Landmarking Manifolds with Gaussian Processes
Dawen Liang, John William Paisley · 2015
We present an algorithm for finding landmarks along a manifold. These landmarks provide a small set of locations spaced out along the man-ifold such that they capture the low-dimensional nonlinear structure of the data embedded in the high-dimensional space. The approach does not select points directly from the dataset, but instead we optimize each landmark by moving along the continuous manifold space (as approximated by the data) according to the gradient of an objec-tive function. We borrow ideas from active learn-ing with Gaussian processes to define the ob-jective, which has the property that a new land-mark is “repelled ” by those currently selected, allowing for exploration of the manifold. We de-rive a stochastic algorithm for learning with large datasets and show results on several datasets, in-cluding the Million Song Dataset and articles from the New York Times. 1.