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Stochastic neighbor embedding (SNE) and related nonlinear manifold learningalgorithms achieve high-quality low-dimensional representations of similaritydata, but are notoriously slow to train. We propose a generic formulation ofembedding algorithms that includes SNE and other existing algorithms, and studytheir relation with spectral methods and graph Laplacians. This allows us todefine several partial-Hessian optimization strategies, characterize theirglobal and local convergence, and evaluate them empirically. We achieve up totwo orders of magnitude speedup over existing training methods with a strategy(which we call the spectral direction) that adds nearly no overhead to thegradient and yet is simple, scalable and applicable to several existing andfuture embedding algorithms.

Partial-Hessian Strategies for Fast Learning of Nonlinear Embeddings