遗传算法优化的投影寻踪程序

收录时间:2015-04-06
资源分类:Matlab

自己编写的遗传算法优化投影寻踪的程序,为MATLAB 函数文件,一个为RAGA是实数编码的遗传算法函数文件,一个Target是投影寻踪的函数文件,需要编写主程序调用即可。

投影寻踪 (projection pursuit, 简称PP)方法是通过高维数据在低维投影上的统计分析, 由此充分获取高维数据本身的统计结构和信息的一类统计方法,并在统计过程控制中得到广泛应用。投影寻踪是处理和分析高维数据的一类新兴的统计方法,其基本思想是将高维数据投影到低维(1~3维)子空间上,寻找出反映原高维数据的结构或特征的投影,以达到研究和分析高维数据的目的。1974年,美国Stan—ford大学的Friedman和Tukey首次将该方法命名为Projection Pursuit,即投影寻踪。

基于实数的加速遗传算法(RAGA)的投影寻踪聚类评价分析过程包括以下4个步骤。
步骤1:评价指标值的归一化处理。
步骤2:构造投影指标函数。投影寻踪方法就是把P维数据综合成l维投影值。然后根据1维投影值进行分类。在求投影值时,要求投影值的散布特征为:局部投影点尽可能密集,最好凝聚成若干个点团;而在整体上,投影点团之间要尽可能散开。基于此,构造投影指标函数。
步骤3:优化投影指标函数。当各指标值的样本集给定时,投影指标函数只随着投影方向的变化而变化。不同的投影方向反应不同的数据结构特征,最佳投影方向就是最大可能暴露高维数据某类特征结构的投影方向,可通过求解投影指标函数最大化问题来估计最佳投影方向。这是一个复杂非线性优化问题,用常规优化方法处理较困难。模拟生物优胜劣汰规则与群体内部染色体信息交换机制的加速遗传算法是一种通用的全局优化方法,用它来求解上述优化问题较简便和有效。    步骤4:排序分类。根据步骤3求得投影值,并进行排序分类。

projection pusruit

Projection pursuit (PP) is a type of statistical technique which involves finding the most "interesting" possible projections in multidimensional data. Often, projections which deviate more from a normal distribution are considered to be more interesting. As each projection is found, the data are reduced by removing the component along that projection, and the process is repeated to find new projections; this is the "pursuit" aspect that motivated the technique known as matching pursuit.
The most exciting feature of projection pursuit is that it is one of the very few multivariate method able to bypass the "curse of dimensionality" caused by the fact that high-dimensional space is mostly empty. In addition, projection pursuit are able to ignore irrelevant (i.e. noisy and information-poor) variables. This is a distinct advantage over methods based on interpoint distances like minimal spanning trees, multidimensional scaling and most clustering techniques.

Many of the methods of classical multivariate analysis turn out to be special cases of projection pursuit. Examples are principal component analysis and discriminant analysis, and the quartimax and oblimax methods in factor analysis.

One serious drawback of projection pursuit methods is their high demand on computer time.

文件下载列表
RAGA-PPC.zip (1.99KB)  
附件内容
RAGA.m  Target.m  
标签: Projection pursuit 投影寻踪 
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