Visualization, Clustering, and Graph Generation of Optimization Search Trajectories for Evolutionary Computation Through Topological Data Analysis: Application of the Mapper
Visualization, Clustering, and Graph Generation of Optimization Search Trajectories for Evolutionary Computation Through Topological Data Analysis: Application of the Mapper
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DOI：
10.1109/cec55065.2022.9870341
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发表时间：
2022-07
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影响因子：
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通讯作者：
Arisa Toda;S. Hiwa;Kensuke Tanioka;Tomoyuki Hiroyasu
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作者：
Arisa Toda;S. Hiwa;Kensuke Tanioka;Tomoyuki Hiroyasu
拓扑数据分析(TDA)是一种分析技术，可以揭示复杂或高维数据中固有的骨架结构。在本研究中，我们将从进化计算的多次试验中获得的优化搜索轨迹视为单个数据集，并将每个搜索轨迹的异同表示为一个拓扑网络。Mapper是TDA工具之一，它包含了图形生成过程中的数据降维和聚类。为了解决这个问题，我们对Mapper算法进行了改进。提出的框架是进化计算的Mapper(EvoMapper)。在数值实验中，在不同的初始点进行了多次搜索，以提供对EvoMapper有效性的基本审查。检验函数为One-max和Rastrigin函数。构建并可视化了一个图表，提供了对分析结果的直观见解。此外，达到最优解的试验和没有达到最优解的试验被聚集在一起，发现它们具有相似的拓扑。
Topological Data Analysis (TDA) is an analytical technique that can reveal the skeletal structure inherent in complex or high-dimensional data. In this study, we considered the optimization search trajectories obtained from multiple trials of evolutionary computation as a single data set and challenged to represent the similarities and differences of each search trajectory as a topological network. Mapper is one of TDA tools and it includes the dimensionality reduction of data and clustering during graph generation. We modified Mapper to apply into this problem. The proposed framework is Mapper for evolutionary computation (EvoMapper). In the numerical experiments, multiple searches were conducted at different initial points to provide a basic review of the effectiveness of EvoMapper. The test functions were the One-max and Rastrigin function. A graph providing intuitive insights on the analysis results was constructed and visualized. In addition, the trials that reached the optimal solution and those that did not were clustered and found to have similar topology.