npj: 扫描探针显微镜插上机器学习的翅膀——材料探幽更为便捷

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材料科学中的 “大数据”不仅指代数据集体量庞大，也指代其种类繁杂。表征材料全参数空间所需的测量次数极多以至难以实现。

因此，有限数据构成的数据集只能算“小”数据，这导致高阶统计方法失效，无监督学习方法的选择仅限于利用低阶统计的方法。扫描探针显微镜的功能成像模式，可测量外部因素（如温度或磁场）变化导致的材料性质变化。来自德国杜伊斯堡-埃森大学和葡萄牙阿威罗大学的Harsh Trivedi及其同事，以此作为一个有趣的“小”数据案例，报道了采用可变磁场压电响应力显微镜（PFM）对多铁复合材料的研究，其中压电响应的磁场依赖性，因实验限制而采取粗步长测量；他们基于密度聚类（DBSCAN）和主成分分析算法（PCA）所得到的关键特征，成功地反映了两种材料之间的磁电响应差异，从而证明了运用无监督机器学习技术能从较少的测量结果中提取重要规律。这一技术方便又成本低廉，有望在功能材料的分析中得到更广泛的应用。

该文近期发表于npj Computational Materials 4: 28 (2018) ，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。

Sequential piezoresponse force microscopy and the ‘small-data’ problem

Harsh Trivedi, Vladimir V. Shvartsman, Marco S. A. Medeiros, Robert C. Pullar & Doru C. Lupascu 

The term big-data in the context of materials science not only stands for the volume, but also for the heterogeneous nature of the characterization data-sets. This is a common problem in combinatorial searches in materials science, as well as chemistry. However, these data-sets may well be ‘small’ in terms of limited step-size of the measurement variables. Due to this limitation, application of higher-order statistics is not effective, and the choice of a suitable unsupervised learning method is restricted to those utilizing lower-order statistics. As an interesting case study, we present here variable magnetic-field Piezoresponse Force Microscopy (PFM) study of composite multiferroics, where due to experimental limitations the magnetic field dependence of piezoresponse is registered with a coarse step-size. An efficient extraction of this dependence, which corresponds to the local magnetoelectric effect, forms the central problem of this work. We evaluate the performance of Principal Component Analysis (PCA) as a simple unsupervised learning technique, by pre-labeling possible patterns in the data using Density Based Clustering (DBSCAN). Based on this combinational analysis, we highlight how PCA using non-central second-moment can be useful in such cases for extracting information about the local material response and the corresponding spatial distribution

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