Recognition of effective signal separation as an emergence of semantic framework: beyond the indeterminacy of non-negative matrix factorization

Can mathematical indeterminacy explain human wandering and recognition? Non-negative matrix factorization (NMF) inherently suffers from solution indeterminacy. Reframing this ambiguity as a functional domain mirroring perception, derived from physical boundary conditions of non-negative chemical reality, we propose Intellectual NMF. This model mimics how the brain applies constraints to resolve ambiguous perception and construct semantic frameworks, showing isomorphism to solving physical boundary value problems. By integrating data-driven frameworks with constraints, Intellectual NMF successfully resolves overlapping physical chemistry signals—such as hair protein Raman spectra—and distinguishes human perceptual patterns, bridging computational signal separation and human recognition.