# [译]Vector space model(向量空间模型)

Vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as, for example, index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. Its first use was in the SMART Information Retrieval System.

Clotho注: 词项(term)一般情况下就是一个词(word),特别是在文本索引领域.

Definitions

A document is represented as a vector. Each dimension corresponds to a separate term. If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, also known as (term) weights, have been developed. One of the best known schemes is tf-idf weighting (see the example below).

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary (the number of distinct words occurring in the corpus).

Applications

Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.

In practice, it is easier to calculate the cosine of the angle between the vectors instead of the angle:

$\cos{\theta} = \frac{\mathbf{v_1} \cdot \mathbf{v_2}}{\left\| \mathbf{v_1} \right\| \left \| \mathbf{v_2} \right\|}$

A cosine value of zero means that the query and document vector are orthogonal and have no match (i.e. the query term does not exist in the document being considered). See cosine similarity for further information.

(Clotho注:其实就是两个文档向量之间比较)

$\cos{\theta} = \frac{\mathbf{v_1} \cdot \mathbf{v_2}}{\left\| \mathbf{v_1} \right\| \left \| \mathbf{v_2} \right\|}$

Example: tf-idf weights

In the classic vector space model proposed by Salton, Wong and Yang [1] the term specific weights in the document vectors are products of local and global parameters. The model is known as term frequency-inverse document frequency model. The weight vector for document d is $\mathbf{v}_d = [w_{1,d}, w_{2,d}, \ldots, w_{N,d}]^T$, where

$w_{t,d} = \mathrm{tf}_t \cdot \log{\frac{|D|}{|\{t \in d\}|}}$

and

• tft is term frequency of term t in document d (a local parameter)
• $\log{\frac{|D|}{|\{t \in d\}|}}$ is inverse document frequency (a global parameter). | D | is the total number of documents in the document set; $|\{t \in d\}|$ is the number of documents containing the term t.

In a simpler Term Count Model the term specific weights do not include the global parameter. Instead the weights are just the counts of term occurrences: wt,d = tft.

* tft 是词项t在文档d中的频率(一个局部参数)

* $\log{\frac{|D|}{|\{t \in d\}|}}$是倒文档频率(一个全局参数). | D | 是文档集合中的文档总数; $|\{t \in d\}|$是包含词项t的文档数.

Limitations

The vector space model has the following limitations:

1. Long documents are poorly represented because they have poor similarity values (a small scalar product and a large dimensionality)
2. Search keywords must precisely match document terms; word substrings might result in a "false positive match"
3. Semantic sensitivity; documents with similar context but different term vocabulary won't be associated, resulting in a "false negative match".
4. The order in which the terms appear in the document is lost in the vector space representation.

1. 长篇的文档会被表示得不符合实际,因为它们只有较低的相似度值(一个小的乘积和一个大的维度数).
2. 检索的关键字必须精确匹配文档中的词项;词素的检索可能会得到"错误肯定匹配".(Clotho注:不相似被当成相似)
3. 语义敏感;那些拥有相似语义但使用的词汇不同的文档,会被当成"错误否定匹配".(Clotho注:相似被当成不相似)
4. 词项在文档中的顺序会在向量空间的表示中忽略.

posted @ 2009-12-30 10:10  Clotho_Lee  阅读(3725)  评论(1编辑  收藏