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We consider the problem of estimating the gradient lines of a density, which can be used to cluster points sampled from that density, for example via the mean-shift algorithm of Fukunaga and Hostetler (1975). We prove general convergence bounds that we then specialize to kernel density estimation.

We study the approximation of a continuous function field over a compact set T , by a continuous field of ridge ap-proximants over T , named ridge function fields. We first give general density results about function fields, and show how they apply to ridge function fields. We next discuss the parametrization of sets of ridge function fields, and give… (More)

Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the underlying submanifold is isometric to a convex subset, and we provide some simple examples where it fails to be consistent.

- Bruno Pelletier, Bruno, Pelletier@univ-Rennes Fr, Pierre, Pudlo@univ-Montp Fr
- 2011

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… (More)

Following Hartigan [1975], 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… (More)

In the context of nonlinear regression, we consider the problem of explaining a variable y from a vector x of explanatory variables and from a vector t of conditionning variables, that influences the link function between y and x. A neural based solution is proposed in the form of a field of nonlinear regression models, by which it is meant that the… (More)

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