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.NET下文本相似度算法余弦定理和SimHash浅析及应用实例分析

时间:2015年01月05日 信息来源:本站原创 点击: 【】【 【字体: 】 】

这篇文章主要介绍了.NET下文本相似度算法余弦定理和SimHash浅析及应用,实例形式详细讲述了相似度算法余弦定理和SimHash的原理与用法,需要的朋友可以参考下

余弦相似性

原理:首先我们先把两段文本分词,列出来所有单词,其次我们计算每个词语的词频,最后把词语转换为向量,这样我们就只需要计算两个向量的相似程度.
 
我们简单表述如下
 
文本1:我/爱/北京/天安门/ 经过分词求词频得出向量(伪向量)  [1,1,1,1]
 
文本2:我们/都爱/北京/天安门/ 经过分词求词频得出向量(伪向量)  [1,0,1,2]
 
我们可以把它们想象成空间中的两条线段,都是从原点([0, 0, ...])出发,指向不同的方向。两条线段之间形成一个夹角,如果夹角为0度,意味着方向相同、线段重合;如果夹角为90度,意味着形成直角,方向完全不相似;如果夹角为180度,意味着方向正好相反。因此,我们可以通过夹角的大小,来判断向量的相似程度。夹角越小,就代表越相似。
 
C#核心算法:

复制代码 代码如下:

    public class TFIDFMeasure
    {
        private string[] _docs;
        private string[][] _ngramDoc;
        private int _numDocs=0;
        private int _numTerms=0;
        private ArrayList _terms;
        private int[][] _termFreq;
        private float[][] _termWeight;
        private int[] _maxTermFreq;
        private int[] _docFreq;
 
        public class TermVector
        {       
            public static float ComputeCosineSimilarity(float[] vector1, float[] vector2)
            {
                if (vector1.Length != vector2.Length)               
                    throw new Exception("DIFER LENGTH");
               
 
                float denom=(VectorLength(vector1) * VectorLength(vector2));
                if (denom == 0F)               
                    return 0F;               
                else               
                    return (InnerProduct(vector1, vector2) / denom);
               
            }
 
            public static float InnerProduct(float[] vector1, float[] vector2)
            {
           
                if (vector1.Length != vector2.Length)
                    throw new Exception("DIFFER LENGTH ARE NOT ALLOWED");
               
           
                float result=0F;
                for (int i=0; i < vector1.Length; i++)               
                    result += vector1[i] * vector2[i];
               
                return result;
            }
       
            public static float VectorLength(float[] vector)
            {           
                float sum=0.0F;
                for (int i=0; i < vector.Length; i++)               
                    sum=sum + (vector[i] * vector[i]);
                       
                return (float)Math.Sqrt(sum);
            }
        }
 
        private IDictionary _wordsIndex=new Hashtable() ;
 
        public TFIDFMeasure(string[] documents)
        {
            _docs=documents;
            _numDocs=documents.Length ;
            MyInit();
        }
 
        private void GeneratNgramText()
        {
           
        }
 
        private ArrayList GenerateTerms(string[] docs)
        {
            ArrayList uniques=new ArrayList() ;
            _ngramDoc=new string[_numDocs][] ;
            for (int i=0; i < docs.Length ; i++)
            {
                Tokeniser tokenizer=new Tokeniser() ;
                string[] words=tokenizer.Partition(docs[i]);           
 
                for (int j=0; j < words.Length ; j++)
                    if (!uniques.Contains(words[j]) )               
                        uniques.Add(words[j]) ;
            }
            return uniques;
        }


        private static object AddElement(IDictionary collection, object key, object newValue)
        {
            object element=collection[key];
            collection[key]=newValue;
            return element;
        }
 
        private int GetTermIndex(string term)
        {
            object index=_wordsIndex[term];
            if (index == null) return -1;
            return (int) index;
        }
 
        private void MyInit()
        {
            _terms=GenerateTerms (_docs );
            _numTerms=_terms.Count ;
 
            _maxTermFreq=new int[_numDocs] ;
            _docFreq=new int[_numTerms] ;
            _termFreq =new int[_numTerms][] ;
            _termWeight=new float[_numTerms][] ;
 
            for(int i=0; i < _terms.Count ; i++)           
            {
                _termWeight[i]=new float[_numDocs] ;
                _termFreq[i]=new int[_numDocs] ;
 
                AddElement(_wordsIndex, _terms[i], i);           
            }
           
            GenerateTermFrequency ();
            GenerateTermWeight();           
        }
       
        private float Log(float num)
        {
            return (float) Math.Log(num) ;//log2
        }
 
        private void GenerateTermFrequency()
        {
            for(int i=0; i < _numDocs  ; i++)
            {                               
                string curDoc=_docs[i];
                IDictionary freq=GetWordFrequency(curDoc);
                IDictionaryEnumerator enums=freq.GetEnumerator() ;
                _maxTermFreq[i]=int.MinValue ;
                while (enums.MoveNext())
                {
                    string word=(string)enums.Key;
                    int wordFreq=(int)enums.Value ;
                    int termIndex=GetTermIndex(word);
 
                    _termFreq [termIndex][i]=wordFreq;
                    _docFreq[termIndex] ++;
 
                    if (wordFreq > _maxTermFreq[i]) _maxTermFreq[i]=wordFreq;                   
                }
            }
        }

        private void GenerateTermWeight()
        {           
            for(int i=0; i < _numTerms   ; i++)
            {
                for(int j=0; j < _numDocs ; j++)               
                    _termWeight[i][j]=ComputeTermWeight (i, j);
            }
        }
 
        private float GetTermFrequency(int term, int doc)
        {           
            int freq=_termFreq [term][doc];
            int maxfreq=_maxTermFreq[doc];           
           
            return ( (float) freq/(float)maxfreq );
        }
 
        private float GetInverseDocumentFrequency(int term)
        {
            int df=_docFreq[term];
            return Log((float) (_numDocs) / (float) df );
        }
 
        private float ComputeTermWeight(int term, int doc)
        {
            float tf=GetTermFrequency (term, doc);
            float idf=GetInverseDocumentFrequency(term);
            return tf * idf;
        }
       
        private  float[] GetTermVector(int doc)
        {
            float[] w=new float[_numTerms] ;
            for (int i=0; i < _numTerms; i++)
                w[i]=_termWeight[i][doc];
            return w;
        }
 
        public float GetSimilarity(int doc_i, int doc_j)
        {
            float[] vector1=GetTermVector (doc_i);
            float[] vector2=GetTermVector (doc_j);
            return TermVector.ComputeCosineSimilarity(vector1, vector2);
        }
       
        private IDictionary GetWordFrequency(string input)
        {
            string convertedInput=input.ToLower() ;
            Tokeniser tokenizer=new Tokeniser() ;
            String[] words=tokenizer.Partition(convertedInput);
            Array.Sort(words);
           
            String[] distinctWords=GetDistinctWords(words);
                       
            IDictionary result=new Hashtable();
            for (int i=0; i < distinctWords.Length; i++)
            {
                object tmp;
                tmp=CountWords(distinctWords[i], words);
                result[distinctWords[i]]=tmp;
            }
            return result;
        }               
               
        private string[] GetDistinctWords(String[] input)
        {               
            if (input == null)           
                return new string[0];           
            else
            {
                ArrayList list=new ArrayList() ;
               
                for (int i=0; i < input.Length; i++)
                    if (!list.Contains(input[i])) // N-GRAM SIMILARITY?
                        list.Add(input[i]);
                return Tokeniser.ArrayListToArray(list) ;
            }
        }

        private int CountWords(string word, string[] words)
        {
            int itemIdx=Array.BinarySearch(words, word);
           
            if (itemIdx > 0)           
                while (itemIdx > 0 && words[itemIdx].Equals(word))
                    itemIdx--;               
            int count=0;
            while (itemIdx < words.Length && itemIdx >= 0)
            {
                if (words[itemIdx].Equals(word)) count++;
                itemIdx++;
                if (itemIdx < words.Length)               
                    if (!words[itemIdx].Equals(word)) break;
            }
            return count;
        }               
}


 
缺点:
 
由于有可能一个文章的特征向量词特别多导致整个向量维度很高,使得计算的代价太大不适合大数据量的计算。
 
SimHash原理:
 
算法的主要思想是降维,将高维的特征向量映射成一个f-bit的指纹(fingerprint),通过比较两篇文章的f-bit指纹的Hamming Distance来确定文章是否重复或者高度近似。由于每篇文章我们都可以事先计算好Hamming Distance来保存,到时候直接通过Hamming Distance来计算,所以速度非常快适合大数据计算。
 
Google就是基于此算法实现网页文件查重的。我们假设有以下三段文本:
 
1,the cat sat on the mat
 
2,the cat sat on a mat
 
3,we all scream for ice cream
 
如何实现这种hash算法呢?以上述三个文本为例,整个过程可以分为以下六步:
1、选择simhash的位数,请综合考虑存储成本以及数据集的大小,比如说32位
2、将simhash的各位初始化为0
3、提取原始文本中的特征,一般采用各种分词的方式。比如对于"the cat sat on the mat",采用两两分词的方式得到如下结果:{"th", "he", "e ", " c", "ca", "at", "t ", " s", "sa", " o", "on", "n ", " t", " m", "ma"}
4、使用传统的32位hash函数计算各个word的hashcode,比如:"th".hash = -502157718
,"he".hash = -369049682,……
5、对各word的hashcode的每一位,如果该位为1,则simhash相应位的值加1;否则减1
6、对最后得到的32位的simhash,如果该位大于1,则设为1;否则设为0


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