  Extracting meaningful information from high-dimensional data poses a
formidable modeling challenge, particularly when the data is obscured by noise
or represented through different modalities. This research proposes a novel
non-parametric modeling approach, leveraging the Gaussian process (GP), to
characterize high-dimensional data by mapping it to a latent low-dimensional
manifold. This model, named the latent discriminative generative decoder
(LDGD), employs both the data and associated labels in the manifold discovery
process. We derive a Bayesian solution to infer the latent variables, allowing
LDGD to effectively capture inherent stochasticity in the data. We demonstrate
applications of LDGD on both synthetic and benchmark datasets. Not only does
LDGD infer the manifold accurately, but its accuracy in predicting data points'
labels surpasses state-of-the-art approaches. In the development of LDGD, we
have incorporated inducing points to reduce the computational complexity of
Gaussian processes for large datasets, enabling batch training for enhanced
efficient processing and scalability. Additionally, we show that LDGD can
robustly infer manifold and precisely predict labels for scenarios in that data
size is limited, demonstrating its capability to efficiently characterize
high-dimensional data with limited samples. These collective attributes
highlight the importance of developing non-parametric modeling approaches to
analyze high-dimensional data.
