We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. %The accuracy of the scaling method decreases for systems of small size, which are however the most interesting ones both experimentally and computationally. 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最近提出的波约束分析标度方法[1]的准确性。对于小尺寸系统，标度方法的准确性会下降，而这些系统在实验和计算中却是最令人感兴趣的。我们使用了标准的k-means++算法以及我们自己的基于模型的算法。我们研究了聚类有效性指标，以此作为找到正确的约束维数集的方法，并将其用作聚类算法的输入。随后，我们分析了两种聚类算法与直接应用标度方法（无聚类）相比的性能。我们发现，聚类方法能提供更具物理意义的结果，但可能在识别正确的约束维数集方面存在困难。我们得出结论，最准确的结果是通过首先应用直接标度法找到正确的约束维数集，然后使用聚类来细化结果。此外，我们基于模型的算法优于标准的k-means++聚类。