Deep-sea sediments highly enriched in rare-earth elements (REE), termed “REE-rich mud,” have recently attracted attention as a potential mineral resource for industrially critical metals. Biogenic apatite or fish teeth and bone debris comprises the mineral phase which primarily hosts REE in deep-sea sediments; thus, biogenic apatite is a key material to decipher the formation process of REE-rich mud. We investigated the key process(es) controlling REE-enrichment in biogenic apatite through a novel data-driven approach. We analyzed the in situ chemical composition of biogenic apatite grains collected from REE-rich mud in the western North Pacific Ocean. Subsequently, the dataset of 685 analytical points × 35 elements was statistically analyzed via independent component analysis. Our new approach extracted four independent components (ICs) as geochemically meaningful and statistically independent signatures: substitution of elements into apatite lattice (IC1), the relatively rapid adsorption process that occurred at the sediment-water interface (IC2), elemental transfer from volcanic materials during early diagenesis (IC3), and metalliferous or detrital impurities physically adhering to or infiltrating apatite grains (IC4). Data distributions within the real and IC spaces provide insights into physicochemical processes involving elemental incorporation into biogenic apatite. We argue that after settlement on the seafloor, the fish bones and dentine in teeth adsorb REE from the overlying seawater and REE-enriched porewater at the sediment-water interface, resulting in the preferential enrichment of light rare-earth elements into apatite from these solutions. Further, that REE adsorbed on the apatite crystal surface was incorporated into the crystal lattice via substitution. The IC2 signal was intensified in the layers of “extremely REE-rich mud”, suggesting that the REE adsorption process was facilitated during the formation of layers with remarkably high bulk-sediment REE contents. This may reflect an increased supply of REE-carrier substances such as organic matter, which degraded on the seafloor and released REE at the sediment-water interface, which is associated with changes in paleoceanographic conditions including ocean surface bioproductivity.