of symbols that may have substituted it in the garbled word. This matrix can be used to reduce the number of candidate corrections if incorporated into the Levenshtein-transducer. For any symbol [math]\displaystyle{ x }[/math], we add an arc [math]\displaystyle{ x:y }[/math] between states zero, and one in the transducer where [math]\displaystyle{ y \in \text{Confusion_Matrix} (x) }[/math] rather than for all symbols [math]\displaystyle{ y }[/math] in the vocabulary.

The confusion matrix can help adopt the methods to different applications. For example, we can build a confusion matrix for use with optical character recognition error correction that captures errors that usually occur with OCRs. When used with a text editing system, we can use a confusion matrix that predicts the confused characters according to their phonetic similarity, and their spatial location on the keyboard.

3.2.4 Using Degrees Greater Than One

To create a Levenshtein-transducer that can generate all words within edit distance two of the input word, we create a new state (2) that maps to two edit operations, and repeat all arcs that moves from state 0 to state 1 to move from state 1 to state 2.

To allow the Levenshtein-transducer of degree two to produce words with edit distance 1 and 2 from the input word, we mark both state 1, and 2 as final states. We may also favor corrections with lower edit distances by assigning costs to final states, such that final states with lower number of edit operations get lower costs. A Levenshtein-transducer of degree 2 for the limited vocabulary (a and b) is shown in figure 4.

Figure 4: A Levenshtein-transducer for edit distance 2 with transposition.

3.3 Ranking Corrections

To select the best correction from a set of candidate corrections, we use a language model to assign a probability to a sequence of words containing the corrected word. To get that word sequence, we go back to the context where the misspelled word appeared, replace the misspelled word with the candidate correction, and extract 71 n-grams containing the candidate correction word in all possible positions in the n-gram. We then assign a score to each n-gram using the language model, and assign a score to the candidate correction that equals the average score of all n-grams. Before selecting the best scoring correction, we penalize corrections that resulted from higher edit operations to favor corrections with the minimal number of editing operations.

4 Experimental Setup

4.1 Time Performance

The proposed method was implemented in C++ on a 2GHZ processor machine under Linux. We used 11,000 words of length 3, 4,..., and 13, 1,000 word for each word length, that have a single error and computed correction candidates. We report both the average correction time, and the average number of corrections for each word length. The experiment was run twice on different test data, one with considering transposition as primitive operation, and the other without. We also repeated the experiments for edit distance 2 errors, and also considered the two cases where transposition is considered as a primitive operation or not. Table 1 shows the results for an English dictionary of size 225, 400 entry, and Table 2 shows the results for an Arabic dictionary that has 526, 492 entries.

Edit 1/with trans. Edit 1/no trans. Edit 2/with trans. Edit 2/no trans.
word len. av. time av. correcs. av. time av. correcs. av. time av. correcs. av. time av. correcs.
3 3.373273 18.769 2.983733 18.197 73.143538 532.637 69.709387 514.174
4 3.280419 4.797 2.796275 4.715 67.864291 136.230 66.279842 131.680
5 3.321769 1.858 2.637421 1.838 73.718353 33.434 68.695935 32.461
6 3.590046 1.283 2.877242 1.277 75.465624 11.489 69.246055 11.258
7 3.817453 1.139 2.785156 1.139 78.231015 6.373 72.2057 6.277
8 4.073228 1.063 5.593761 1.062 77.096026 4.127 73.361455 4.066
9 4.321661 1.036 3.124661 1.036 76.991945 3.122 73.058418 3.091
10 4.739503 1.020 3.2084 1.020 75.427416 2.706 72.2143 2.685
11 4.892105 1.007 3.405101 1.007 77.045616 2.287 71.293116 2.281
12 5.052191 0.993 3.505089 0.993 78.616536 1.910 75.709801 1.904
13 5.403557 0.936 3.568391 0.936 81.145124 1.575 78.732955 1.568
Table 1: Results for English

Edit 1/with trans. Edit 1/no trans. Edit 2/with trans. Edit 2/no trans.
word len. av. time av. correcs. av. time av. correcs. av. time av. correcs. av. time av. correcs.
3 5.710543 31.702 4.308018 30.697 83.971263 891.579 75.539547 862.495
4 6.033066 12.555 4.036479 12.196 80.481281 308.910 71.042372 296.776
5 7.060306 6.265 4.360373 6.162 79.320644 104.661 69.71572 100.428
6 9.08935 4.427 4.843784 4.359 79.878962 51.392 74.197127 48.991
7 8.469497 3.348 5.419919 3.329 82.231107 24.663 70.681298 23.781
8 10.078842 2.503 5.593761 2.492 85.32005 13.586 71.557569 13.267
9 10.127946 2.140 6.027077 2.136 83.788916 8.733 76.199034 8.645
10 11.04873 1.653 6.259901 1.653 92.671732 6.142 81.007893 6.089
11 12.060286 1.130 7.327353 1.129 94.726469 4.103 77.464609 4.084
12 13.093397 0.968 7.194902 0.967 95.35985 2.481 82.40306 2.462
13 13.925067 0.924 7.740105 0.921 106.66238 1.123 78.966914 1.109
Table 2: Results for Arabic

4.2 Auto-Correction Accuracy

To measure the accuracy of the auto-correction process, we used a list of 556 words having common spelling errors of both edit distances 1 and 2. We put a threshold on the number of characters per word to decide whether it will be considered for edit distance 1 or 2 errors. When using a threshold of 7, the spell engine managed to correct 87% of the words. This percentage raised to 89% when all words were considered for edit distance 2 errors. The small degradation in the performance occurred because in 2% of the cases, the words were checked for edit distance 1 errors although they had edit distance 2 errors. Figure 6 shows the effect of varying the character's limit on the correction accuracy.

 Figure 5 shows the effect of varying the weight assigned to corrections with lower edit distances on the accuracy. As indicated in the figure, when we only consider the language model weight, we get accuracies as low as 79%. As we favor corrections with lower edit distances the correction accuracy raises, but occasionally starts to decay again when emphasis on the low edit distance is much larger than that on the language model weights.

Finally, we repeated the experiments but with us ing a confusion matrix, as 3.2.3. We found out that the average computation time dropped by 78% (be - low 1 ms for edit distance 1 errors) at the price of losing only 8% of the correction accuracy.

Figure 5: Effect of increasing lower edit distance favoring factor on accuracy.

Figure 6: Effect of increasing Edl/Ed2 char limits on accuracy.

5 Conclusion

In this work, we present a finite state automata based spelling errors detection and correction method. The new method avoids calculating the edit distances at all steps of the correction process. It also avoids building a Levenshtein-automata for each input word. The method is multilingual and may work for any language for which we have an electronic dictionary, and a language model to assign probability to word sequences. The preliminary experimental results show that the new method achieves good performance for both correction time and accuracy. The experiments done in this paper can be extended in several directions. First, there is still much room for optimizing the code to make it faster especially the FST composition process. Second, we can allow further editing operations like splitting and merging.

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 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
2008 LanguageIndependentTextCorrectiHany Hassan
Sara Noeman
Ahmed Hassan Awadallah		Language Independent Text Correction Using Finite State Automata2008
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