Weighted-Sum of Gaussian Process Latent Variable Models
This work addresses signal separation in spectroscopy and similar fields where conditions cause signal variations, but it is incremental as it builds on existing GPLVM methods.
The authors tackled the problem of signal separation when signals vary non-linearly with latent variables by augmenting Gaussian Process Latent Variable Models to handle weighted sums of pure component signals, demonstrating applicability in spectroscopy and other domains with datasets like near-infrared spectroscopy under varying temperatures.
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) for 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 arbitrary non-linear variations in the signals while being able to incorporate useful priors for the linear weights, such as summing-to-one. 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 dataset with varying temperatures, a simulated dataset for identifying flow configuration through a pipe, and a dataset for determining the type of rock from its reflectance.