In many fields of science there are
multivariate observations which are generated by
a (physical) linear mixing process of contributions from different sources.
If it is assumed that the composition of the sources
is constant for different observations, these observations are, up to
measurement error, non-negative
linear combinations of a fixed set of so-called source profiles which
characterize the sources. The goal of linear unmixing is to recover
both the source profiles and the source activities (also called scores)
from a multivariate dataset.
We present a new parametric mixing model which assumes a multivariate
lognormal distribution for the scores. This model is proved to be
identifiable. To calculate the MLE we propose the combination of
two variants of the MCEM algorithm. The proposed model is applied
to simulated datasets and to air pollution measurements from Zurich.
In addition to the basic model we discuss several extensions.
Keywords: linear mixing model, source apportionment, latent variables, identifiability, MCEM algorithm