TY - GEN
T1 - A sparse-grid-based out-of-sample extension for dimensionality reduction and clustering with Laplacian eigenmaps
AU - Peherstorfer, Benjamin
AU - Pflüger, Dirk
AU - Bungartz, Hans Joachim
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - clustering
KW - manifold learning
KW - sparse grids
KW - spectral methods
UR - http://www.scopus.com/inward/record.url?scp=83755187922&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=83755187922&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-25832-9_12
DO - 10.1007/978-3-642-25832-9_12
M3 - Conference contribution
AN - SCOPUS:83755187922
SN - 9783642258312
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 112
EP - 121
BT - AI 2011
T2 - 24th Australasian Joint Conference on Artificial Intelligence, AI 2011
Y2 - 5 December 2011 through 8 December 2011
ER -