Akgüller Ömer, Balcı Mehmet Ali, Cioca Gabriela
Faculty of Science, Department of Mathematics, Mugla Sitki Kocman University, Muğla 48000, Turkey.
Faculty of Medicine, Preclinical Department, Lucian Blaga University of Sibiu, 550024 Sibiu, Romania.
Molecules. 2024 Aug 17;29(16):3902. doi: 10.3390/molecules29163902.
This study conducts an in-depth analysis of clustering small molecules using spectral geometry and deep learning techniques. We applied a spectral geometric approach to convert molecular structures into triangulated meshes and used the Laplace-Beltrami operator to derive significant geometric features. By examining the eigenvectors of these operators, we captured the intrinsic geometric properties of the molecules, aiding their classification and clustering. The research utilized four deep learning methods: Deep Belief Network, Convolutional Autoencoder, Variational Autoencoder, and Adversarial Autoencoder, each paired with k-means clustering at different cluster sizes. Clustering quality was evaluated using the Calinski-Harabasz and Davies-Bouldin indices, Silhouette Score, and standard deviation. Nonparametric tests were used to assess the impact of topological descriptors on clustering outcomes. Our results show that the DBN + k-means combination is the most effective, particularly at lower cluster counts, demonstrating significant sensitivity to structural variations. This study highlights the potential of integrating spectral geometry with deep learning for precise and efficient molecular clustering.
本研究使用光谱几何和深度学习技术对小分子聚类进行了深入分析。我们应用了一种光谱几何方法将分子结构转换为三角网格，并使用拉普拉斯 - 贝尔特拉米算子来推导重要的几何特征。通过检查这些算子的特征向量，我们捕捉到了分子的内在几何特性，有助于对其进行分类和聚类。该研究使用了四种深度学习方法：深度信念网络、卷积自动编码器、变分自动编码器和对抗自动编码器，每种方法都与不同聚类大小的k均值聚类相结合。使用卡林斯基 - 哈拉巴斯指数和戴维斯 - 布尔丁指数、轮廓系数和标准差来评估聚类质量。使用非参数检验来评估拓扑描述符对聚类结果的影响。我们的结果表明，深度信念网络 + k均值组合是最有效的，特别是在聚类数量较少时，对结构变化表现出显著的敏感性。本研究突出了将光谱几何与深度学习相结合用于精确高效分子聚类的潜力。
