Generative Simplex Mapping: Non-Linear Endmember Extraction and Spectral Unmixing for Hyperspectral Imagery

We introduce a new model for non-linear endmember extraction and spectral unmixing of hyperspectral imagery called Generative Simplex Mapping (GSM). The model represents endmember mixing using a latent space with points sampled within a (n−1)-simplex corresponding to the abundance of n unique sources. Points in this latent space are non-linearly mapped to reflectance spectra via a flexible function combining linear and non-linear mixing. Due to the probabilistic formulation of the GSM, spectral variability is also estimated by a precision parameter describing the distribution of observed spectra. Model parameters are determined using a generalized expectation-maximization algorithm. In the event of purely linear mixing, non-linear contributions are naturally driven to zero. The GSM outperforms three varieties of non-negative matrix factorization for both endmember extraction accuracy and abundance estimation on a synthetic data set of linearly mixed spectra from the USGS spectral library. In a second experiment, the GSM is applied to real hyperspectral imagery captured over a pond in North Texas. The model is able to accurately identify spectral signatures corresponding to near-shore algae, water, and rhodmaine tracer dye introduced into the pond to simulate water contamination by a localized source. Abundance maps generated using the GSM accurately track evolution of the dye plume as it mixes into the surrounding water.