Abstract Alternating least squares within the multivariate curve resolution framework has seen a lot of practical applications and shows their distinction with their relatively simple and flexible implementation. However, the limitations of least squares should be carefully considered when deviating from the standard assumed data structure. Within this work, we highlight the effects of noise in the presence of minor components, and we propose a novel weighting scheme within the weighted multivariate curve‐resolution‐alternating least squares framework to resolve it. Two simulated and one Raman imaging case are investigated by comparing the novel methodology against standard multivariate curve resolution‐alternating least squares and essential spectral pixel selection. A trade‐off is observed between current methods, whereas the novel weighting scheme demonstrates a balance where the benefits of the previous two methods are retained.