Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering

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Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering (2004)

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by Yoshua Bengio , Jean-François Paiement , Pascal Vincent , Olivier Delalleau , Nicolas Le Roux , Marie Ouimet

Venue:	In Advances in Neural Information Processing Systems
Citations:	139 - 3 self

BibTeX

@INPROCEEDINGS{Bengio04out-of-sampleextensions,
    author = {Yoshua Bengio and Jean-François Paiement and Pascal Vincent and Olivier Delalleau and Nicolas Le Roux and Marie Ouimet},
    title = {Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering},
    booktitle = {In Advances in Neural Information Processing Systems},
    year = {2004},
    pages = {177--184},
    publisher = {MIT Press}
}

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Abstract

Several unsupervised learning algorithms based on an eigendecomposition provide either an embedding or a clustering only for given training points, with no straightforward extension for out-of-sample examples short of recomputing eigenvectors. This paper provides a unified framework for extending Local Linear Embedding (LLE), Isomap, Laplacian Eigenmaps, Multi-Dimensional Scaling (for dimensionality reduction) as well as for Spectral Clustering. This framework is based on seeing these algorithms as learning eigenfunctions of a data-dependent kernel.

Keyphrases

spectral clustering out-of-sample extension straightforward extension multi-dimensional scaling out-of-sample example laplacian eigenmaps learning eigenfunctions eigendecomposition provide unified framework data-dependent kernel training point dimensionality reduction local linear embedding

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