Receptor models are mathematical approaches for quantifying the contribution of sources to samples based on the composition or fingerprints of the sources. The composition or speciation is determined using analytical methods appropriate for the media, and key species or combinations of species are needed to separate impacts. A speciated data set can be viewed as a data matrix X of i by j dimensions, in which i number of samples and j chemical species were measured, with uncertainties u. The goal of receptor models is to solve the chemical mass balance (CMB) between measured species concentrations and source profiles with number of factors p, the species profile f of each source, and the amount of mass g contributed by each factor to each individual sample.