We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate cluster validity indices as a means to find the correct number of confinement dimensionalities to be used as an input to the clustering algorithms. Subsequently, we analyze the performance of the two clustering algorithms when compared to the direct application of the scaling method without clustering. We find that the clustering approach provides more physically meaningful results, but may struggle with identifying the correct set of confinement dimensionalities. We conclude that the most accurate outcome is obtained by first applying the direct scaling to find the correct set of confinement dimensionalities and subsequently employing clustering to refine the results. Moreover, our model-based algorithm outperforms the standard k-means++ clustering.

翻译：我们采用无监督机器学习来提高我们最近提出的波约束分析缩放方法[1]的准确性。该方法运用了标准的k-means++算法以及我们基于模型的算法。我们研究聚类有效性指标，以确定作为聚类算法输入的正确约束维度数量。随后，我们分析了两种聚类算法与直接应用无聚类缩放方法相比的性能。研究发现，聚类方法能够提供更具物理意义的结果，但可能在识别正确的约束维度集合方面存在困难。我们得出结论，最准确的结果是通过先应用直接缩放方法找到正确的约束维度集合，再使用聚类来优化结果。此外，我们的基于模型算法优于标准的k-means++聚类。