2009 Ninth IEEE International Conference on Data Mining 2009
DOI: 10.1109/icdm.2009.74
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Non-negative Laplacian Embedding

Abstract: Laplacian embedding provides a low dimensional representation for a matrix of pairwise similarity data using the eigenvectors of the Laplacian matrix. The true power of Laplacian embedding is that it provides an approximation of the Ratio Cut clustering. However, Ratio Cut clustering requires the solution to be nonnegative. In this paper, we propose a new approach, nonnegative Laplacian embedding, which approximates Ratio Cut clustering in a more direct way than traditional approaches. From the solution of our… Show more

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Cited by 31 publications
(43 citation statements)
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“…Our result is different from that in [19], where the authors proved that spectral clustering with Ncut objective function is equivalent to the symmetrical NMF which factorizes the symmetrical pairwise similarity matrix as a symmetrical product (i.e., product of a non-negative matrix with its transpose). Our result is also different from that of [20] where the authors consider the non-negative Laplacian embedding (which is equivalent to Rcut spectral clustering), which is also to factorize a symmetrical non-negative matrix into a symmetrical product. In the present work, we consider the data matrix itself.…”
Section: Introductioncontrasting
confidence: 77%
See 3 more Smart Citations
“…Our result is different from that in [19], where the authors proved that spectral clustering with Ncut objective function is equivalent to the symmetrical NMF which factorizes the symmetrical pairwise similarity matrix as a symmetrical product (i.e., product of a non-negative matrix with its transpose). Our result is also different from that of [20] where the authors consider the non-negative Laplacian embedding (which is equivalent to Rcut spectral clustering), which is also to factorize a symmetrical non-negative matrix into a symmetrical product. In the present work, we consider the data matrix itself.…”
Section: Introductioncontrasting
confidence: 77%
“…Luo et al [20] have drawn similar conclusion for the nonnegative Laplacian embedding (which is equivalent to Rcut spectral clustering), which says that the nonnegative Laplacian embedding is equivalent to the following symmetric NMF:…”
Section: Spectral Clustering As Nmfmentioning
confidence: 71%
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“…The graph spectral techniques are also adopted for dimensionality reduction in multidimensional space. Representative works such as Isomap [5], Locally Linear Embedding [6], and Laplacian Embedding [7], can all be interpreted in a general graph embedding framework with different choices of the graph structures. Tetsuo et al [8] study the trade-off between time and space of graph embedding.…”
Section: Related Workmentioning
confidence: 99%