一、层次聚类
1）距离和相似系数
r语言中使用dist(x, method = "euclidean",diag = FALSE, upper = FALSE, p = 2) 来计算距离。其中x是样本矩阵或者数据框。method表示计算哪种距离。method的取值有：
euclidean 欧几里德距离，就是平方再开方。
maximum 切比雪夫距离
manhattan 绝对值距离
canberra Lance 距离
minkowski 明科夫斯基距离，使用时要指定p值
binary 定性变量距离
定性变量距离： 记m个项目里面的 0:0配对数为m0 ,1:1配对数为m1，不能配对数为m2，距离=m1/(m1+m2);
diag 为TRUE的时候给出对角线上的距离。upper为TURE的时候给出上三角矩阵上的值。
r语言中使用scale(x, center = TRUE, scale = TRUE) 对数据矩阵做中心化和标准化变换。
如只中心化 scale(x,scale=F) ,
r语言中使用sweep(x, MARGIN, STATS, FUN="-", ) 对矩阵进行运算。MARGIN为1，表示行的方向上进行运算，为2表示列的方向上运算。STATS是运算的参数。FUN为运算函数，默认是减法。下面利用sweep对矩阵x进行极差标准化变换
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>center <-sweep(x, 2, apply(x, 2, mean)) #在列的方向上减去均值。
>R <-apply(x, 2, max) -apply(x,2,min) #算出极差，即列上的最大值-最小值
>x_star <-sweep(center, 2, R, "/") #把减去均值后的矩阵在列的方向上除以极差向量
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>center <-sweep(x, 2, apply(x, 2, min)) #极差正规化变换
>R <-apply(x, 2, max) -apply(x,2,min)
>x_star <-sweep(center, 2, R, "/")
有时候我们不是对样本进行分类，而是对变量进行分类。这时候，我们不计算距离，而是计算变量间的相似系数。常用的有夹角和相关系数。
r语言计算两向量的夹角余弦：
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y <-scale(x, center =F, scale =T)/sqrt(nrow(x)-1)
C <-t(y) %%y
相关系数用cor函数
2）层次聚类法
层次聚类法。先计算样本之间的距离。每次将距离最近的点合并到同一个类。然后，再计算类与类之间的距离，将距离最近的类合并为一个大类。不停的合并，直到合成了一个类。其中类与类的距离的计算方法有：最短距离法，最长距离法，中间距离法，类平均法等。比如最短距离法，将类与类的距离定义为类与类之间样本的最段距离。。。
r语言中使用hclust(d, method = "complete", members=NULL) 来进行层次聚类。
其中d为距离矩阵。
method表示类的合并方法，有：
single 最短距离法
complete 最长距离法
median 中间距离法
mcquitty 相似法
average 类平均法
centroid 重心法
ward 离差平方和法
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> x <-c(1,2,6,8,11) #试用一下
> dim(x) <-c(5,1)
> d <-dist(x)
> hc1 <-hclust(d,"single")
> plot(hc1)
> plot(hc1,hang=-1,type="tirangle") #hang小于0时，树将从底部画起。
#type = c("rectangle", "triangle"),默认树形图是方形的。另一个是三角形。
#horiz TRUE 表示竖着放，FALSE表示横着放。
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> z <-scan()
1: 10000846080508590473039803010382
9: 08461000088108260376032602770277
17: 08050881100008010380031902370345
25: 08590826080110000436032903270365
33: 04730376038004361000076207300629
41: 03980326031903290762100005830577
49: 03010277023703270730058310000539
57: 03820415034503650629057705391000
65:
Read 64items
> names
[1] "shengao""shoubi""shangzhi""xiazhi""tizhong"
[6] "jingwei""xiongwei""xiongkuang"
> r <-matrix(z,nrow=8,dimnames=list(names,names))
> d <-asdist(1-r)
> hc <-hclust(d)
> plot(hc)
然后可以用recthclust(tree, k = NULL, which = NULL, x = NULL, h = NULL,border = 2, cluster = NULL)来确定类的个数。 tree就是求出来的对象。k为分类的个数，h为类间距离的阈值。border是画出来的颜色，用来分类的。
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> plot(hc)
> recthclust(hc,k=2)
> recthclust(hc,h=05)
result=cutree(model,k=3) 该函数可以用来提取每个样本的所属类别
二、动态聚类k-means
层次聚类，在类形成之后就不再改变。而且数据比较大的时候更占内存。
动态聚类，先抽几个点，把周围的点聚集起来。然后算每个类的重心或平均值什么的，以算出来的结果为分类点，不断的重复。直到分类的结果收敛为止。r语言中主要使用kmeans(x, centers, itermax = 10, nstart = 1, algorithm =c("Hartigan-Wong", "Lloyd","Forgy", "MacQueen"))来进行聚类。centers是初始类的个数或者初始类的中心。itermax是最大迭代次数。nstart是当centers是数字的时候，随机集合的个数。algorithm是算法，默认是第一个。
使用knn包进行Kmean聚类分析
将数据集进行备份，将列newiris$Species置为空，将此数据集作为测试数据集
> newiris <- iris
> newiris$Species <- NULL
在数据集newiris上运行Kmean聚类分析， 将聚类结果保存在kc中。在kmean函数中，将需要生成聚类数设置为3
> (kc <- kmeans(newiris, 3))
K-means clustering with 3 clusters of sizes 38, 50, 62: K-means算法产生了3个聚类，大小分别为38,50,62
Cluster means: 每个聚类中各个列值生成的最终平均值
SepalLength SepalWidth PetalLength PetalWidth
1 5006000 3428000 1462000 0246000
2 5901613 2748387 4393548 1433871
3 6850000 3073684 5742105 2071053
Clustering vector: 每行记录所属的聚类（2代表属于第二个聚类，1代表属于第一个聚类，3代表属于第三个聚类）
[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[37] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[73] 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 3 3 3 2 3
[109] 3 3 3 3 3 2 2 3 3 3 3 2 3 2 3 2 3 3 2 2 3 3 3 3 3 2 3 3 3 3 2 3 3 3 2 3
[145] 3 3 2 3 3 2
Within cluster sum of squares by cluster: 每个聚类内部的距离平方和
[1] 1515100 3982097 2387947
(between_SS / total_SS = 884 %) 组间的距离平方和占了整体距离平方和的的884%，也就是说各个聚类间的距离做到了最大
Available components: 运行kmeans函数返回的对象所包含的各个组成部分
[1] "cluster" "centers" "totss" "withinss"
[5] "totwithinss" "betweenss" "size"
("cluster"是一个整数向量，用于表示记录所属的聚类
"centers"是一个矩阵，表示每聚类中各个变量的中心点
"totss"表示所生成聚类的总体距离平方和
"withinss"表示各个聚类组内的距离平方和
"totwithinss"表示聚类组内的距离平方和总量
"betweenss"表示聚类组间的聚类平方和总量
"size"表示每个聚类组中成员的数量)
创建一个连续表,在三个聚类中分别统计各种花出现的次数
> table(iris$Species, kc$cluster)
1 2 3
setosa 0 50 0
versicolor 2 0 48
virginica 36 0 14
根据最后的聚类结果画出散点图，数据为结果集中的列"SepalLength"和"SepalWidth"，颜色为用1，2，3表示的缺省颜色
> plot(newiris[c("SepalLength", "SepalWidth")], col = kc$cluster)
在图上标出每个聚类的中心点
〉points(kc$centers[,c("SepalLength", "SepalWidth")], col = 1:3, pch = 8, cex=2)
三、DBSCAN
动态聚类往往聚出来的类有点圆形或者椭圆形。基于密度扫描的算法能够解决这个问题。思路就是定一个距离半径，定最少有多少个点，然后把可以到达的点都连起来，判定为同类。在r中的实现
dbscan(data, eps, MinPts, scale, method, seeds, showplot, countmode)
其中eps是距离的半径，minpts是最少多少个点。 scale是否标准化（我猜) ,method 有三个值raw,dist,hybird,分别表示，数据是原始数据避免计算距离矩阵，数据就是距离矩阵，数据是原始数据但计算部分距离矩阵。showplot画不画图，0不画，1和2都画。countmode，可以填个向量，用来显示计算进度。用鸢尾花试一试
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> installpackages("fpc", dependencies=T)
> library(fpc)
> newiris <-iris[1:4]
> model <-dbscan(newiris,15,5,scale=T,showplot=T,method="raw")# 画出来明显不对 把距离调小了一点
> model <-dbscan(newiris,05,5,scale=T,showplot=T,method="raw")
> model #还是不太理想……
dbscan Pts=150MinPts=5eps=05
012
border 34518
seed 04053
total 344571
the us
美国
例句
1But even if the U S economy is losing jobs at a slower pace than half a year ago
即使美国企业裁员速度比半年前有所放缓，整体的失业状况还是令人感到沮丧。
2The U S Centers for Disease Control and Prevention has more about physical activity
美国疾病控制和预防中心提供更多有关身体活动的资料。
我上去看了一下,没有问题我是今早9点50分上的
A
Chinatown
is
a
section
of
an
urban
area
with
a
large
number
of
Chinese
residents,
usually
outside
of
Greater
China
Chinatowns
are
present
throughout
the
world,
including
those
in
East
Asia,
Southeast
Asia,
the
Americas,
Australasia,
and
Europe
In
the
past,
crowded
Chinatowns
in
urban
areas
were
seen
as
places
of
cultural
insularity
Nowadays,
many
old
and
new
Chinatowns
are
considered
significant
centers
of
commercialism
and
tourism
Some
of
them
also
serve,
to
varying
degrees,
as
centers
of
multiculturalism
Many
Chinatowns
are
focused
on
commercial
tourism,
whereas
others
are
actual
living
and
working
communities;
some
are
a
synthesis
of
both
Chinatowns
also
range
from
rundown
ghettos
to
modern
sites
of
recent
development
In
some,
recent
investments
have
revitalized
run-down
and
blighted
areas
and
turned
them
into
centers
of
economic
and
social
activity
In
certain
cases,
this
has
led
to
gentrification
and
a
reduction
in
the
specifically
Chinese
character
of
the
neighborhoods
Some
Chinatowns
have
a
long
history,Manila
being
the
oldest,
such
as
the
Chinatown
in
Nagasaki,
Japan,
or
Yaowarat
Road
in
Bangkok,
both
of
which
were
founded
by
Chinese
traders
more
than
200
years
ago
Honolulu's
Chinatown
is
the
first
Chinatown
to
be
established
outside
Asia
Chinatown,
San
Francisco
was
the
first,
and
is
the
largest,
Chinatown
to
be
established
on
the
West
Coast
of
the
United
States
Other
cities
in
North
America
where
Chinatowns
were
established
in
the
mid-nineteenth
century
include
almost
every
major
settlement
along
the
West
Coast
from
San
Diego
to
Victoria,
BC
By
the
second
half
of
the
nineteenth
century,
bustling
Chinatowns
were
also
established
in
Vancouver,
BC,
New
York
City,
Boston,
Chicago,
and
Detroit
The
discovery
of
gold
in
Australia
caused
the
establishment
of
relatively
small
Chinatowns
in
cities
there,
and
similar
migrations
of
Chinese
resulted
in
tiny
settlements
termed
"Chinatowns"
being
established
in
New
Zealand
and
even
South
Africa
European
Chinatowns,
such
as
those
in
Germany,
the
Netherlands,
and
the
United
Kingdom,
are
for
the
most
part
smaller
and
more
recent
than
North
American
Chinatowns
Other
Chinatowns
are
newer,
such
as
in
Chinatown,
Las
Vegas
in
1995,
Dubai,
and
Santo
Domingo
and
have
received
official
recognition
Chinatown,
MelbourneIn
the
past,
Chinatown
has
also
been
used
to
refer
to
the
Chinese
sections
of
non-Chinese-administered
cities
within
Greater
China
For
example,
the
walled
city
of
Shanghai
was
referred
to
as
a
"Chinatown"
because
it
was
surrounded
by
foreign
concessions
administered
by
European
powers
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