Rmixmod-package(Rmixmod)
Rmixmod-package()所属R语言包：Rmixmod
Rmixmod a MIXture MODelling package
Rmixmod的混合建模软件包
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Rmixmod is a package based on the existing MIXMOD software. MIXMOD is a tool for fitting a mixture model of multivariate gaussian or multinomial components to a given data set with either a clustering, a density estimation or a discriminant analysis point of view.
rmixmod是的软件包基于现有MIXMOD软件。 MIXMOD是一个工具，一个多元高斯或多项组分的混合模型的拟合给定数据集的聚类，密度估计判别分析的角度来看。
Details
详细信息----------Details----------
The general purpose of the package is to discover, or explain, group structures in multivariate data sets with unknown (cluster analysis or clustering) or known class discriminant analysis or classification). It is an exploratory data analysis tool for solving clustering and classification problems. But it can also be regarded as a semi-parametric tool to estimate densities with Gaussian mixture distributions and multinomial distributions.
的包是通用的发现，解释，组结构在多元与未知的数据集（聚类分析聚类）或已知的类判别分析或分类）。这是一个探索性数据分析工具，用于解决聚类和分类问题。但它也可以被视为一个半参数估计高斯混合分布和多元分布的密度与工具。
Mathematically, mixture probability density function (pdf) f is a weighted sum of K components densities :
在数学上，混合概率密度函数（PDF）f是K组件密度的加权总和：
where h(.|{λ}_k) denotes a d-dimensional distribution parametrized by λ_k. The parameters are the mixing proportions p_k and the component of the distribution λ_k.<br>
其中h(.|{λ}_k)表示d参数化的三维分布的λ_k。参数的混合比例p_k和成分分布λ_k。<br>物理化学学报
In the Gaussian case, h is the density of a Gaussian distribution with mean μ_k and variance matrix Σ_k, and thus λ_k = (μ_k,Σ_k).
在高斯的情况下，h是一个高斯分布的密度，平均μ_k和方差矩阵Σ_k，从而λ_k = (μ_k,Σ_k)。
In the qualitative case, h is a multinomial distribution and λ_k=(a_k,ε_k) is the parameter of the distribution.
在定性的情况下，h是多项分布和λ_k=(a_k,ε_k)是参数的分布。
Estimation of the mixture parameters is performed either through maximum likelihood via the EM (Expectation Maximization, Dempster et al. 1977), the SEM (Stochastic EM, Celeux and Diebolt 1985) algorithm or through classification maximum likelihood via the CEM algorithm (Clustering EM, Celeux and Govaert 1992). These three algorithms can be chained to obtain original fitting strategies (e.g. CEM then EM with results of CEM) to use advantages of each of them in the estimation process. As mixture problems usually have multiple relative maxima, the program will produce different results, depending on the initial estimates supplied by the user. If the user does not input his own initial estimates, some initial estimates procedures are proposed (random centers for instance).
的混合物参数执行，也可以通过最大似然估计通过EM（期望最大化，登普斯特等。人，1977年），SEM（随机EM，Celeux和Diebolt 1985的）算法或通过分类的最大似然通过CEM算法（聚类EM， celeux和Govaert 1992年）。这三种算法可以链接，以获得最初装配的策略（CEM然后EM结果CEM），他们每个人在估算过程中使用的优势。由于混合物的问题通常有多个相对极大值，该程序将产生不同的结果，根据由用户提供的初始估计。如果用户没有输入自己的初步估计，提出一些初步的估算程序（例如随机中心）。
It is possible to constrain some input parameters. For example, dispersions can be equal between classes, etc.
这是可能的约束某些输入参数。例如，分散体可以是相等的类等。
In the Gaussian case, fourteen models are implemented. They are based on the eigenvalue decomposition, are most generally used. They depend on constraints on the variance matrix such as same variance matrix between clusters, spherical variance matrix... and they are suitable for data sets in any dimension.
在高斯的情况下，14个型号的贯彻落实。它们是基于特征值分解，最普遍使用的。他们依赖于约束之间的协方差矩阵聚类，球形方差矩阵的协方差矩阵，如...和，它们是适用于任何尺寸的数据集。
In the qualitative case, five multinomial models are available. They are based on a reparametrization of the multinomial probabilities.
在定性的情况下，多项模型。它们是基于一个重新参数化的多项式概率。
In both cases, the models and the number of clusters can be chosen by different criteria : BIC (Bayesian Information Criterion), ICL (Integrated Completed Likelihood, a classification version of BIC), NEC (Entropy Criterion), or Cross-Validation (CV).
在这两种情况下，选择的模式和聚类的数量可以按不同的标准：BIC（贝叶斯信息准则），ICL（集成完成的可能性，分类版本的BIC），NEC（熵判据），或交叉验证（CV ）。
（作者）----------Author(s)----------
Author: Remi Lebret and Serge Iovleff and Florent
Langrognet, with contributions from C. Biernacki and G.
Celeux and G. Govaert <a href="mailto:contact@mixmod.org">contact@mixmod.org</a>
参考文献----------References----------
"Model-Based Cluster and Discriminant Analysis with the MIXMOD Software". Computational Statistics and Data Analysis, vol. 51/2, pp. 587-600.
实例----------Examples----------
## Clustering Analysis[＃聚类分析]
# load quantitative data set[加载定量数据集]
data(geyser)
# Clustering in gaussian case[在高斯的情况下的聚类]
xem1<-mixmodCluster(geyser,3)
summary(xem1)
plot(xem1)
hist(xem1)
# load qualitative data set[加载定性数据集]
data(birds)
# Clustering in multinomial case[多项式情况下的聚类]
xem2<-mixmodCluster(birds, 2)
summary(xem2)
barplot(xem2)
## Discriminant Analysis[＃判别分析]
# start by extract 10 observations from iris data set[开始提取物10个观察虹膜数据]
remaining.obs<-sample(1:nrow(iris),10)
# then run a mixmodLearn() analysis without those 10 observations[然后运行mixmodLearn的（）分析，而这10个观察]
learn<-mixmodLearn(iris[-remaining.obs,1:4], iris$Species[-remaining.obs])
# create a MixmodPredict to predict those 10 observations[，创建一个MixmodPredict预测这10个观察]
prediction <- mixmodPredict(data=iris[remaining.obs,1:4], classificationRule=learn["bestResult"])
# show results[显示结果]
prediction
# compare prediction with real results[预测与实际结果比较]
as.integer(iris$Species[remaining.obs]) == prediction["partition"]
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-27 00:06:31
