The radiogenic isotope heterogeneity of oceanic basalts is often assessed using 2D isotope ratio diagrams. But because the underlying data are at least six dimensional (87Sr/86Sr, 143Nd/144Nd, 176Hf/177Hf, and 208,207,206Pb/204Pb), it is important to examine isotopic affinities in multi-dimensional data space. Here, we apply t-distributed stochastic neighbor embedding (t-SNE), a multi-variate statistical data analysis technique, to a recent compilation of radiogenic isotope data of mid ocean ridge (MORB) and ocean island basalts (OIB). The t-SNE results show that the apparent overlap of MORB-OIB data trends in 2-3D isotope ratios diagrams does not exist in multi-dimensional isotope data space, revealing that there is no discrete "component" that is common to most MORB-OIB mantle sources on a global scale. Rather, MORB-OIB sample stochastically distributed small-scale isotopic heterogeneities. Yet, oceanic basalts with the same isotopic affinity, as identified by t-SNE, delineate several globally distributed regional domains. In the regional geodynamic context, the isotopic affinity of MORB and OIB is caused by capturing of actively upwelling mantle by adjacent ridges, and thus melting of mantle with similar origin in on, near, and off-ridge settings. Moreover, within a given isotopic domain, subsidiary upwellings rising from a common deep mantle root often feed OIB volcanism over large surface areas. Overall, the t-SNE results define a fundamentally new basis for relating isotopic variations in oceanic basalts to mantle geodynamics, and may launch a 21st century era of "chemical geodynamics."