Fig. 3

Unsupervised learning analysis of the 3D Ce valence map. a Scatter plot of mean Ce valence (m) and its standard deviation (sd) for 42 × 42 × 42 nm3 (3 × 3 × 3 voxels) domains of partially oxidized Pt/CZ-x particles, and classification of correlation trends using a Gaussian mixture model. Red: G1; orange: G2; green: G3; blue: G4. The white crosses indicate the Gaussian centers for G1–G4; μk (k = 1–4): Gaussian center; Σk: covariance matrix. b 3D rendering of the distribution of the four correlation groups between m and sd for 42 × 42 × 42 nm3 (3 × 3 × 3 voxels) domains of partially oxidized Pt/CZ-x particles, and c series of slices showing the 3D distributions of the four correlation groups along the z direction. The scale bar for b and c is 700 nm. d Plot of the proportion of each correlation group in c with respect to distance from the particle surface