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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)
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)
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)
We consider the high order moments estimator of the frontier of a random pair, intro-high order moments. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.
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 the context of network traffic analysis, we address the problem of estimating the tail index of flow (or more generally of any group) size distribution from the observation of a sampled population of packets (individuals). We give an exhaustive bibliography of the existing methods and show the relations between them. The main contribution of this work is(More)
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity between these predictors or small sample sizes compared to the dimension, the inversion is not possible and a regularization(More)