说明：使用neo4j算法库时需引入跟neo4j数据库对应的算法库插件或自定义算法库

1.简介

      欧几里德距离算法原理是计算n维坐标系中点与点之间地距离，如在三维坐标系中点A(p1,p2,p3),点B(q1,q2,q3),两个点之间得距离则为 ：,
如果在n维坐标系中，两个点得距离则变为：
      根据以上特性拓展：距离越小则A点和B点重合度越高，由此可衍生出A点和B点在n维空间中距离相似度公式为： 
 

        neo4j自带算法包提供了欧几里得相似度算法得函数和过程，函数适合少量数据计算，过程适合批量数据得计算

2.使用场景

        何时使用欧几里得算法呢，我们可以使用欧几里的距离算法来计算两件事之间得相似性，然后，我们可能会将相似性用作推荐查询得一部分，比如用户A和用户B之间共同爱看得电影，比如根据用户A和用户B共同出入得场所，判定用户A和B职业预测，用户A和用户B共同好友，实现可能好友推荐

3.neo4j中欧几里得函数使用示例

在neo4j中存在algo.similarity.euclideanDistance计算距离函数，也存在algo.similarity.euclidean计算相似度得函数

1.计算两个硬编码列表距离

RETURN algo.similarity.euclideanDistance([3,8,7,5,2,9], [10,8,6,6,4,5]) AS similarity

结果：8.426149773176359

2.计算两个硬编码列表相似度

ETURN algo.similarity.euclidean([3,8,7,5,2,9], [10,8,6,6,4,5]) AS similarity

结果：0.1060878539025194

3.我们还可以使用它来计算节点关联节点相似性

初始化数据

MERGE (french:Cuisine {name:'French'})
MERGE (italian:Cuisine {name:'Italian'})
MERGE (indian:Cuisine {name:'Indian'})
MERGE (lebanese:Cuisine {name:'Lebanese'})
MERGE (portuguese:Cuisine {name:'Portuguese'})
MERGE (british:Cuisine {name:'British'})
MERGE (mauritian:Cuisine {name:'Mauritian'})MERGE (zhen:Person {name: "Zhen"})
MERGE (praveena:Person {name: "Praveena"})
MERGE (michael:Person {name: "Michael"})
MERGE (arya:Person {name: "Arya"})
MERGE (karin:Person {name: "Karin"})MERGE (praveena)-[:LIKES {score: 9}]->(indian)
MERGE (praveena)-[:LIKES {score: 7}]->(portuguese)
MERGE (praveena)-[:LIKES {score: 8}]->(british)
MERGE (praveena)-[:LIKES {score: 1}]->(mauritian)MERGE (zhen)-[:LIKES {score: 10}]->(french)
MERGE (zhen)-[:LIKES {score: 6}]->(indian)
MERGE (zhen)-[:LIKES {score: 2}]->(british)MERGE (michael)-[:LIKES {score: 8}]->(french)
MERGE (michael)-[:LIKES {score: 7}]->(italian)
MERGE (michael)-[:LIKES {score: 9}]->(indian)
MERGE (michael)-[:LIKES {score: 3}]->(portuguese)MERGE (arya)-[:LIKES {score: 10}]->(lebanese)
MERGE (arya)-[:LIKES {score: 10}]->(italian)
MERGE (arya)-[:LIKES {score: 7}]->(portuguese)
MERGE (arya)-[:LIKES {score: 9}]->(mauritian)MERGE (karin)-[:LIKES {score: 9}]->(lebanese)
MERGE (karin)-[:LIKES {score: 7}]->(italian)
MERGE (karin)-[:LIKES {score: 10}]->(portuguese)

查询'Zhen'和Praveena喜好相似度：

MATCH (p1:Person {name: 'Zhen'})-[likes1:LIKES]->(cuisine)
MATCH (p2:Person {name: "Praveena"})-[likes2:LIKES]->(cuisine)
RETURN p1.name AS from,p2.name AS to,algo.similarity.euclidean(collect(likes1.score), collect(likes2.score)) AS similarity

结果：

 4.以下将返回Zhen和其它有共同美食爱好得欧几里得相似度

MATCH (p1:Person {name: 'Zhen'})-[likes1:LIKES]->(cuisine)
MATCH (p2:Person)-[likes2:LIKES]->(cuisine) WHERE p2 <> p1
RETURN p1.name AS from,p2.name AS to,algo.similarity.euclidean(collect(likes1.score), collect(likes2.score)) AS similarity
ORDER BY similarity DESC

结果：

4.源码解析

algo.similarity.euclidean欧几里得相似度计算函数源码如下：

    public double euclideanSimilarity(@Name("vector1") List<Number> vector1, @Name("vector2") List<Number> vector2) {return 1.0d / (1 + euclideanDistance(vector1, vector2));}

algo.similarity.euclideanDistance欧几里得距离计算函数源码如下：

    public double euclideanDistance(@Name("vector1") List<Number> vector1, @Name("vector2") List<Number> vector2) {if (vector1.size() != vector2.size() || vector1.size() == 0) {throw new RuntimeException("Vectors must be non-empty and of the same size");}int len = Math.min(vector1.size(), vector2.size());double[] weights1 = new double[len];double[] weights2 = new double[len];for (int i = 0; i < len; i++) {weights1[i] = vector1.get(i).doubleValue();weights2[i] = vector2.get(i).doubleValue();}return Math.sqrt(Intersections.sumSquareDelta(weights1, weights2, len));}

Intersections.sumSquareDelta()方法源码如下：

    public static double sumSquareDelta(double[] vector1, double[] vector2, int len) {double result = 0;for (int i = 0; i < len; i++) {double delta = vector1[i] - vector2[i];result += delta * delta;}return result;}

总结：由以上两端代码可知，欧几里得相似度算法函数依赖于欧几里的距离函数，Intersections.sumSquareDelta()欧几里得中对两个vector集合求了方差，euclideanDistance中对方差结果开根方。由此可知欧几里得相似度算法传入得参数值必须长度一致

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