With the development of machine learning technology, research cases for spatial estimation through machine learning approach (MLA) in addition to the traditional geostatistical techniques are increasing. MLA has the advantage that spatial estimation is possible without stationary hypotheses of data, but it is possible for the prediction results to ignore spatial autocorrelation. In recent studies, it was considered by using a distance matrix instead of raw coordinates. Although, the performance of spatial estimation could be improved through this approach, the computational complexity of MLA increased rapidly as the number of sample points increased. In this study, we developed a method to reduce the computational complexity of MLA while considering spatial autocorrelation. Principal component analysis is applied to it for extracting spatial features and reducing dimension of inputs. To verify the proposed approach, indicator Kriging was used as a benchmark model, and each performance of MLA was compared when using raw coordinates, distance vector, and spatial features extracted from distance vector as inputs. The proposed approach improved the performance compared to previous MLA and showed similar performance compared with Kriging. We confirmed that extracted features have characteristics of rigid classification in spatial estimation; on this basis, we conclude that the model could improve performance.

中文翻译：

---

基于机器学习的坐标信息空间特征空间估计方法

随着机器学习技术的发展，除传统的地统计技术外，通过机器学习方法（MLA）进行空间估计的研究案例也在不断增加。MLA具有以下优点：无需数据的固定假设就可以进行空间估计，但是预测结果有可能忽略空间自相关。在最近的研究中，考虑通过使用距离矩阵代替原始坐标。尽管可以通过这种方法提高空间估计的性能，但是MLA的计算复杂度随着采样点数量的增加而迅速增加。在这项研究中，我们开发了一种在考虑空间自相关的同时降低MLA的计算复杂度的方法。主成分分析可用于提取空间特征并减小输入的维数。为了验证所提出的方法，指标Kriging被用作基准模型，并且在使用原始坐标，距离矢量和从距离矢量提取的空间特征作为输入时，比较了MLA的每种性能。与以前的MLA相比，所提出的方法提高了性能，并且与Kriging相比显示了相似的性能。我们确认提取的特征在空间估计中具有刚性分类的特征；在此基础上，我们得出结论，该模型可以提高性能。从距离矢量提取的空间特征作为输入。与先前的MLA相比，所提出的方法提高了性能，并且与Kriging相比显示了相似的性能。我们确认提取的特征在空间估计中具有刚性分类的特征；在此基础上，我们得出结论，该模型可以提高性能。从距离矢量提取的空间特征作为输入。与以前的MLA相比，所提出的方法提高了性能，并且与Kriging相比显示了相似的性能。我们确认提取的特征在空间估计中具有刚性分类的特征；在此基础上，我们得出结论，该模型可以提高性能。