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