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Clustering in high-dimensional spaces is a recurrent problem in many domains, for example in object recognition. High-dimensional data usually live in different low-dimensional subspaces hidden in the original space. This paper presents a clustering approach which estimates the specific subspace and the intrinsic dimension of each class. Our approach adapts(More)
In this paper, a statistical method is proposed to evaluate the 4 physical properties of surface materials on Mars from hyperspectral images 5 collected by the OMEGA instrument aboard the Mars express spacecraft. 6 The approach is based on the estimation of the functional relationship F be-7 tween some observed spectra and some physical parameters. To this(More)
In the supervised classification framework, human supervision is required for labeling a set of learning data which are then used for building the classifier. However, in many applications, human supervision is either imprecise, difficult or expensive. In this paper, the problem of learning a supervised multi-class classifier from data with uncertain labels(More)
In Li and Yin (2008, Biometrics 64, 124-131), a ridge SIR estimator is introduced as the solution of a minimization problem and computed thanks to an alternating least-squares algorithm. This methodology reveals good performance in practice. In this note, we focus on the theoretical properties of the estimator. It is shown that the minimization problem is(More)
Several risk measures have been proposed in the literature. In this paper, we focus on the estimation of the Conditional Tail Expectation (CTE). Its asymptotic normality has been first established in the literature under the classical assumption that the second moment of the loss variable is finite, this condition being very restrictive in practical(More)
This paper is concerned with the estimation of a local measure of intrinsic dimensionality (ID) recently proposed by Houle. The local model can be regarded as an extension of Karger and Ruhl's expansion dimension to a statistical setting in which the distribution of distances to a query point is modeled in terms of a continuous random variable. This form of(More)
Visible and near infrared imaging spectroscopy is a key remote sensing technique to study and monitor planet Mars. Indeed it allows the detection, mapping and characterization of minerals as well as volatile species that often constitute the first step toward the resolution of key climatic and geological issues. These tasks are carried out by the spectral(More)
We propose new estimates for the frontier of a set of points. They are de ned as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinations of kernel functions applied to the points of the sample. The coe cients of the linear combination are then computed by solving a linear(More)
Reference curves which take time into account, such as those for age, are often required in medicine, but simple systematic and efficient statistical methods for constructing them are lacking. Classical methods are based on parametric fitting (polynomial curves). Semi-parametric methods are also widely used especially in Europe. Here, we propose a new(More)