endmemberien

Endmember analysis is a multivariate statistical technique used to identify and quantify the constituent components, or "endmembers," of a mixed system. In essence, it decomposes a set of observed data into a linear combination of a smaller number of idealized, pure components and their respective proportions. This method is particularly useful when the underlying pure components are not directly measurable or are not known a priori.

The fundamental assumption of endmember analysis is that any observed data point can be represented as a convex combination of the endmembers. This means that the proportions of the endmembers must be non-negative and sum to one. The technique aims to find the smallest number of endmembers that can adequately explain the variance in the data.

Common applications of endmember analysis include atmospheric science, where it is used to identify sources of air pollution; geology, for analyzing mineral mixtures and sediment compositions; and remote sensing, to unmix spectral signatures of pixels containing multiple surface types. The identified endmembers often represent distinct physical, chemical, or biological entities contributing to the observed variability. The output of the analysis typically includes the spectral or chemical signatures of the endmembers and their fractional abundances within each sample or observation.