Manifold denoising with Gaussian Process Latent Variable Models

For a finite set of points lying on a lower dimensional manifold embedded in a high-dimensional data space, algorithms have been developed to study the manifold structure. However, many algorithms will fail if data are noisy. We propose a method based on Gaussian process latent variable models for manifold denoising with the following advantages: (1), it is probabilistic, which naturally handles noise and missing data; (2), it works well for very high dimensional data with small sample size; (3), it can recover the low-dimensional submanifolds corrupted by high-dimensional noise; and (4), it deals well with multimodal manifolds.