Cluster analysis: a further approach based on density estimation
Computational Statistics & Data Analysis
Clustering Algorithms
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Clustering via nonparametric density estimation
Statistics and Computing
A survey of kernel and spectral methods for clustering
Pattern Recognition
A tutorial on spectral clustering
Statistics and Computing
Graph Laplacians and their Convergence on Random Neighborhood Graphs
The Journal of Machine Learning Research
On Learning with Integral Operators
The Journal of Machine Learning Research
Towards a theoretical foundation for laplacian-based manifold methods
COLT'05 Proceedings of the 18th annual conference on Learning Theory
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Following Hartigan (1975), a cluster is defined as a connected component of the t-level set of the underlying density, that is, 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 data set into the feature space, which establishes the strong consistency of our proposed algorithm.