MiPPS: A Generative Model for Multi-Manifold Clustering

We propose a generative model for high dimensional data consisting of intrinsically low dimensional clusters that are noisily sampled. The proposed model is a mixture of probabilistic principal surfaces (MiPPS) optimized using expectation maximization. We use a Bayesian prior on the model parameters to maximize the corresponding marginal likelihood. We also show empirically that this optimization can be biased towards a good local optimum by using our prior intuition to guide the initialization phase. The proposed unsupervised algorithm naturally handles cases where the data lies on multiple connected components of a single manifold and where the component manifolds intersect. In addition to clustering, we learn a functional model for the underlying structure of each component cluster as a parameterized hyper-surface in ambient noise. This model is used to learn a global embedding that we use for visualization of the entire dataset. We demonstrate the performance of MiPPS in separating and visualizing land cover types in a hyperspectral dataset.