[译]Cosine similarity

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最新推荐文章于 2024-10-02 11:50:30 发布

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原文链接：http://www.cnblogs.com/live41/archive/2010/01/03/1638222.html

本文介绍了余弦相似度的概念及应用,特别是在文本挖掘中的作用。余弦相似度通过计算两个向量之间的夹角余弦值来衡量它们的相似度,适用于文档比较。文章还讨论了该方法在信息检索领域的特点。

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Cosine similarity ^[1]^[2] is a measure of similarity between two vectors of n dimensions by finding the cosine of the angle between them, often used to compare documents in text mining. Given two vectors of attributes, A and B, the cosine similarity, θ, is represented using a dot product and magnitude as

余弦相似度是利用两个n维向量的夹角余弦值来计算它们相似度的方法,经常用于在文本挖掘中比较文档.给定两个向量的属性(维度)A和B,它们的夹角θ,余弦相似度以点积和向量长度表示为

$\text{similarity} = \cos(\theta) = {A \cdot B \over \|A\| \|B\|}.$

For text matching, the attribute vectors A and B are usually the term frequency vectors of the documents. The cosine similarity can be seen as a method of normalizing document length during comparison.

在文本匹配中,属性(维度)向量通常是文档的词频向量.余弦相似度可以看作一个在比较中规范化文档长度的方法.

The resulting similarity ranges from −1 meaning exactly opposite, to 1 meaning exactly the same, with 0 indicating independence, and in-between values indicating intermediate similarity or dissimilarity.

相似度的结果的范围从-1(表示完全相反)到1(表示完全相同),0表示互相独立,其余的值表示文档的相似度和相反度.

In the case of information retrieval, the cosine similarity of two documents will range from 0 to 1, since the term frequencies (tf-idf weights) cannot be negative. The angle between two term frequency vectors cannot be greater than 90°.

在信息检索的领域,余弦相似度的值的范围是从0到1,因为词频(tf-idf权重)不可能为负数.两个词频向量的夹角不可能大于90度.

This cosine similarity metric may be extended such that it yields the Jaccard coefficient in the case of binary attributes. This is the Tanimoto coefficient, T(A, B), represented as

余弦相似度的公式在二进制的情况下可以扩展到以Jaccard系数作为除数的值(分母).这是Tanimoto系数(广义Jaccard系数),T(A, B),表示为

$T(A,B) = {A \cdot B \over \|A\|^2 +\|B\|^2 - A \cdot B}.$