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Page 6 of 19 Tang et al. J. Mater. Inf. 2025, 5, 38 https://dx.doi.org/10.20517/jmi.2025.05

Figure 2. The distribution of features (scaled on unit cube) of different subsets: blue - Nb, red - Nb -Nb Si , green - Nb -Nb Si , black -
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Si -Nb Si , magenta - Si -Nb Si alloys.
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Data distribution
The CE features result in a D = 40-dimensional space in this work [Supplementary Table 1]. The analysis of
data distribution in high-dimensional spaces is difficult, but we can get some insight from the distributions
of individual features for the five subsets shown in Figure 2. While the extent of their overlap is feature-
dependent, overall, these distributions indicate that the subsets only partially overlap and extend the volume
of feature space rather than increase the sampling density internally. This is also corroborated by Figure 3
where distributions of pairwise distances in the feature space are plotted. Within individual datasets,
pairwise distances are distributed around 1-2 and taper off after about 3. Among the subsets, the
distributions indicate that Si -Nb Si data occupy a relatively larger extent of space. The distances of the
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combined dataset are distributed until about 5, which is an indication that subsets cover different parts of
the feature space. Figure 4 shows the distribution of energy values in different datasets; these also only
partially overlap. Most of the elementary property features are relatively independent of each other due to
the nature of their definitions associated with alloying elements. Moreover, the structural characteristics of
various substitutions add further distinctions to the uniqueness of CE features. The variations in both
elements/compositions and structures lead to somewhat different feature distributions among each sub-
dataset. The partial decoupling of feature distributions implies that dataset combination in this case might
not necessarily facilitate ML; this is exactly what would be observed below.
ML methods
Kernel regression
In this study, we employed support vector regression (SVR) [44,45] with a radial basis function (RBF) kernel.
SVR is a powerful regression technique that excels in non-linear scenarios under sparse data, as the
nonlinear kernel provides high expressive power while regression coefficients are linear contributing to the
method’s robustness associated with linear regression. To optimize the performance of the SVR model, we
implemented hyperparameter optimization through a grid search strategy. This method involved
systematically exploring a pre-defined set of hyperparameter values to identify the optimal combination that
minimizes prediction error. Key hyperparameters optimized for the SVR include the penalty
(regularization) parameter and the coefficient gamma g for the kernel function, which significantly