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On Spectral Clustering: Analysis and an algorithm

On Spectral clustering : Analysis and an algorithm Andrew Y. Ng CS Division Berkeley Michael I. Jordan CS Div. & Dept. of Stat. Berkeley Abstract Yair Weiss School of CS & Engr. The Hebrew Univ. Despite many empirical successes of Spectral clustering methods-algorithms that cluster points using eigenvectors of matrices de-rived from the data-there are several unresolved issues. First, there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering .

lReaders familiar with spectral graph theory [3) may be more familiar with the Lapla­ cian 1-L. But as replacing L with 1-L would complicate our later discussion, and only changes the eigenvalues (from Ai to 1 - Ai) and not the eigenvectors, we instead use L.

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