Linear Unmixing of Multivariate Observations: A Structural Model
نویسندگان
چکیده
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.
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