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.

翻译：本文提出了一种贝叶斯非参数方法，用于解决信号随潜变量变化的分离问题。核心贡献在于扩展高斯过程潜变量模型（GPLVMs），使其能够处理每个数据点由已知数量的纯成分信号加权求和（在多个输入位置观测）的情况。该框架允许为每个观测的权重采用多种先验分布，这种灵活性使得我们能够表征包括成分比例估算的求和为一约束和分类的二元权重在内的应用场景。本研究的贡献对光谱学领域尤为重要——在该领域，变化的环境条件可能导致潜在纯成分信号在样本间发生变化。为展示该方法在光谱学及其他领域的适用性，我们验证了三个应用：含温度变化的近红外光谱数据集、用于识别管道流动配置的模拟数据集，以及通过岩石反射率判定岩石类型的数据集。