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基于密度算法(DBSCAN)
             :



1、基本定义:



点的ε邻域,以选定点为中心,以ε为半径的区域:



①核心点,如果一个点的ε邻域包含最小数目(minps)个点,则称该点为核心点;



②直接密度可达,如果点p在点q的ε邻域内,而q是一个核心点,则称点p是从点q直接

密度可达;



③间接密度可达:给定一个点集M,如果存在一个点链p1,p2…pn,p1=q,pn

=p,对pi∈M,1≦i≦n,pi+1是从pi关于ε和minps直接密度可达的,则

点p是从点q关于ε和minps间接密度可达;



④密度相连,如果点集M中存在一个点o,使得点p和q是从o关于ε和minps间接密

度可达,则称点p和q是关于ε和minps密度相连;



⑤噪声,不属于密度可达或密度相连集合的点(即孤立点),称为噪声。



2、算法解析:



输入:数据集 S、参数ε、Minpts。



输出:关于ε和 Minpts 的所有类。



数据结构:float[n][3]   (n 个三维点)
mark[n][3]    (每个数据点三个标签项:b_tagged:是否已经标记,标记为噪声

或属于某一聚类;



b_core:是否为核心点;sort:隶属的类别)



1)、初始化类别标记 Cid



2)、for S 中每个数据对象 p



   2.1) p 是未标记类别的数据对象 then
       、if



       2.1.1) p 不是核心对象 then
            、if



                    、将 p 标记为噪声
             2.1.1.1)



            、else
       2.1.2)



                    、将 p 标记为 Cid
             2.1.2.1)



                    、将所有从 p 出发关于ε和minps直接密度可达的标记为噪声
             2.1.2.2)

的对象标记为 Cid



                    、将所有从 p 出发关于ε和minps直接密度可达的未标记的对
             2.1.2.3)

象标记为 Cid,



                      并放入到队列 Q 中。//关键部分,从 p 出发通过队列 Q 的入

队出队找到一个聚类
、while Q 不空
         2.1.2.4)



                        、从 Q 中取出队头元素 O
               2.1.2.4.1)



               2.1.2.4.2)、if O 是核心对象 then



                      2.1.2.4.2.1)、将所有从 O 出发关于ε和minps直接密

度可达的标记为噪声的对象标记为 Cid



                      2.1.2.4.2.2)、将所有从 O 出发关于ε和minps直接密

度可达的未标记的对象标记为 Cid,



                                  并放入到队列 Q 中。



                、改变类别标记 Cid。
         2.1.2.5)

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5、基于密度算法(dbscan)原理

  • 1. 基于密度算法(DBSCAN) : 1、基本定义: 点的ε邻域,以选定点为中心,以ε为半径的区域: ①核心点,如果一个点的ε邻域包含最小数目(minps)个点,则称该点为核心点; ②直接密度可达,如果点p在点q的ε邻域内,而q是一个核心点,则称点p是从点q直接 密度可达; ③间接密度可达:给定一个点集M,如果存在一个点链p1,p2…pn,p1=q,pn =p,对pi∈M,1≦i≦n,pi+1是从pi关于ε和minps直接密度可达的,则 点p是从点q关于ε和minps间接密度可达; ④密度相连,如果点集M中存在一个点o,使得点p和q是从o关于ε和minps间接密 度可达,则称点p和q是关于ε和minps密度相连; ⑤噪声,不属于密度可达或密度相连集合的点(即孤立点),称为噪声。 2、算法解析: 输入:数据集 S、参数ε、Minpts。 输出:关于ε和 Minpts 的所有类。 数据结构:float[n][3] (n 个三维点)
  • 2. mark[n][3] (每个数据点三个标签项:b_tagged:是否已经标记,标记为噪声 或属于某一聚类; b_core:是否为核心点;sort:隶属的类别) 1)、初始化类别标记 Cid 2)、for S 中每个数据对象 p 2.1) p 是未标记类别的数据对象 then 、if 2.1.1) p 不是核心对象 then 、if 、将 p 标记为噪声 2.1.1.1) 、else 2.1.2) 、将 p 标记为 Cid 2.1.2.1) 、将所有从 p 出发关于ε和minps直接密度可达的标记为噪声 2.1.2.2) 的对象标记为 Cid 、将所有从 p 出发关于ε和minps直接密度可达的未标记的对 2.1.2.3) 象标记为 Cid, 并放入到队列 Q 中。//关键部分,从 p 出发通过队列 Q 的入 队出队找到一个聚类
  • 3. 、while Q 不空 2.1.2.4) 、从 Q 中取出队头元素 O 2.1.2.4.1) 2.1.2.4.2)、if O 是核心对象 then 2.1.2.4.2.1)、将所有从 O 出发关于ε和minps直接密 度可达的标记为噪声的对象标记为 Cid 2.1.2.4.2.2)、将所有从 O 出发关于ε和minps直接密 度可达的未标记的对象标记为 Cid, 并放入到队列 Q 中。 、改变类别标记 Cid。 2.1.2.5)