MySQL 如何查找两行之间的相似度

在MySQL中，我们经常需要对数据进行相似度分析。这种分析方法通常用于推荐系统、搜索引擎和广告推荐等应用中。本文将介绍如何在MySQL中查找两行之间的相似度。

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相似度的计算方法

相似度可以用不同的计算方法来估算。以下是一些常见的相似度计算方法：

欧几里得相似度：该方法使用勾股定理计算两个向量之间的距离。两个向量之间的欧几里得距离越小，它们之间的相似度就越高。这种方法用于数值型数据，如用户评分和商品价格等。
余弦相似度：该方法计算两个向量之间的夹角余弦值。两个向量越接近，它们之间的夹角余弦值越接近1，意味着它们之间的相似度越高。这种方法用于文本分类和推荐系统等应用中。
杰卡德相似度：该方法用于集合数据，例如用户喜欢的电影或商品类型。它将两个集合中相同元素的数量除以所有元素的数量之和来计算相似度。

接下来，我们将介绍如何在MySQL中使用上述方法来计算相似度。

示例：使用余弦相似度计算相似度

这里我们将使用余弦相似度计算两个向量之间的相似度。我们使用一个实际的数据集来说明如何计算相似度。假设我们有一个包含电影名称和相应标签的表movies。我们将使用标签向量来表示每个电影。标签向量是一个长度为N的二进制向量，其中第i位等于1表示该电影包含第i个标签，否则为0。

电影名	标签向量
Movie1	1,0,1,0,1,0,1,0
Movie2	1,1,0,1,0,1,0,1
Movie3	0,1,1,0,1,0,0,0
Movie4	1,1,1,1,0,0,1,0
Movie5	1,0,0,1,1,0,1,1
Movie6	0,0,1,0,0,1,1,0
Movie7	0,1,0,0,1,0,1,1
Movie8	0,0,0,0,1,1,1,1
Movie9	1,0,0,1,0,0,0,0
…	…

假设我们要计算Movie1和Movie2之间的相似度。我们可以使用以下SQL查询：

SELECT
    (SELECT SUM(v1.*v2) FROM (
        SELECT SUBSTRING_INDEX(m1.tags, ',', 1) as t1, SUBSTRING_INDEX(m2.tags, ',', 1) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
        UNION ALL
        SELECT SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 2), ',', -1) as t1, SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 2), ',', -1) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
        UNION ALL
        SELECT SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 3), ',', -1) as t1, SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 3), ',', -1) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
        UNION ALL
        SELECT SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 4), ',', -1) as t1, SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 4), ',', -1) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
        UNION ALL
        SELECT SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 5), ',', -1) as t1, SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 5), ',', -1) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
        UNION ALL
        SELECT SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 6), ',', -1) as t1, SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 6), ',', -1) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
        UNION ALL
        SELECT SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 7), ',', -1) as t1, SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 7), ',', -1) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
        UNION ALL
        SELECT SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 8), ',', -1) as t1, SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 8), ',', -1) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
    ) as v1, (
        SELECT SQRT(SUM(t1*t1)) as norm1, SQRT(SUM(t2*t2)) as norm2 FROM (
            SELECT POW(SUBSTRING_INDEX(m1.tags, ',', 1), 2) as t1, POW(SUBSTRING_INDEX(m2.tags, ',', 1), 2) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
            UNION ALL
            SELECT POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 2), ',', -1), 2) as t1, POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 2), ',', -1), 2) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
            UNION ALL
            SELECT POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 3), ',', -1), 2) as t1, POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 3), ',', -1), 2) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
            UNION ALL
            SELECT POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 4), ',', -1), 2) as t1, POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 4), ',', -1), 2) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
            UNION ALL
            SELECT POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 5), ',', -1), 2) as t1, POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 5), ',', -1), 2) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
            UNION ALL
            SELECT POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 6), ',', -1), 2) as t1, POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 6), ',', -1), 2) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
            UNION ALL
            SELECT POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 7), ',', -1), 2) as t1, POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 7), ',', -1), 2) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
            UNION ALL
            SELECT POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m1.tags, ',', 8), ',', -1), 2) as t1, POW(SUBSTRING_INDEX(SUBSTRING_INDEX(m2.tags, ',', 8), ',', -1), 2) as t2 FROM movies m1, movies m2 WHERE m1.id=1 AND m2.id=2
        ) as t
    ) as v2) / (v1.norm1*v2.norm2) as cos_sim;