Dimensionality reduction of clustered data sets

We present a novel probabilistic latent variable model to perform linear dimensionality reduction on data sets which contain clusters. We prove that the maximum likelihood solution of the model is an unsupervised generalisation of linear discriminant analysis. This provides a completely new approach to one of the most established and widely used classification algorithms. The performance of the model is then demonstrated on a number of real and artificial data sets

A new analysis strategy for detection of faint gamma-ray sources with Imaging Atmospheric Cherenkov Telescopes

A new background rejection strategy for gamma-ray astrophysics with stereoscopic Imaging Atmospheric Cherenkov Telescopes (IACT), based on Monte Carlo (MC) simulations and real background data from the H.E.S.S. [High Energy Stereoscopic System, see [1].] experiment, is described. The analysis is based on a multivariate combination of both previously-known and newly-derived discriminant variables using the physical shower properties, as well as its multiple images, for a total of eight variables. Two of these new variables are defined thanks to a new energy evaluation procedure, which is also presented here. The method allows an enhanced sensitivity with the current generation of ground-based Cherenkov telescopes to be achieved, and at the same time its main features of rapidity and flexibility allow an easy generalization to any type of IACT. The robustness against Night Sky Background (NSB) variations of this approach is tested with MC simulated events. The overall consistency of the analysis chain has been checked by comparison of the real gamma-ray signal obtained from H.E.S.S. observations with MC simulations and through reconstruction of known source spectra. Finally, the performance has been evaluated by application to faint H.E.S.S. sources. The gain in sensitivity as compared to the best standard Hillas analysis ranges approximately from 1.2 to 1.8 depending on the source characteristics, which corresponds to an economy in observation time of a factor 1.4 to 3.2.Comment: 26 pages, 13 figure

Nonstimulated early visual areas carry information about surrounding context

Even within the early sensory areas, the majority of the input to any given cortical neuron comes from other cortical neurons. To extend our knowledge of the contextual information that is transmitted by such lateral and feedback connections, we investigated how visually nonstimulated regions in primary visual cortex (V1) and visual area V2 are influenced by the surrounding context. We used functional magnetic resonance imaging (fMRI) and pattern-classification methods to show that the cortical representation of a nonstimulated quarter-field carries information that can discriminate the surrounding visual context. We show further that the activity patterns in these regions are significantly related to those observed with feed-forward stimulation and that these effects are driven primarily by V1. These results thus demonstrate that visual context strongly influences early visual areas even in the absence of differential feed-forward thalamic stimulation

Statistical applications of the multivariate skew-normal distribution

Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further probabilistic properties of the distribution, with special emphasis on aspects of statistical relevance. Inferential and other statistical issues are discussed in the following part, with applications to some multivariate statistics problems, illustrated by numerical examples. Finally, a further extension is described which introduces a skewing factor of an elliptical density.Comment: full-length version of the published paper, 32 pages, with 7 figures, uses psfra

The DDG^G-classifier in the functional setting

The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some issues still remain. This paper is devoted to extending the DD-classifier in the following ways: first, to surpass the limitation of the DD-classifier when more than two groups are involved. Second to apply regular classification methods (like $k$NN, linear or quadratic classifiers, recursive partitioning,...) to DD-plots to obtain useful insights through the diagnostics of these methods. And third, to integrate different sources of information (data depths or multivariate functional data) in a unified way in the classification procedure. Besides, as the DD-classifier trick is especially useful in the functional framework, an enhanced revision of several functional data depths is done in the paper. A simulation study and applications to some classical real datasets are also provided showing the power of the new proposal.Comment: 29 pages, 6 figures, 6 tables, Supplemental R Code and Dat