摘要： 高维多目标优化问题的高维解集由于目标和解的个数众多,对其可视化较为困难。针对上述问题,结合降维和非降维数据分析技术,提出一种高维多目标优化的可视化方法。该方法对高维多目标算法运行后的一组解集进行预处理,运用主成分分析方法分析数据特征,获取转换后的数据及其对应的贡献率。按照贡献率由大到小的顺序调整转换后的数据列顺序;利用主成分贡献率求解转换后数据的行间距离,运行分级聚类算法并对转换后的数据按行排序,重新组织数据,将最终的结果用热图显示。实验结果表明,该方法既能使用户明确转换后每个目标所占的贡献率,又能取得较满意的视觉效果,便于用户理解数据的整体分布并做出决策。
关键词:
主成分分析,
热图,
高维多目标优化,
可视化,
分级聚类,
降维
Abstract: It is very difficult to visualize the high dimensional solution set of the multi-objective optimization problem
for its large number of objective and solution． To solve the above problems,this paper proposes a new method to visualize the high dimensional solution sets with dimensionality reduction and non-dimensionality reduction techniques of data analysis． This method pretreats the solution set of the multi-objective optimization algorithm,uses Principal Component Analysis(PCA) to analyze the characteristics of the data and get the converted data and its corresponding contribution rate． According to the contribution rate order,it adjusts the the order of columns of the converted data,and calculates the distance between the rows of the converted data with the contribution rate use and runs the hierarchical clustering algorithms based on the row distance to reorder the rows and reorganize the data． It displays the result on heat map． Experimental results show that the method can let the user know the contribution rate of the each converted target, offer satisfactory visual effects,facilitate the understanding of the distribution of the data and make decisions．
Key words:
Principal Component Analysis ( PCA ),
heat map,
high dimensional multi-objective optimization,
visualization,
hierarchical clustering,
dimension reduction
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