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In this study, we establish a basis for selecting similarity measures whenapplying machine learning techniques to solve materials science problems. Thisselection is considered with an emphasis on the distinctiveness betweenmaterials that reflect their nature well. We perform a case study with adataset of rare-earth transition metal crystalline compounds represented usingthe Orbital Field Matrix descriptor and the Coulomb Matrix descriptor. Weperform predictions of the formation energies using k-nearest neighborsregression, ridge regression, and kernel ridge regression. Through detailedanalyses of the yield prediction accuracy, we examine the relationship betweenthe characteristics of the material representation and similarity measures, andthe complexity of the energy function they can capture. Empirical experimentsand theoretical analysis reveal that similarity measures and kernels thatminimize the loss of materials distinctiveness improve the predictionperformance.

Measuring the Similarity between Materials with an Emphasis on the Materials Distinctiveness