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.

在材料科学中，大数据一词不仅代表体积，而且代表表征数据集的异构性质。在材料科学和化学的组合搜索中，这是一个普遍的问题。但是，就测量变量的有限步长而言，这些数据集可能很小。由于该限制，高阶统计的应用无效，并且适合的无监督学习方法的选择仅限于那些利用低阶统计的学习方法。作为一个有趣的案例研究，我们在这里介绍了复合多铁磁材料的可变磁场压电响应力显微镜（PFM）研究，其中由于实验限制，压电响应的磁场依赖性被记录为一个大步长。这种依赖关系的有效提取对应于局部磁电效应，构成了这项工作的核心问题。通过使用基于密度的聚类（DBSCAN）预先标记数据中的可能模式，我们评估了主成分分析（PCA）作为一种简单的无监督学习技术的性能。基于此组合分析，我们强调了使用非中心第二矩的PCA在此类情况下如何可用于提取有关局部材料响应和相应空间分布的信息。