  This work develops a Bayesian non-parametric approach to signal separation
where the signals may vary according to latent variables. Our key contribution
is to augment Gaussian Process Latent Variable Models (GPLVMs) to incorporate
the case where each data point comprises the weighted sum of a known number of
pure component signals, observed across several input locations. Our framework
allows the use of a range of priors for the weights of each observation. This
flexibility enables us to represent use cases including sum-to-one constraints
for estimating fractional makeup, and binary weights for classification. Our
contributions are particularly relevant to spectroscopy, where changing
conditions may cause the underlying pure component signals to vary from sample
to sample. To demonstrate the applicability to both spectroscopy and other
domains, we consider several applications: a near-infrared spectroscopy data
set with varying temperatures, a simulated data set for identifying flow
configuration through a pipe, and a data set for determining the type of rock
from its reflectance.
