Kansara, S., Parashar, S., and Xue, Z., "Effective Decision Making and Data Visualization Using Partitive Clustering and Principal Component Analysis (PCA) for High Dimensional Pareto Frontier Data," SAE Int. J. Mater. Manf. 8(2):336-343, 2015, doi:10.4271/2015-01-0460.
Decision making in engineering design is complicated, especially when dealing with high-dimensional data. Modern software tools are able to produce a large amount of data while performing optimization studies. A typical optimization problem with many objectives may produce 100s or even 1000s of Pareto Optimal solutions. It is a challenge to analyze this data and make a decision about which design/s to choose for further testing or as a final design.To tackle the problem, two data analysis techniques are used in this paper. Partitive Clustering (PC) is used to locate groups of similar designs in the dataset while Principal Component Analysis (PCA) is used to reduce the dimensionality of the data and visualize it in two and three dimensions. Although these techniques can be used independently, when used together, they prove to be a tremendous help in decision making. This paper underlines the benefit of using these two methods together.Two multi-objective engineering design optimization problems are chosen to demonstrate the use of PC and PCA together. It is assumed that optimization has been performed and Pareto data is available. The task is to choose a handful of representative designs from this set for further analysis. The aforementioned technique of using Partitive Clustering and Principal Component Analysis together is applied to dataset for both problems. It will be shown how PC+PCA together can easily and effectively reduce the decision set while preserving the overall trade-off. Fewer design choices and fewer decision attributes can be visualized and communicated more easily and can certainly help the decision maker to pick a reasonable final solution.