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Posted 10 Sep 2007


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N-gram and Fast Pattern Extraction Algorithm

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31 Oct 2007GPL38 min read
This article demonstrates N-gram construction and Fast Text Pattern Extraction using a modified LZW algorithm.
Sample Image - Patterns.jpg



In this article, I introduce a very fast algorithm to extract text patterns from large size text and give statistical information about patterns' frequency and length. Actually, the idea of this algorithm came to me when one of my friends asked me to give him an idea for extracting patterns from text. I told him immediately that he could use the LZW compression algorithm, take the final dictionary and drop the compressed buffer, and then he could have a dictionary containing all text patterns with each pattern frequency. I don't know if he understood me or not, but I decided to do it later. If pattern word count is fixed (N), then it is a generation for N-gram of the input sequence.



An n-gram is a sub-sequence of n items from a given sequence. n-grams are used in various areas of statistical natural language processing and genetic sequence analysis. The items in question can be characters, words or base pairs according to the application. For example, the sequence of characters "Hatem mostafa helmy" has a 3-gram of ("Hat", "ate", "tem", "em ", "m m", ...), and has a 2-gram of ("Ha", "at", "te", "em", "m ", " m", ...). This n-gram output can be used for a variety of R&D subjects, such as Statistical machine translation and Spell checking.

Pattern Extraction

Pattern extraction is the process of parsing a sequence of items to find or extract a certain pattern of items. Pattern length can be fixed, as in the n-gram model, or it can be variable. Variable length patterns can be directives to certain rules, like regular expressions. They can also be random and depend on the context and pattern repetition in the patterns dictionary.

Algorithm Idea for Variable Length Pattern Extraction

The algorithm introduced here is derived from the LZW compression algorithm, which includes a magic idea about generating dictionary items at compression time while parsing the input sequence. If you have no idea about LZW, you can check it out at my article, Fast LZW compression. And of course, the algorithm inherits the speed of my implementation to LZW, plus extra speed for two reasons:

  1. The parsing item is a word, not a letter
  2. There's no destination buffer, as there is no need for a compressed buffer

The algorithm uses a binary tree to keep extracted patterns that give the algorithm excellent speed at run-time to find and fetch new items to the dictionary. Let us discuss the algorithm pseudo code. We have some figures to clarify the idea with an algorithm flow chart and a simple example.

Image 2

Example: the input words sequence w0w1w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6

Assume n equals 2; then the initial pattern will be w0w1. After applying the algorithm steps, the resultant dictionary would be as in the fourth column:

Image 3

Input SequencePatternStepDictionaryFrequency
w0w1w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w0w1Words available?
w0w1w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w0w1Add to dictionaryw0w13
w0w1w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w0w1Pattern exists?
w1w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w1w2Take new pattern
w1w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w1w2Words available?
w1w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w1w2Add to dictionaryw1w21
w1w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w1w2Pattern exists?
w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w2w3Take new pattern
w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w2w3Words available?
w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w2w3Add to dictionaryw2w32
w2w3w4w0w1w5w6w7w2w3w4w0w1w5w6w2w3Pattern exists?
w3w4w0w1w5w6w7w2w3w4w0w1w5w6w3w4Take new pattern
w3w4w0w1w5w6w7w2w3w4w0w1w5w6w3w4Words available?
w3w4w0w1w5w6w7w2w3w4w0w1w5w6w3w4Add to dictionaryw3w42
w3w4w0w1w5w6w7w2w3w4w0w1w5w6w3w4Pattern exists?
w4w0w1w5w6w7w2w3w4w0w1w5w6w4w0Take new pattern
w4w0w1w5w6w7w2w3w4w0w1w5w6w4w0Words available?
w4w0w1w5w6w7w2w3w4w0w1w5w6w4w0Add to dictionaryw4w02
w4w0w1w5w6w7w2w3w4w0w1w5w6w4w0Pattern exists?
w0w1w5w6w7w2w3w4w0w1w5w6w0w1Take new pattern
w0w1w5w6w7w2w3w4w0w1w5w6w0w1Words available?
w0w1w5w6w7w2w3w4w0w1w5w6w0w1Add to dictionary
w0w1w5w6w7w2w3w4w0w1w5w6w0w1Pattern exists?
w0w1w5w6w7w2w3w4w0w1w5w6w0w1w5Add word to pattern
w0w1w5w6w7w2w3w4w0w1w5w6w0w1w5Words available?
w0w1w5w6w7w2w3w4w0w1w5w6w0w1w5Add to dictionaryw0w1w52
w0w1w5w6w7w2w3w4w0w1w5w6w0w1w5Pattern exists?
w1w5w6w7w2w3w4w0w1w5w6w1w5Take new pattern
w1w5w6w7w2w3w4w0w1w5w6w1w5Words available?
w1w5w6w7w2w3w4w0w1w5w6w1w5Add to dictionaryw1w52
w1w5w6w7w2w3w4w0w1w5w6w1w5Pattern exists?
w5w6w7w2w3w4w0w1w5w6w5w6Take new pattern
w5w6w7w2w3w4w0w1w5w6w5w6Words available?
w5w6w7w2w3w4w0w1w5w6w5w6Add to dictionaryw5w61
w5w6w7w2w3w4w0w1w5w6w5w6Pattern exists?
w6w7w2w3w4w0w1w5w6w6w7Take new pattern
w6w7w2w3w4w0w1w5w6w6w7Words available?
w6w7w2w3w4w0w1w5w6w6w7Add to dictionaryw6w71
w6w7w2w3w4w0w1w5w6w6w7Pattern exists?
w7w2w3w4w0w1w5w6w7w2Take new pattern
w7w2w3w4w0w1w5w6w7w2Words available?
w7w2w3w4w0w1w5w6w7w2Add to dictionaryw7w21
w7w2w3w4w0w1w5w6w7w2Pattern exists?
w2w3w4w0w1w5w6w2w3Take new pattern
w2w3w4w0w1w5w6w2w3Words available?
w2w3w4w0w1w5w6w2w3Add to dictionary
w2w3w4w0w1w5w6w2w3Pattern exists?
w2w3w4w0w1w5w6w2w3w4Add word to pattern
w2w3w4w0w1w5w6w2w3w4Words available?
w2w3w4w0w1w5w6w2w3w4Add to dictionaryw2w3w41
w2w3w4w0w1w5w6w2w3w4Pattern exists?
w3w4w0w1w5w6w3w4Take new pattern
w3w4w0w1w5w6w3w4Words available?
w3w4w0w1w5w6w3w4Add to dictionary
w3w4w0w1w5w6w3w4Pattern exists?
w3w4w0w1w5w6w3w4w0Add word to pattern
w3w4w0w1w5w6w3w4w0Words available?
w3w4w0w1w5w6w3w4w0Add to dictionaryw3w4w01
w3w4w0w1w5w6w3w4w0Pattern exists?
w4w0w1w5w6w4w0Take new pattern
w4w0w1w5w6w4w0Words available?
w4w0w1w5w6w4w0Add to dictionary
w4w0w1w5w6w4w0Pattern exists?
w4w0w1w5w6w4w0w1Add word to pattern
w4w0w1w5w6w4w0w1Words available?
w4w0w1w5w6w4w0w1Add to dictionaryw4w0w11
w4w0w1w5w6w4w0w1Pattern exists?
w0w1w5w6w0w1Take new pattern
w0w1w5w6w0w1Words available?
w0w1w5w6w0w1Add to dictionary
w0w1w5w6w0w1Pattern exists?
w0w1w5w6w0w1w5Add word to pattern
w0w1w5w6w0w1w5Words available?
w0w1w5w6w0w1w5Add to dictionary
w0w1w5w6w0w1w5Pattern exists?
w0w1w5w6w0w1w5w6Add word to pattern
w0w1w5w6w0w1w5w6Words available?
w0w1w5w6w0w1w5w6Add to dictionaryw0w1w5w61
w0w1w5w6w0w1w5w6Pattern exists?
w1w5w6w1w5Take new pattern
w1w5w6w1w5Add to dictionary
w1w5w6w1w5Pattern exists?
w1w5w6w1w5w6Add word to pattern
w1w5w6w1w5w6Words available?
w1w5w6w1w5w6Add to dictionaryw1w5w61
w1w5w6w1w5w6Pattern exists?
w5w6w5w6Take new pattern
w5w6w5w6Words available?
w5w6w5w6Add to dictionary
w5w6w5w6Pattern exists?
Take new pattern
Words available?

Algorithm Pseudo Code

ConstructPatterns(src, delimiters, n, fixed)
    des = AllocateBuffer()
    Copy(des, src)
    DiscardDelimiters(des, delimiters)
    dic = InitializePatternsDictionary()

    pattern = InitializeNewPattern(des)
        node = dic.Insert(pattern)
        if(!fixed AND node.IsRepeated)
            AddWordToPattern(des, pattern)
            pattern = InitializeNewPattern(des)

Code Description


This function receives the input buffer, copies it to a destination buffer, and parses it to add found patterns to the dictionary. The constructed dictionary is a binary tree template CBinaryTree<CPattern, CPattern*, int, int> m_alpDic with a key of type CPattern.

void CPatternAlaysis::ConstructPatterns(BYTE *pSrc, int nSrcLen,
    LPCSTR lpcsDelimiters /*= NULL*/,
    int nMinPatternWords /*= 2*/,
    bool bFixedNGram /*= false*/)
    // discard initial spaces
    // allocate destination buffer
    // discard delimiters
    // discard repeated spaces
    // initialize dictionary
    // tree node to keep last success search to start with
    CBinaryTreeNode<CPattern, int>* pNode = m_alpDic.Root;
    // left m_alpDic Samples points to the source buffer
    int nPrevLength;
    CPattern node(m_pDes, GetPatternLength(
        m_pDes, nPrevLength, nMinPatternWords));
    // scan the input buffer
    while(node.m_pBuffer < m_pDes+nDesLen)
        pNode = m_alpDic.Insert(&node, -1, pNode);
        pNode->Key.m_nFrequency = pNode->Count;
        if(bFixedNGram == false && pNode->Count > 1)
        // (repeated pattern), increment node length
        // by a new word length
        node.m_nLength += AddWordToPattern(node.m_pBuffer+node.m_nLength);
        {   // initialize node to next entity
            node.m_pBuffer += nPrevLength;
            node.m_nLength = GetPatternLength(node.m_pBuffer,
                nPrevLength, nMinPatternWords);
            // initialize binary tree search root
            pNode = m_alpDic.Root;

Note: The first good point in this function is that it allocates one buffer for the dictionary and all dictionary nodes point to their start buffer, keeping their buffer length in the class CPattern. So, no allocation or reallocation is done during the algorithm.

class CPattern
    CPattern()    {}
    CPattern(BYTE* pBuffer, int nLength)
    m_pBuffer = pBuffer, m_nLength = nLength;
    CPattern(const CPattern& buffer)
    *this = buffer;

    BYTE* m_pBuffer;
    int m_nLength;
    int m_nFrequency;
    inline int compare(const CPattern* buffer);
    {    ...  }
    inline void operator=(const CPattern* buffer)
    m_pBuffer = buffer->m_pBuffer;
    m_nLength = buffer->m_nLength;

The function does the steps of the pseudo code. The second good point is the usage of a binary tree CBinaryTree to keep the dictionary, with a very good trick here:

The function Insert() of the tree takes a third parameter to start the search from. In normal cases, this parameter should be the tree Root. However, if a pattern is found and a new word is added to it, then we can start the search for the pattern from the current node, as it must be under current node. This is because it is only the previous pattern plus a new word.

In the case of a new pattern, we should start the search from the tree root, so we have this line at the bottom of the function:

// initialize binary tree search root
pNode = m_alpDic.Root;


This function doesn't construct patterns. It just retrieves the constructed patterns with three types of sort: Alphabetical, Frequency and Pattern length. The returned patterns are stored in a vector of patterns (OUT vector<CPattern*>& vPatterns).

  1. Alphabetical

    CBinaryTreeNode<CPattern, int>* pAlpNode = m_alpDic.Min(m_alpDic.Root);
        if(pAlpNode->Count > 1 || !bIgnoreUniquePatterns)
            // ignore unique pattern
        pAlpNode = m_alpDic.Successor(pAlpNode);
  2. Frequency

    // construct a new dictionary to sort stored patterns
    // depending on frequency
    CBinaryTree<CValue<int>, int, vector<CPattern*>,
        vector<CPattern*>* >  displayDic;
    CBinaryTreeNode<CPattern, int>* pAlpNode = m_alpDic.Min(m_alpDic.Root);
    while(pAlpNode != NULL)
        if(pAlpNode->Count >    1 || !bIgnoreUniquePatterns)
            // ignore unique pattern
        pAlpNode = m_alpDic.Successor(pAlpNode);
    // iterate through the binary tree to get sorted pattern
    // (depend on frequency)
    CBinaryTreeNode<CValue<int>, vector<CPattern*>* pNode =
        for(vector<CPattern*>::iterator i = pNode->Data.begin(),
            end = pNode->Data.end(); i != end; i++)
        pNode = displayDic.Predecessor(pNode);
  3. Pattern length

    // construct a new dictionary to sort stored patterns
    // depending on Pattern length
    CBinaryTree<CValue<int>, int, vector<CPattern*>,
        vector<CPattern*>* >  displayDic;
    CBinaryTreeNode<CPattern, int>* pAlpNode = m_alpDic.Min(m_alpDic.Root);
    while(pAlpNode != NULL)
        if(pAlpNode->Count >    1 || !bIgnoreUniquePatterns)
           // ignore unique pattern
        pAlpNode = m_alpDic.Successor(pAlpNode);
    // iterate through the binary tree to get sorted pattern
    // (depend on Pattern length)
    CBinaryTreeNode<CValue<int>, vector<CPattern*>* pNode =
        for(vector<CPattern*>::iterator i = pNode->Data.begin(),
            end = pNode->Data.end(); i != end; i++)
        pNode = displayDic.Predecessor(pNode);


This function retrieves the stored patterns count.

int CPatternAlaysis::GetPatternCount()
    return m_alpDic.Count;

Points of Interest

  1. Algorithm Accuracy

    The algorithm doesn't give accuracy about pattern frequency in the case of variable length patterns (not n-gram with fixed n). That is because the algorithm constructs patterns while parsing the sequence and checks each constructed pattern with the dynamic dictionary. So, if any pattern is first added to the dictionary, a new pattern is constructed starting from the second word of the previous pattern with length n (min pattern length).

  2. Cross-Document Co-reference

    Cross-Document Co-reference is the process of finding a relation between documents. In other words, we can say that two documents are related if the two documents contain similar patterns. This subject is studied in many articles, but I found that the best one is "A Methodology for Cross-Document Coreference" by Amit Bagga and Alan W.Biermann. My algorithm may be helpful to generate patterns that can be taken to find a relation between patterns. The good point here is the very good speed of the algorithm, so it can be used for large numbers of documents like the web. However, directed patterns are better than random patterns to find documents' co-reference.

  3. DIPRE: Dual Iterative Pattern Relation Expansion

    This is an algorithm introduced by Sergey Brin to collect related information from scattered web sources. I like this idea very much and invite all of you to read his article and search the web for its implementation or even its flowchart. My algorithm can't be used here, as it collects patterns without any guided information about retrieved patterns. However, the FIPRE algorithm is a semi-directed algorithm, as it guides the initial pattern search with regular expressions to identify the required pattern, like "book title" and "author name." Alternatively, if the algorithm collects mails, it will include all regular expressions for mails like that:

    [^ \:\=@;,,$$**++\t\r\n""'<>/\\%??()&]+@[Hh]
    [^ \:\=@;,,$$**++\t\r\n""'<>/\\%??()&]+@[Yy]
    [^ \:\=@;,,$$**++\t\r\n""'<>/\\%??()&]+@(AOL|aol|Aol).com


  • 10/09/2007: Posted version v0.9000
  • 23/09/2007: Updated the source file vector.cpp to initialize the vector buffer with zeros
  • 31/10/2007: Updated the header file vector.h to solve "insert" function bug


Thanks to...



This article, along with any associated source code and files, is licensed under The GNU General Public License (GPLv3)


About the Author

Hatem Mostafa
Software Developer (Senior)
Egypt Egypt

Comments and Discussions

GeneralMy vote of 5 Pin
Manoj Kumar Choubey28-Mar-12 0:55
professionalManoj Kumar Choubey28-Mar-12 0:55 
QuestionHow fast is your fast? Pin
Sanmayce7-Jan-12 10:06
MemberSanmayce7-Jan-12 10:06 
QuestionArticle "Fast LZW compression" not found Pin
JohnPool23-Sep-11 4:58
MemberJohnPool23-Sep-11 4:58 
AnswerRe: Article "Fast LZW compression" not found Pin
Hatem Mostafa24-Sep-11 1:59
MemberHatem Mostafa24-Sep-11 1:59 
GeneralRe: Article "Fast LZW compression" not found Pin
Joao Araujo10-Jan-12 9:50
MemberJoao Araujo10-Jan-12 9:50 
GeneralRe: Article "Fast LZW compression" not found Pin
Hatem Mostafa11-Jan-12 21:37
MemberHatem Mostafa11-Jan-12 21:37 
GeneralMy vote of 5 Pin
RedDk1-Jun-11 10:51
MemberRedDk1-Jun-11 10:51 
General~CPatternAlaysis(); // had to add this desctructor declaration to PE.h to avoid VS2010 compile error C2600 Pin
wycoder7-Apr-11 2:25
Memberwycoder7-Apr-11 2:25 
GeneralC# implementation Pin
dde21-Jul-09 17:52
Memberdde21-Jul-09 17:52 
GeneralC# implementation Pin
navbas19-Sep-08 7:54
Membernavbas19-Sep-08 7:54 
GeneralRe: C# implementation Pin
dde21-Jul-09 17:44
Memberdde21-Jul-09 17:44 
GeneralBorn Analyst!! Pin
vamsidhar sunkari22-Feb-08 7:15
Membervamsidhar sunkari22-Feb-08 7:15 
GeneralRe: Born Analyst!! Pin
Hatem Mostafa7-Aug-11 12:59
MemberHatem Mostafa7-Aug-11 12:59 
GeneralGreat! Pin
Mohamed Y. Elamrani30-Dec-07 9:27
MemberMohamed Y. Elamrani30-Dec-07 9:27 
Questionmissing n+1 length patterns? Pin
b-yond18-Nov-07 7:58
Memberb-yond18-Nov-07 7:58 
AnswerRe: missing n+1 length patterns? Pin
Hatem Mostafa18-Nov-07 9:24
MemberHatem Mostafa18-Nov-07 9:24 
GeneralRe: missing n+1 length patterns? Pin
b-yond18-Nov-07 16:14
Memberb-yond18-Nov-07 16:14 
GeneralRe: missing n+1 length patterns? Pin
yulin113-Dec-07 18:42
Memberyulin113-Dec-07 18:42 
Generalplease help me!!!!!!!!!!!!11 Pin
allooba8-Nov-07 9:43
Memberallooba8-Nov-07 9:43 
GeneralNice Pin
Paul Conrad4-Nov-07 15:06
professionalPaul Conrad4-Nov-07 15:06 
QuestionDo you see a use for code breaking? Pin
Midnight4891-Oct-07 3:05
MemberMidnight4891-Oct-07 3:05 
AnswerRe: Do you see a use for code breaking? !!! Pin
Hatem Mostafa1-Oct-07 23:02
MemberHatem Mostafa1-Oct-07 23:02 
GeneralRe: Do you see a use for code breaking? Pin
Midnight4892-Oct-07 3:53
MemberMidnight4892-Oct-07 3:53 
Generalvery good ! Pin
gogac26-Sep-07 12:25
Membergogac26-Sep-07 12:25 
AnswerRe: very good ! Pin
Hatem Mostafa26-Sep-07 19:29
MemberHatem Mostafa26-Sep-07 19:29 

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