R语言:cmdscale()函数中文帮助文档(中英文对照)

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cmdscale(stats)
cmdscale()所属R语言包：stats

                                        Classical (Metric) Multidimensional Scaling
                                         古典（公制）多维尺度

                                         译者：生物统计家园网 机器人LoveR

描述----------Description----------

Classical multidimensional scaling of a data matrix. Also known as principal coordinates analysis (Gower, 1966).
古典多维尺度的数据矩阵。也被称为主坐标分析（高尔，1966）。


用法----------Usage----------


cmdscale(d, k = 2, eig = FALSE, add = FALSE, x.ret = FALSE)



参数----------Arguments----------

参数：d
a distance structure such as that returned by dist or a full symmetric matrix containing the dissimilarities.
距离结构，如dist或全对称矩阵的异同返回。


参数：k
the maximum dimension of the space which the data are to be represented in; must be in {1, 2, …, n-1}.
其中的数据是代表空间的最大尺寸;必须在{1, 2, …, n-1}。


参数：eig
indicates whether eigenvalues should be returned.
指示是否应该返回的特征值。


参数：add
logical indicating if an additive constant c* should be computed, and added to the non-diagonal dissimilarities such that the modified dissimilarities are Euclidean.
逻辑表示，如果加常数c*应计算，并补充，修改后的异同是欧几里德的非对角线的异同。


参数：x.ret
indicates whether the doubly centred symmetric distance matrix should be returned.
指示是否应该返回的双中心对称的距离矩阵。


Details

详情----------Details----------

Multidimensional scaling takes a set of dissimilarities and returns a set of points such that the distances between the points are approximately equal to the dissimilarities.  (It is a major part of what ecologists call "ordination".)
多维标度的异同，并返回一组点之间的距离大致相等的异同点。 （这是一个什么生态学家所谓的“协调”的重要组成部分。）

A set of Euclidean distances on n points can be represented exactly in at most n - 1 dimensions.  cmdscale follows the analysis of Mardia (1978), and returns the best-fitting k-dimensional representation, where k may be less than the argument k.
一套n点的欧氏距离，可以在最n - 1尺寸精确表示。 cmdscale如下Mardia（1978）的分析，并返回最佳拟合k立体的代表性，其中k可能比参数k少。

The representation is only determined up to location (cmdscale takes the column means of the configuration to be at the origin), rotations and reflections.  The configuration returned is given in principal-component axes, so the reflection chosen may differ between R platforms (see prcomp).
表示只确定位置（cmdscale列的配置是指在原点），旋转和反射。返回配置中的主要成分轴，所以选择的反射可能会有所不同（见prcomp）研发平台。

When add = TRUE, a minimal additive constant c* is computed such that the the dissimilarities d[i,j] +   c* are Euclidean and hence can be represented in n - 1 dimensions.  Whereas S (Becker et al., 1988) computes this constant using an approximation suggested by Torgerson, R uses the analytical solution of Cailliez (1983), see also Cox and Cox (2001). Note that because of numerical errors the computed eigenvalues need not all be non-negative, and even theoretically the representation could be in fewer than n - 1 dimensions.
当add = TRUE，最小的添加剂不断c*计算的异同d[i,j] +   c*是欧几里德，因此可以代表n - 1尺寸。而S（Becker等人，1988年）计算这个常量使用一个近似托格森建议，R使用的Cailliez（1983）的解析解，也考克斯和Cox（2001）。请注意，由于数值错误的计算特征值并不需要所有非负，连理论上的代表性在少于n - 1尺寸的可能。


值----------Value----------

If eig = FALSE, add = FALSE and x.ret = FALSE (default), a matrix with k columns whose rows give the coordinates of the points chosen to represent the dissimilarities.
如果eig = FALSE，add = FALSE和x.ret = FALSE（默认），k列，其行给予选为代表的异同点的坐标矩阵。

Otherwise, a list containing the following components.
否则，一个列表，其中包含以下组件。


参数：points
a matrix with up to k columns whose rows give the coordinates of the points chosen to represent the dissimilarities.
k列其行给予选为代表的异同点的坐标矩阵。


参数：eig
the n eigenvalues computed during the scaling process if eig is true.  <STRONG>NB</STRONG>: versions of R before 2.12.1 returned only k but were documented to return n - 1.
n特征值计算缩放过程中，如果eig是真实的。 <STRONG>注：</强>：，研发2.12.1之前的版本只返回k但记录返回n - 1。


参数：x
the doubly centered distance matrix if x.ret is true.
如果x.ret是真正的双中心的距离矩阵。


参数：ac
the additive constant c*, 0 if add = FALSE.
加常数c*，0如果add = FALSE。


参数：GOF
a numeric vector of length 2, equal to say (g.1,g.2), where g.i = (sum{j=1..k} &lambda;[j]) / (sum{j=1..n} T.i(&lambda;[j])), where &lambda;[j] are the eigenvalues (sorted in decreasing order), T.1(v) = abs(v), and T.2(v) = max(v, 0).  
一个长度为2的数字向量，等于说(g.1,g.2)，其中g.i = (sum{j=1..k} &lambda;[j]) / (sum{j=1..n} T.i(&lambda;[j]))，&lambda;[j]的特征值（按递减顺序排序），T.1(v) = abs(v)，T.2(v) = max(v, 0) 。


参考文献----------References----------

The New S Language. Wadsworth &amp; Brooks/Cole.
The analytical solution of the additive constant problem. Psychometrika 48, 343&ndash;349.
Multidimensional Scaling.  Second edition. Chapman and Hall.
Some distance properties of latent root and vector  methods used in multivariate analysis.   Biometrika 53, 325&ndash;328.
Multivariate Analysis. Part I. Distributions, Ordination and Inference.  London: Edward Arnold. (Especially pp. 108&ndash;111.)
Some properties of classical multidimensional scaling. Communications on Statistics &ndash; Theory and Methods, A7, 1233&ndash;41.
Multivariate Analysis, London: Academic Press.
Multivariate Observations. New York: Wiley.
Theory and Methods of Scaling. New York: Wiley.

参见----------See Also----------

dist.
dist。

isoMDS and sammon in package MASS provide alternative methods of multidimensional scaling.
isoMDS和sammon包中MASS提供多维尺度的替代方法。


举例----------Examples----------


require(graphics)

loc <- cmdscale(eurodist)
x <- loc[, 1]
y &lt;- -loc[, 2] # reflect so North is at the top[反思，让北顶端]
## note asp = 1, to ensure Euclidean distances are represented correctly[＃注意ASP = 1，以确保正确表示欧氏距离]
plot(x, y, type = "n", xlab = "", ylab = "", asp = 1, axes = FALSE,
     main = "cmdscale(eurodist)")
text(x, y, rownames(loc), cex = 0.6)

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