Very fast Data cleaning of product names, company names & street names

The correction of product names, company names, street names & addresses is a frequent task of data cleaning and deduplication. Often those names are misspelled, either due to OCR errors or mistakes of the human data collectors.

The difference is that those names often consist of multiple words, white space and punctuation. For large data or even Big data applications also speed is very important.

Our algorithm supports both requirements and is up to 1 million times faster compared to conventional approaches (see benchmark). The C# source code is available as Open Source in another Blog post and GitHub). A simple modification of the original source code will add support of names with multiple words, white space and punctuation:

Instead of 357 CreateDictionary("big.txt",""); which parses the a given text file into single words simply use CreateDictionaryEntry("company/street/product name", "") to add company, street & product names to the dictionary.

Then with Correct("misspelled street",""); you will get the correct street name from the dictionary. In line 35..38 you may specify whether you want only the best match or all matches within a certain edit distance (number of character operations difference):

35 private static int verbose = 0;
36 //0: top suggestion
37 //1: all suggestions of smallest edit distance
38 //2: all suggestions <= editDistanceMax (slower, no early termination)

For every similar term (or phrase) found in the dictionary the algorithm gives you the Damerau-Levenshtein edit distance to your input term (look for suggestion.distance in the source code). The edit distance describes how many characters have been added, deleted, altered or transposed between the input term and the dictionary term. This is a measure of similarity between the input term (or phrase) and similar terms (or phrases) found in the dictionary.

Fast approximate string matching with large edit distances in Big Data

1000x faster

1 million times faster spelling correction for edit distance 3
After my blog post 1000x times faster spelling correction got more than 50.000 views I revisited both algorithm and implementation to see if it could be further improved.

While the basic idea of Symmetric Delete spelling correction algorithm remains unchanged the implementation has been significantly improved to unleash the full potential of the algorithm.

This results in a 10 times faster spelling correction and 5 times faster dictionary generation and 2…7 times less memory consumption in v3.0 compared to v1.6 .

Compared to Peter Norvig’s algorithm it is now 1,000,000 times faster for edit distance=3 and 10,000 times faster for edit distance=2.

In Norvig’s tests 76% of spelling errors had an edit distance 1. 98.9% of spelling errors got covered with edit distance 2. For simple spelling correction of natural language with edit distance 2 the accuracy is good enough and the performance Norvig’s algorithm is sufficient.

The speed of our algorithm enables edit distance 3 for spell checking and thus improves the accuracy by 1%. Beyond the accuracy improvement the speed advantage of our algorithm is useful for automatic spelling correction in large corpora as well as in search engines, where many requests in parallel need to be processed.

Billion times faster approximate string matching for edit distance > 4
But the true potential of the algorithm lies in edit distances > 3 and beyond spell checking.

The many orders of magnitude faster algorithm opens up new application fields for approximate string matching and a scaling sufficient for big data and real-time. Our algorithm enables fast approximate string and pattern matching with long strings or feature vectors, huge alphabets, large edit distances, in very large data bases, with many concurrent processes and real time requirements.

Application fields:

  • Spelling correction in search engines, with many parallel requests
  • Automatic Spelling correction in large corpora
  • Genome data analysis,
  • Matching DNA sequences
  • Browser fingerprint analysis
  • Realtime Image recognition (search by image, autonomous cars, medicine)
  • Face recognition
  • Iris recognition
  • Speech recognition
  • Voice recognition
  • Feature recognition
  • Fingerprint identification
  • Signature Recognition
  • Plagiarism detection (in music /in text)
  • Optical character recognition
  • Audio fingerprinting
  • Fraud detection
  • Address deduplication
  • Misspelled names recognition
  • Spectroscopy based chemical and biological material identification
  • File revisioning
  • Spam detection
  • Similarity search,
  • Similarity matching
  • Approximate string matching,
  • Fuzzy string matching,
  • Fuzzy string comparison,
  • Fuzzy string search,
  • Pattern matching,
  • Data cleaning
  • and many more

Edit distance metrics
While we are using the Damerau-Levenshtein distance for spelling correction for other applications it could be easily exchanged with the Levenshtein distance or similar other edit distances by simply modifying the respective function.

In our algorithm the speed of the edit distance calculation has only a very small influence on the overall lookup speed. That’s why we are using only a basic implementation rather than a more sophisticated variant.

Benchmark
Because of all the applications for approximate string matching beyond spell check we extended the benchmark to lookups with higher edit distances. That’s where the power of the symmetric delete algorithm truly shines and excels other solutions. With previous spell checking algorithms the required time explodes with larger edit distances.

Below are the results of a benchmark of our Symmetric Delete algorithm and Peter Norvig’s algorithm for different edit distances, each with 1000 lookups:

input term best correction edit distance maximum edit distance SymSpell
ms per 1000 lookups
Peter Norvig
ms per 1000 lookups
factor
marsupilamimarsupilami no correction* >20 9 568,568,000
marsupilamimarsupilami no correction >20 8 161,275,000
marsupilamimarsupilami no correction >20 7 37,590,000
marsupilamimarsupilami no correction >20 6 5,528,000
marsupilamimarsupilami no correction >20 5 679,000
marsupilamimarsupilami no correction >20 4 46,592
marsupilami no correction >4 4 459
marsupilami no correction >4 3 159 159,421,000 1:1,000,000
marsupilami no correction >4 2 31 257,597 1:8,310
marsupilami no correction >4 1 4 359 1:90
hzjuwyzacamodation accomodation 10 10 7,598,000
otuwyzacamodation accomodation 9 9 1,727,000
tuwyzacamodation accomodation 8 8 316,023
uwyzacamodation accomodation 7 7 78,647
wyzacamodation accomodation 6 6 19,599
yzacamodation accomodation 5 5 2,963
zacamodation accomodation 4 4 727
acamodation accomodation 3 3 180 173,232,000 1:962,000
acomodation accomodation 2 2 33 397,271 1:12,038
hous hous 1 1 24 161 1:7
house house 0 1 1 3 1:3

*Correct or unknown word, which is not in the dictionary and there are also no suggestions within an edit distance of <=maximum edit distance. This is a quite common case (e.g. rare words, new words, domain specific words, foreign words, names), in applications beyond spelling correction (e.g. fingerprint recognition) it might be the default case.

For the benchmark we used the C# implementation of our SymSpell as well as a faithful C# port from Lorenzo Stoakes of Peter Norvig’s algorithm, which has been extended to support edit distance 3. The use of C# implementations for both cases allows to focus solely on the algorithm and should exclude language specific bias.

Dictionary corpus:
The English text corpus used to generate the dictionary used in the above benchmarks has a size 6.18 MByte, 1,105,286 terms, 29,157 unique terms, longest term with 18 characters.
The dictionary size and the number of indexed terms have almost no influence on the average lookup time of o(1).

Speed gain
The speed advantage grows exponentially with the edit distance:

  • For an edit distance=1 it’s 1 order of magnitude faster,
  • for an edit distance=2 it’s 4 orders of magnitude faster,
  • for an edit distance=3 it’s 6 orders of magnitude faster.
  • for an edit distance=4 it’s 8 orders of magnitude faster.

Computational complexity and findings from benchmark
Our algorithm is constant time ( O(1) time ), i.e. independent of the dictionary size (but depending on the average term length and maximum edit distance), because our index is based on a Hash Table which has an average search time complexity of O(1).

Precalculation cost
In our algorithm we need auxiliary dictionary entries with precalculated deletes and their suggestions. While the number of the auxiliary entries is significant compared to the 29,157 original entries the dictionary size grows only sub-linear with edit distance: log(ed)

maximum edit distance number of dictionary entries (including precalculated deletes)
20 11,715,602
15 11,715,602
10 11,639,067
9 11,433,097
8 10,952,582
7 10,012,557
6 8,471,873
5 6,389,913
4 4,116,771
3 2,151,998
2 848,496
1 223,134

The precalculation costs consist of additional memory usage and creation time for the auxiliary delete entries in the dictionary:

cost maximum edit distance SymSpell Peter Norvig factor
memory usage 1 32 MB 229 MB 1:7.2
memory usage 2 87 MB 229 MB 1:2.6
memory usage 3 187 MB 230 MB 1:1.2
dictionary creation time 1 3341 ms 3640 ms 1:1.1
dictionary creation time 2 4293 ms 3566 ms 1:0.8
dictionary creation time 3 7962 ms 3530 ms 1:0.4

Due to an efficient implementation those costs are negligible for edit distances <=3:

  • 7 times less memory requirement and a similar dictionary creation time (ed=1).
  • 2 times less memory requirement and a similar dictionary creation time (ed=2).
  • similar memory requirement and a 2 times higher dictionary creation time (ed=3).

Source code
The C# implementation of our Symmetric Delete Spelling Correction algorithm is released on GitHub as Open Source under the GNU Lesser General Public License (LGPL).

C# (original)
https://github.com/wolfgarbe/symspell

Ports
The following third party ports to other programming languages have not been tested by myself whether they are an exact port, error free, provide identical results or are as fast as the original algorithm:

C++ (third party port)
https://github.com/erhanbaris/SymSpellPlusPlus

Go (third party port)
https://github.com/heartszhang/symspell
https://github.com/sajari/fuzzy

Java (third party port)
https://github.com/gpranav88/symspell

Javascript (third party port)
https://github.com/itslenny/SymSpell.js
https://github.com/dongyuwei/SymSpell
https://github.com/IceCreamYou/SymSpell
https://github.com/Yomguithereal/mnemonist/blob/master/symspell.js

Python (third party port)
https://github.com/ppgmg/spark-n-spell-1/blob/master/symspell_python.py

Ruby (third party port)
https://github.com/PhilT/symspell

Swift (third party port)
https://github.com/Archivus/SymSpell

Comparison to other approaches and common misconceptions

A Trie as standalone spelling correction
Why don’t you use a Trie instead of your algorithm?
Tries have a comparable search performance to our approach. But a Trie is a prefix tree, which requires a common prefix. This makes it suitable for autocomplete or search suggestions, but not applicable for spell checking. If your typing error is e.g. in the first letter, than you have no common prefix, hence the Trie will not work for spelling correction.

A Trie as replacement for the hash table
Why don’t you use a Trie for the dictionary instead of the hash table?
Of course you could replace the hash table with a Trie (that is just a arbitrary lookup component of O(1) speed for a *single* lookup) at the cost of added code complexity, but without performance gain.
A HashTable is slower than a Trie only if there are collisions, which are unlikely in our case. For a maximum edit distance of 2 and an average word length of 5 and 100,000 dictionary entries we need to additionally store (and hash) 1,500,000 deletes. With a 32 bit hash (4,294,967,296 possible distinct hashes) the collision probability seems negligible.
With a good hash function even a similarity of terms (locality) should not lead to increased collisions, if not especially desired e.g. with Locality sensitive hashing.

BK-Trees
Would be BK-Trees an alternative option?
Yes, but BK-Trees have a search time of O(log dictionary_size), whereas our algorithm is constant time ( O(1) time ), i.e. independent of the dictionary size.

Ternary search tree
Why don’t you use a ternary search tree?
The lookup time in a Ternary Search Tree is O(log n), while it is only 0(1) in our solution. Also, while a Ternary Search Tree could be used for the dictionary lookup instead of a hash table, it doesn’t address the spelling error candidate generation. And the tremendous reduction of the number of spelling error candidates to be looked-up in the dictionary is the true innovation of our Symmetric Delete Spelling Correction algorithm.

Precalculation
Does the speed advantage simply comes from precalulation of candidates?
No! The speed is a result of the combination of all three components outlined below:

  • Pre-calculation, i.e. the generation of possible spelling error variants (deletes only) and storing them at index time is just the first precondition.
  • A fast index access at search time by using a hash table with an average search time complexity of O(1) is the second precondition.
  • But only our Symmetric Delete Spelling Correction on top of this allows to bring this O(1) speed to spell checking, because it allows a tremendous reduction of the number of spelling error candidates to be pre-calculated (generated and indexed).
  • Applying pre-calculation to Norvig’s approach would not be feasible because pre-calculating all possible delete + transpose + replace + insert candidates of all terms would result in a huge time and space consumption.

Correction vs. Completion
How can I add auto completion similar to Google’s Autocompletion?
There is a difference between correction and suggestion/completion!

Correction: Find the correct word for a word which contains errors. Missing letters/errors can be on start/middle/end of the word. We can find only words equal/below the maximum edit distance, as the computational complexity is dependent from the edit distance.

Suggestion/completion: Find the complete word for an already typed substring (prefix!). Missing letters can be only at the end of the word. We can find words/word combinations of any length, as the computational complexity is independent from edit distance and word length.

The code above implements only correction, but not suggestion/completion!
It still finds suggestions/completions equal/below the maximum edit distance, i.e. it starts to show words only if there are <= 2 letters missing (for maximum edit distance=2). Nevertheless the code can be extended to handle both correction and suggestion/completion. During the process of dictionary creation you have to add also all substrings (prefixes only!) of a word to the dictionary, when you are adding a new word to the dictionary. All substring entries of a specific term then have to contain a link to the complete term. Alternatively, for suggestion/completion you could use a completely different algorithm/structure like a Trie, which inherently lists all complete words for a given prefix.

Spelling correction, Query completion and Instant search

In the previous posts we described our new spelling correction algorithm, announced the release of the c# code as Open Source and presented some pretty compelling benchmark results.

FAROO: Spelling Correction and Query completion

Today we are introducing spelling correction, query completion and an improved instant search as integral part of our FAROO search service:

Spelling correction
For a misspelled term the suggested corrections are displayed in a dropdown list.

Query completion (aka query suggestions, autocomplete)
As you type a dropdown list of popular terms and combinations is displayed, which start with the letters you typed so far.

Improved instant search
Results are automatically displayed for the best suggestion/correction, “Enter” searches always for originally entered term.

 

Opposite to traditional implementations we are not using a predefined dictionary:

  • The whole web serves as a corpus, from which we automatically derive the spelling and completion dictionary.
  • The dictionary is automatically updated as part of the indexing process and learns new terms as they appear on the web.
  • The whole process is fully automated, no manual auditing steps are involved.

The algorithm is completely language independent (pure statistics, no linguistic knowledge).
Of course corrections and suggestions are given only within the scope of the selected search language.

 

Try it out at faroo.com

1000x Faster Spelling Correction: Source Code released

In a followup to our recent post 1000x Faster Spelling Correction algorithm we are releasing today a C# implementation of our Symmetric Delete Spelling Correction algorithm as Open Source:

Update1: The source code is now also on GitHub.
Update2: Improved implementation now 1,000,000 times faster for edit distance=3.

// SymSpell: 1000x faster through Symmetric Delete spelling correction algorithm
//
// The Symmetric Delete spelling correction algorithm reduces the complexity of edit candidate generation and dictionary lookup 
// for a given Damerau-Levenshtein distance. It is three orders of magnitude faster and language independent.
// Opposite to other algorithms only deletes are required, no transposes + replaces + inserts.
// Transposes + replaces + inserts of the input term are transformed into deletes of the dictionary term.
// Replaces and inserts are expensive and language dependent: e.g. Chinese has 70,000 Unicode Han characters!
//
// Copyright (C) 2012 Wolf Garbe, FAROO Limited
// Version: 1.6
// Author: Wolf Garbe <wolf.garbe@faroo.com>
// Maintainer: Wolf Garbe <wolf.garbe@faroo.com>
// URL: http://blog.faroo.com/2012/06/07/improved-edit-distance-based-spelling-correction/
// Description: http://blog.faroo.com/2012/06/07/improved-edit-distance-based-spelling-correction/
//
// License:
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License, 
// version 3.0 (LGPL-3.0) as published by the Free Software Foundation.
// http://www.opensource.org/licenses/LGPL-3.0
//
// Usage: single word + Enter:  Display spelling suggestions
//        Enter without input:  Terminate the program

using System;
using System.Linq;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.IO;
using System.Diagnostics;

static class SymSpell
{
    private static int editDistanceMax=2;
    private static int verbose = 0;
    //0: top suggestion
    //1: all suggestions of smallest edit distance 
    //2: all suggestions <= editDistanceMax (slower, no early termination)

    private class dictionaryItem
    {
        public string term = "";
        public List<editItem> suggestions = new List<editItem>();
        public int count = 0;

        public override bool Equals(object obj)
        {
            return Equals(term, ((dictionaryItem)obj).term);
        }
     
        public override int GetHashCode()
        {
            return term.GetHashCode(); 
        }       
    }

    private class editItem
    {
        public string term = "";
        public int distance = 0;

        public override bool Equals(object obj)
        {
            return Equals(term, ((editItem)obj).term);
        }
     
        public override int GetHashCode()
        {
            return term.GetHashCode();
        }       
    }

    private class suggestItem
    {
        public string term = "";
        public int distance = 0;
        public int count = 0;

        public override bool Equals(object obj)
        {
            return Equals(term, ((suggestItem)obj).term);
        }
     
        public override int GetHashCode()
        {
            return term.GetHashCode();
        }       
    }

    private static Dictionary<string, dictionaryItem> dictionary = new Dictionary<string, dictionaryItem>();

    //create a non-unique wordlist from sample text
    //language independent (e.g. works with Chinese characters)
    private static IEnumerable<string> parseWords(string text)
    {
        return Regex.Matches(text.ToLower(), @"[\w-[\d_]]+")
                    .Cast<Match>()
                    .Select(m => m.Value);
    }

    //for every word there all deletes with an edit distance of 1..editDistanceMax created and added to the dictionary
    //every delete entry has a suggestions list, which points to the original term(s) it was created from
    //The dictionary may be dynamically updated (word frequency and new words) at any time by calling createDictionaryEntry
    private static bool CreateDictionaryEntry(string key, string language)
    {
        bool result = false;
        dictionaryItem value;
        if (dictionary.TryGetValue(language+key, out value))
        {
            //already exists:
            //1. word appears several times
            //2. word1==deletes(word2) 
            value.count++;
        }
        else
        {
            value = new dictionaryItem();
            value.count++;
            dictionary.Add(language+key, value);
        }

        //edits/suggestions are created only once, no matter how often word occurs
        //edits/suggestions are created only as soon as the word occurs in the corpus, 
        //even if the same term existed before in the dictionary as an edit from another word
        if (string.IsNullOrEmpty(value.term))
        {
            result = true;
            value.term = key;

            //create deletes
            foreach (editItem delete in Edits(key, 0, true))
            {
                editItem suggestion = new editItem();
                suggestion.term = key;
                suggestion.distance = delete.distance;

                dictionaryItem value2;
                if (dictionary.TryGetValue(language+delete.term, out value2))
                {
                    //already exists:
                    //1. word1==deletes(word2) 
                    //2. deletes(word1)==deletes(word2) 
                    if (!value2.suggestions.Contains(suggestion)) AddLowestDistance(value2.suggestions, suggestion);
                }
                else
                {
                    value2 = new dictionaryItem();
                    value2.suggestions.Add(suggestion);
                    dictionary.Add(language+delete.term, value2);
                }
            }
        }
        return result;
    }

    //create a frequency disctionary from a corpus
    private static void CreateDictionary(string corpus, string language)
    {
        if (!File.Exists(corpus))
        {
            Console.Error.WriteLine("File not found: " + corpus);
            return;
        }

        Console.Write("Creating dictionary ...");
        long wordCount = 0;
        foreach (string key in parseWords(File.ReadAllText(corpus)))
        {
            if (CreateDictionaryEntry(key, language)) wordCount++;
        }
        Console.WriteLine("\rDictionary created: " + wordCount.ToString("N0") + " words, " + dictionary.Count.ToString("N0") + " entries, for edit distance=" + editDistanceMax.ToString());
    }

    //save some time and space
    private static void AddLowestDistance(List<editItem> suggestions, editItem suggestion)
    {
        //remove all existing suggestions of higher distance, if verbose<2
        if ((verbose < 2) && (suggestions.Count > 0) && (suggestions[0].distance > suggestion.distance)) suggestions.Clear();
        //do not add suggestion of higher distance than existing, if verbose<2
        if ((verbose == 2) || (suggestions.Count == 0) || (suggestions[0].distance >= suggestion.distance)) suggestions.Add(suggestion);
    }

    //inexpensive and language independent: only deletes, no transposes + replaces + inserts
    //replaces and inserts are expensive and language dependent (Chinese has 70,000 Unicode Han characters)
    private static List<editItem> Edits(string word, int editDistance, bool recursion)
    {
        editDistance++;
        List<editItem> deletes = new List<editItem>();
        if (word.Length > 1)
        {
            for (int i = 0; i < word.Length; i++)
            {
                editItem delete = new editItem();
                delete.term=word.Remove(i, 1);
                delete.distance=editDistance;
                if (!deletes.Contains(delete))
                {
                    deletes.Add(delete);
                    //recursion, if maximum edit distance not yet reached
                    if (recursion && (editDistance < editDistanceMax)) 
                    {
                        foreach (editItem edit1 in Edits(delete.term, editDistance,recursion))
                        {
                            if (!deletes.Contains(edit1)) deletes.Add(edit1); 
                        }
                    }                   
                }
            }
        }

        return deletes;
    }

    private static int TrueDistance(editItem dictionaryOriginal, editItem inputDelete, string inputOriginal)
    {
        //We allow simultaneous edits (deletes) of editDistanceMax on on both the dictionary and the input term. 
        //For replaces and adjacent transposes the resulting edit distance stays <= editDistanceMax.
        //For inserts and deletes the resulting edit distance might exceed editDistanceMax.
        //To prevent suggestions of a higher edit distance, we need to calculate the resulting edit distance, if there are simultaneous edits on both sides.
        //Example: (bank==bnak and bank==bink, but bank!=kanb and bank!=xban and bank!=baxn for editDistanceMaxe=1)
        //Two deletes on each side of a pair makes them all equal, but the first two pairs have edit distance=1, the others edit distance=2.

        if (dictionaryOriginal.term == inputOriginal) return 0; else
        if (dictionaryOriginal.distance == 0) return inputDelete.distance;
        else if (inputDelete.distance == 0) return dictionaryOriginal.distance;
        else return DamerauLevenshteinDistance(dictionaryOriginal.term, inputOriginal);//adjust distance, if both distances>0
    }

    private static List<suggestItem> Lookup(string input, string language, int editDistanceMax)
    {
        List<editItem> candidates = new List<editItem>();

        //add original term
        editItem item = new editItem();
        item.term = input;
        item.distance = 0;
        candidates.Add(item);
 
        List<suggestItem> suggestions = new List<suggestItem>();
        dictionaryItem value;

        while (candidates.Count>0)
        {
            editItem candidate = candidates[0];
            candidates.RemoveAt(0);

            //save some time
            //early termination
            //suggestion distance=candidate.distance... candidate.distance+editDistanceMax                
            //if canddate distance is already higher than suggestion distance, than there are no better suggestions to be expected
            if ((verbose < 2)&&(suggestions.Count > 0)&&(candidate.distance > suggestions[0].distance)) goto sort;
            if (candidate.distance > editDistanceMax) goto sort;  

            if (dictionary.TryGetValue(language+candidate.term, out value))
            {
                if (!string.IsNullOrEmpty(value.term))
                {
                    //correct term
                    suggestItem si = new suggestItem();
                    si.term = value.term;
                    si.count = value.count;
                    si.distance = candidate.distance;

                    if (!suggestions.Contains(si))
                    {
                        suggestions.Add(si);
                        //early termination
                        if ((verbose < 2) && (candidate.distance == 0)) goto sort;     
                    }
                }

                //edit term (with suggestions to correct term)
                dictionaryItem value2;
                foreach (editItem suggestion in value.suggestions)
                {
                    //save some time 
                    //skipping double items early
                    if (suggestions.Find(x => x.term == suggestion.term) == null)
                    {
                        int distance = TrueDistance(suggestion, candidate, input);
                     
                        //save some time.
                        //remove all existing suggestions of higher distance, if verbose<2
                        if ((verbose < 2) && (suggestions.Count > 0) && (suggestions[0].distance > distance)) suggestions.Clear();
                        //do not process higher distances than those already found, if verbose<2
                        if ((verbose < 2) && (suggestions.Count > 0) && (distance > suggestions[0].distance)) continue;

                        if (distance <= editDistanceMax)
                        {
                            if (dictionary.TryGetValue(language+suggestion.term, out value2))
                            {
                                suggestItem si = new suggestItem();
                                si.term = value2.term;
                                si.count = value2.count;
                                si.distance = distance;

                                suggestions.Add(si);
                            }
                        }
                    }
                }
            }//end foreach

            //add edits 
            if (candidate.distance < editDistanceMax)
            {
                foreach (editItem delete in Edits(candidate.term, candidate.distance,false))
                {
                    if (!candidates.Contains(delete)) candidates.Add(delete);
                }
            }
        }//end while

        sort: suggestions = suggestions.OrderBy(c => c.distance).ThenByDescending(c => c.count).ToList();
        if ((verbose == 0)&&(suggestions.Count>1))  return suggestions.GetRange(0, 1); else return suggestions;
    }

    private static void Correct(string input, string language)
    {
        List<suggestItem> suggestions = null;
    
        /*
        //Benchmark: 1000 x Lookup
        Stopwatch stopWatch = new Stopwatch();
        stopWatch.Start();
        for (int i = 0; i < 1000; i++)
        {
            suggestions = Lookup(input,language,editDistanceMax);
        }
        stopWatch.Stop();
        Console.WriteLine(stopWatch.ElapsedMilliseconds.ToString());
        */
        
        //check in dictionary for existence and frequency; sort by edit distance, then by word frequency
        suggestions = Lookup(input, language, editDistanceMax);

        //display term and frequency
        foreach (var suggestion in suggestions)
        {
            Console.WriteLine( suggestion.term + " " + suggestion.distance.ToString() + " " + suggestion.count.ToString());
        }
        if (verbose == 2) Console.WriteLine(suggestions.Count.ToString() + " suggestions");
    }

    private static void ReadFromStdIn()
    {
        string word;
        while (!string.IsNullOrEmpty(word = (Console.ReadLine() ?? "").Trim()))
        {
            Correct(word,"en");
        }
    }

    public static void Main(string[] args)
    {
        //e.g. http://norvig.com/big.txt , or any other large text corpus
        CreateDictionary("big.txt","en");
        ReadFromStdIn();
    }

    // Damerau–Levenshtein distance algorithm and code 
    // from http://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance
    public static Int32 DamerauLevenshteinDistance(String source, String target)
    {
        Int32 m = source.Length;
        Int32 n = target.Length;
        Int32[,] H = new Int32[m + 2, n + 2];

        Int32 INF = m + n;
        H[0, 0] = INF;
        for (Int32 i = 0; i <= m; i++) { H[i + 1, 1] = i; H[i + 1, 0] = INF; }
        for (Int32 j = 0; j <= n; j++) { H[1, j + 1] = j; H[0, j + 1] = INF; }

        SortedDictionary<Char, Int32> sd = new SortedDictionary<Char, Int32>();
        foreach (Char Letter in (source + target))
        {
            if (!sd.ContainsKey(Letter))
                sd.Add(Letter, 0);
        }

        for (Int32 i = 1; i <= m; i++)
        {
            Int32 DB = 0;
            for (Int32 j = 1; j <= n; j++)
            {
                Int32 i1 = sd[target[j - 1]];
                Int32 j1 = DB;

                if (source[i - 1] == target[j - 1])
                {
                    H[i + 1, j + 1] = H[i, j];
                    DB = j;
                }
                else
                {
                    H[i + 1, j + 1] = Math.Min(H[i, j], Math.Min(H[i + 1, j], H[i, j + 1])) + 1;
                }

                H[i + 1, j + 1] = Math.Min(H[i + 1, j + 1], H[i1, j1] + (i - i1 - 1) + 1 + (j - j1 - 1));
            }

            sd[ source[ i - 1 ]] = i;
        }
        return H[m + 1, n + 1];
    }
}

Updated:
The implementation supports now edit distances of any size (default=2).

Benchmark:
With previous spell checking algorithms the required time explodes with larger edit distances. They try to omit this with early termination when suggestions of smaller edit distances are found.

We did a quick benchmark with 1000 lookups:

Term Best correction Edit distance Faroo
ms/1000
Peter Norvig
ms/1000
Factor
marsupilami no correction* >3 1,772 165,025,000 93,129
acamodation accommodation 3 1,874 175,622,000 93,715
acomodation accommodation 2 162 348,191 2,149
hous house 1 71 179 2
house house 0 0 17 n/a

*Correct word, but not in dictionary and there are also no corrections within an edit distance of <=3. This is a quite common case (e.g. rare words, new words, domain specific words, foreign words, names).

The speed advantage grows exponentially with the edit distance:
For an edit distance=1 it’s the same order of magnitude,
for an edit distance=2 it’s 3 orders of magnitude faster,
for an edit distance=3 it’s 5 orders of magnitude faster.

Source code
The C# implementation of our Symmetric Delete Spelling Correction algorithm is released on GitHub as Open Source under the GNU Lesser General Public License (LGPL).

C# (original)
https://github.com/wolfgarbe/symspell

Ports
The following third party ports to other programming languages have not been tested by myself whether they are an exact port, error free, provide identical results or are as fast as the original algorithm:

C++ (third party port)
https://github.com/erhanbaris/SymSpellPlusPlus

Go (third party port)
https://github.com/heartszhang/symspell
https://github.com/sajari/fuzzy

Java (third party port)
https://github.com/gpranav88/symspell

Javascript (third party port)
https://github.com/itslenny/SymSpell.js
https://github.com/dongyuwei/SymSpell
https://github.com/IceCreamYou/SymSpell
https://github.com/Yomguithereal/mnemonist/blob/master/symspell.js

Python (third party port)
https://github.com/ppgmg/spark-n-spell-1/blob/master/symspell_python.py

Ruby (third party port)
https://github.com/PhilT/symspell

Swift (third party port)
https://github.com/Archivus/SymSpell

1000x Faster Spelling Correction algorithm

1000x faster

Update: We released a C# implementation as Open Source.
Update2: We are 100,000 times faster for edit distance=3.
Update3: Spelling correction is now also part of FAROO search.
Update4: The source code is now also on GitHub.
Update5: Improved implementation now 1,000,000 times faster for edit distance=3.

Recently I answered a question on Quora about spelling correction for search engines. When I described our algorithm I was pointed to Peter Norvig’s page where he outlined his approach.

Both algorithms are based on Edit distance (Damerau-Levenshtein distance).
Both try to find the dictionary entries with smallest edit distance from the query term.
If the edit distance is 0 the term is spelled correctly, if the edit distance is <=2 the dictionary term is used as spelling suggestion. But our way to search the dictionary is different, resulting in a significant performance gain and language independence. Three ways to search for minimum edit distance in a dictionary: 1. Naive approach
The obvious way of doing this is to compute the edit distance from the query term to each dictionary term, before selecting the string(s) of minimum edit distance as spelling suggestion. This exhaustive search is inordinately expensive.
Source: Christopher D. Manning, Prabhakar Raghavan & Hinrich Schütze: Introduction to Information Retrieval.

The performance can be significantly improved by terminating the edit distance calculation as soon as a treshold of 2 or 3 has been reached.

2. Peter Norvig
Generate all possible terms with an edit distance <=2 (deletes + transposes + replaces + inserts) from the query term and search them in the dictionary.
For a word of length n, an alphabet size a, an edit distance d=1, there will be n deletions, n-1 transpositions, a*n alterations, and a*(n+1) insertions, for a total of 2n+2an+a-1 terms at search time.
Source: Peter Norvig: How to Write a Spelling Corrector.

This is much better than the naive approach, but still expensive at search time (114,324 terms for n=9, a=36, d=2) and language dependent (because the alphabet is used to generate the terms, which is different in many languages and huge in Chinese: a=70,000 Unicode Han characters)

3. Symmetric Delete Spelling Correction (FAROO)
Generate terms with an edit distance <=2 (deletes only) from each dictionary term and add them together with the original term to the dictionary. This has to be done only once during a pre-calculation step.
Generate terms with an edit distance <=2 (deletes only) from the input term and search them in the dictionary.
For a word of length n, an alphabet size of a, an edit distance of 1, there will be just n deletions, for a total of n terms at search time.

This is three orders of magnitude less expensive (36 terms for n=9 and d=2) and language independent (the alphabet is not required to generate deletes).
The cost of this approach is the pre-calculation time and storage space of x deletes for every original dictionary entry, which is acceptable in most cases.

The number x of deletes for a single dictionary entry depends on the maximum edit distance: x=n for edit distance=1, x=n*(n-1)/2 for edit distance=2, x=n!/d!/(n-d)! for edit distance=d (combinatorics: k out of n combinations without repetitions, and k=n-d),
E.g. for a maximum edit distance of 2 and an average word length of 5 and 100,000 dictionary entries we need to additionally store 1,500,000 deletes.

Remark 1: During the precalculation, different words in the dictionary might lead to same delete term: delete(sun,1)==delete(sin,1)==sn.
While we generate only one new dictionary entry (sn), inside we need to store both original terms as spelling correction suggestion (sun,sin)

Remark 2: There are four different comparison pair types:

  1. dictionary entry==input entry,
  2. delete(dictionary entry,p1)==input entry
  3. dictionary entry==delete(input entry,p2)
  4. delete(dictionary entry,p1)==delete(input entry,p2)

The last comparison type is required for replaces and transposes only. But we need to check whether the suggested dictionary term is really a replace or an adjacent transpose of the input term to prevent false positives of higher edit distance (bank==bnak and bank==bink, but bank!=kanb and bank!=xban and bank!=baxn).

Remark 3: Instead of a dedicated spelling dictionary we are using the search engine index itself. This has several benefits:

  1. It is dynamically updated. Every newly indexed word, whose frequency is over a certain threshold, is automatically used for spelling correction as well.
  2. As we need to search the index anyway the spelling correction comes at almost no extra cost.
  3. When indexing misspelled terms (i.e. not marked as a correct in the index) we do a spelling correction on the fly and index the page for the correct term as well.

Remark 4: We have implemented query suggestions/completion in a similar fashion. This is a good way to prevent spelling errors in the first place. Every newly indexed word, whose frequency is over a certain threshold, is stored as a suggestion to all of its prefixes (they are created in the index if they do not yet exist). As we anyway provide an instant search feature the lookup for suggestions comes also at almost no extra cost. Multiple terms are sorted by the number of results stored in the index.

Reasoning
In our algorithm we are exploiting the fact that the edit distance between two terms is symmetrical:

  1. We can generate all terms with an edit distance <2 from the query term (trying to reverse the query term error) and checking them against all dictionary terms,
  2. We can generate all terms with an edit distance <2 from each dictionary term (trying to create the query term error) and check the query term against them.
  3. We can combine both and meet in the middle, by transforming the correct dictionary terms to erroneous strings, and transforming the erroneous input term to the correct strings.
    Because adding a char on the dictionary is equivalent to removing a char from the input string and vice versa, we can on both sides restrict our transformation to deletes only.

We are using variant 3, because the delete-only-transformation is language independent and three orders of magnitude less expensive.

Where does the speed come from?

  • Pre-calculation, i.e. the generation of possible spelling error variants (deletes only) and storing them at index time is the first precondition.
  • A fast index access at search time by using a hash table with an average search time complexity of O(1) is the second precondition.
  • But only our Symmetric Delete Spelling Correction on top of this allows to bring this O(1) speed to spell checking, because it allows a tremendous reduction of the number of spelling error candidates to be pre-calculated (generated and indexed).
  • Applying pre-calculation to Norvig’s approach would not be feasible because pre-calculating all possible delete + transpose + replace + insert candidates of all terms would result in a huge time and space consumption.

Computational Complexity
Our algorithm is constant time ( O(1) time ), i.e. independent of the dictionary size (but depending on the average term length and maximum edit distance), because our index is based on a Hash Table which has an average search time complexity of O(1).

Comparison to other approaches
BK-Trees have a search time of O(log dictionary_size), whereas our algorithm is constant time ( O(1) time ), i.e. independent of the dictionary size.
Tries have a comparable search performance to our approach. But a Trie is a prefix tree, which requires a common prefix. This makes it suitable for autocomplete or search suggestions, but not applicable for spell checking. If your typing error is e.g. in the first letter, than you have no common prefix, hence the Trie will not work for spelling correction.

Application
Possible application fields of our algorithm are those of fast approximate dictionary string matching: spell checkers for word processors and search engines, correction systems for optical character recognition, natural language translation based on translation memory, record linkage, de-duplication, matching DNA sequences, fuzzy string searching and fraud detection.

———

BTW, by using a similar principle our web search is three orders of magnitude more efficient as well. While Google touches 1000 servers for every query, we need to query just one (server/peer).
That’s not because of DHT! Vice versa, because even for a complex query in a web scale index only one of the servers needs to be queried, it enables the use of DHT for web search.
Our algorithm improves the efficiency of central servers in a data center to the same extent.