Operator norm convergence of spectral clustering on level sets

Details Operator norm convergence of spectral clustering on level sets Operator norm convergence of spectral clustering on level sets

2010-02-11

arxiv.org/abs/1002.2313v1

Statistics

Machine Learning

Scientific paper

Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our algorithm is composed of two steps. First, a nonparametric density estimate is used to extract the data points for which the estimated density takes a value greater than t. Next, the extracted points are clustered based on the eigenvectors of a graph Laplacian matrix. Under mild assumptions, we prove the almost sure convergence in operator norm of the empirical graph Laplacian operator associated with the algorithm. Furthermore, we give the typical behavior of the representation of the dataset into the feature space, which establishes the strong consistency of our proposed algorithm.

Affiliated with

Also associated with

No associations

Rating

Operator norm convergence of spectral clustering on level sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Operator norm convergence of spectral clustering on level sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Operator norm convergence of spectral clustering on level sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-68173