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—Nearest neighbor search and many other numerical data analysis tools most often rely on the use of the euclidean distance. When data are high dimensional, however, the euclidean distances seem to concentrate; all distances between pairs of data elements seem to be very similar. Therefore, the relevance of the euclidean distance has been questioned in the… (More)

In the context of classification, the dissimilarity between data elements is often measured by a metric defined on the data space. Often, the choice of the metric is often disregarded and the Euclidean distance is used without further inquiries. This paper illustrates the fact that when other noise schemes than the white Gaussian noise are encountered, it… (More)

- DAMIEN FRANCOIS
- 2006

2 Remerciements Ce travail a ´ eté rendu possible grâce au soutien financier du Fonds pour la formationà la Recherche dans l'Industrie et dans l'Agriculture (FRIA) et du P ˆ ole d'Attraction Inter-universitaire IAP V/22 (2002-2006) " Dynamical Systems and Control: Computation , Identification and Modelling ". La fameusé equipe du CESAME, j'y ai reçu un… (More)

Long-term ECG recordings are often required for the monitoring of the cardiac function in clinical applications. Due to the high number of beats to evaluate, inter-patient computer-aided heart beat classification is of great importance for physicians. The main difficulty is the extraction of discriminative features from the heart beat time series. The… (More)

Supervised and interpatient classification of heart beats is primordial in many applications requiring long-term monitoring of the cardiac function. Several classification models able to cope with the strong class unbalance and a large variety of feature sets have been proposed for this task. In practice, over 200 features are often considered, and the… (More)

Data from spectrophotometers form vectors of a large number of exploitable variables. Building quantitative models using these variables most often requires using a smaller set of variables than the initial one. Indeed, a too large number of input variables to a model results in a too large number of parameters, leading to overfitting and poor… (More)

Combining the mutual information criterion with a forward feature selection strategy offers a good trade-off between optimality of the selected feature subset and computation time. However, it requires to set the parameter(s) of the mutual information estimator and to determine when to halt the forward procedure. These two choices are difficult to make… (More)

Modern data analysis tools have to work on high-dimensional data, whose components are not independently distributed. High-dimensional spaces show surprising, counter-intuitive geometrical properties that have a large influence on the performances of data analysis tools. Among these properties, the concentration of the norm phenomenon results in the fact… (More)

The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal approach… (More)

Modern data analysis often faces high-dimensional data. Nevertheless, most neural network data analysis tools are not adapted to high-dimensional spaces, because of the use of conventional concepts (as the Euclidean distance) that scale poorly with dimension. This paper shows some limitations of such concepts and suggests some research directions as the use… (More)