Spectral graph theoretic methods such as Laplacian Eigenmaps are among the most popular algorithms for manifold learning and clustering. One drawback of these methods is, however, that they do not provide a natural out-of-sample extension. They only provide an embedding for the given training data. We propose to use sparse grid functions to approximate the eigenfunctions of the Laplace-Beltrami operator. We then have an explicit mapping between ambient and latent space. Thus, out-of-sample points can be mapped as well. We present results for synthetic and real-world examples to support the effectiveness of the sparse-grid-based explicit mapping. © 2011 Springer-Verlag.
CITATION STYLE
Peherstorfer, B., Pflüger, D., & Bungartz, H. J. (2011). A sparse-grid-based out-of-sample extension for dimensionality reduction and clustering with Laplacian eigenmaps. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7106 LNAI, pp. 112–121). https://doi.org/10.1007/978-3-642-25832-9_12
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