Bio-Microsystems Integration Laboratory, Department of Biomedical Sciences and Engineering, National Central University, Taoyuan City, Taiwan.
Shing-Tung Yau Center, National Chiao Tung University, 1001 University Road, Hsinchu City, Taiwan.
Sci Rep. 2018 Jan 11;8(1):557. doi: 10.1038/s41598-017-18931-5.
By introducing the methods of machine learning into the density functional theory, we made a detour for the construction of the most probable density function, which can be estimated by learning relevant features from the system of interest. Using the properties of universal functional, the vital core of density functional theory, the most probable cluster numbers and the corresponding cluster boundaries in a studying system can be simultaneously and automatically determined and the plausibility is erected on the Hohenberg-Kohn theorems. For the method validation and pragmatic applications, interdisciplinary problems from physical to biological systems were enumerated. The amalgamation of uncharged atomic clusters validated the unsupervised searching process of the cluster numbers and the corresponding cluster boundaries were exhibited likewise. High accurate clustering results of the Fisher's iris dataset showed the feasibility and the flexibility of the proposed scheme. Brain tumor detections from low-dimensional magnetic resonance imaging datasets and segmentations of high-dimensional neural network imageries in the Brainbow system were also used to inspect the method practicality. The experimental results exhibit the successful connection between the physical theory and the machine learning methods and will benefit the clinical diagnoses.
通过将机器学习方法引入密度泛函理论，我们为构建最可能的密度函数找到了一条迂回道路，可以通过从感兴趣的系统中学习相关特征来估计。利用密度泛函理论的重要核心——普遍函数的性质，可以同时自动确定研究系统中的最可能团簇数量和相应的团簇边界，并在 Hohenberg-Kohn 定理的基础上建立合理性。为了验证方法的有效性和实际应用，列举了从物理到生物系统的跨学科问题。未带电原子团簇的融合验证了团簇数量和相应团簇边界的无监督搜索过程。Fisher's iris 数据集的高精度聚类结果表明了所提出方案的可行性和灵活性。从低维磁共振成像数据集进行脑肿瘤检测和 Brainbow 系统中高维神经网络图像的分割也用于检查方法的实用性。实验结果展示了物理理论和机器学习方法之间的成功连接，将有助于临床诊断。
