The article starts by explaining that computing active subspaces is a useful tool for dimension reduction, particularly when dealing with high-dimensional data. The author provides an overview of the problem and its importance in various fields.
Plot of Sufficient Summary Plots
The author introduces the concept of sufficient summary plots, which are used to visualize the quality of the computed active subspace. These plots provide information about the performance of different methods and help select the best one for the task at hand (Figure 3).
Interpreting Sufficient Summary Plots
The author explains how to interpret the sufficient summary plots, which involve comparing the outputs of each function on the original data and the rotated data. This comparison helps identify the best method for dimension reduction. The author highlights the importance of considering both the pairwise plot of the original outputs and their outputs on the rotated data 1 (Appendix A).
Synthetic Problem
The article then shifts focus to a synthetic problem where only a subset of methods has been shown, with the rest given in Figure 4 in Appendix A. The author explains that this plot helps visualize the quality of the computed active subspace and compares the performance of different methods.
Keywords: Dimension Reduction, Symmetric Positive Definites Matrices, Common Principal Component Analysis, Multi-Objective Optimization.
Conclusion
In conclusion, computing active subspaces is an essential tool for dimension reduction in various fields. The plot of sufficient summary plots provides valuable information about the performance of different methods and helps select the best one for the task at hand. By understanding this concept, researchers and practitioners can make informed decisions when dealing with high-dimensional data.
