Learning Manifolds from Non-stationary Streaming Data

Streaming adaptations of manifold learning based dimensionality reduction methods, such as Isomap, typically assume that the underlying data distribution is stationary. Such methods are not equipped to detect or handle sudden changes or gradual drifts in the distribution generating the stream. We prove that a Gaussian Process Regression (GPR) model that uses a manifold-specific kernel function and is trained on an initial batch of sufficient size, can closely approximate the state-of-art streaming Isomap algorithm. The predictive variance obtained from the GPR prediction is then shown to be an effective detector of changes in the underlying data distribution. Results on several synthetic and real data sets show that the resulting algorithm can effectively learns lower dimensional representation of high dimensional data in a streaming setting, while identify shifts in the generative distribution.