À propos d'un résultat de Brailovsky concernant une probabilité d'erreur en analyse discriminante
A proximity based macro stress testing framework
In this a paper a non-linear macro stress testing methodology with focus on early warning is developed. The methodology builds on a variant of Random Forests and its proximity measures. It is embedded in a framework, in which naturally defined contagion and feedback effects transfer the impact of stressing a relatively small part of the observations on the whole dataset, allowing to estimate a stressed future state. It will be shown that contagion can be directly derived from the proximities while...
A rank decision rule for a combined problem of testing and classification
A simple upper bound to the Bayes error probability for feature selection
In this paper, feature selection in multiclass cases for classification of remote-sensing images is addressed. A criterion based on a simple upper bound to the error probability of the Bayes classifier for the minimum error is proposed. This criterion has the advantage of selecting features having a link with the error probability with a low computational load. Experiments have been carried out in order to compare the performances provided by the proposed criterion with the ones of some of the widely...
A unified Lorenz-type approach to divergence and dependence [Book]
A variant of gravitational classification
In this article there is proposed a new two-parametrical variant of the gravitational classification method. We use the general idea of objects' behavior in a gravity field. Classification depends on a test object's motion in a gravity field of training points. To solve this motion problem, we use a simulation method. This classifier is compared to the 1NN method, because our method tends towards it for some parameter values. Experimental results on different data sets demonstrate an improvement...
Aggregated estimators and empirical complexity for least square regression
Agrégation de similarités en classification automatique
Algorithm 44. An abbreviated method of calculating the Mahalanobis distance or residual sum of squares in a linear regression model
Algorithm 55. Multiple regression with stepwise selection of variables
Algorithm 72. Quasi-optimal ordering of objects
Algorithm 82. Stepwise selection of discriminative variables by the use of the Wilks criterion
Algorithm 83. Stepwise selection of discriminative variables by the use of the trace criterion
Algorithm 94. An algorithm for repeated calculations of the generalized Mahalanobis distance
Algorithms 56-59. Cluster analysis by the methods of Hubert
An agglomerative method for automatic forming of hierarchical classification
An alternative extension of the k-means algorithm for clustering categorical data
Most of the earlier work on clustering has mainly been focused on numerical data whose inherent geometric properties can be exploited to naturally define distance functions between data points. Recently, the problem of clustering categorical data has started drawing interest. However, the computational cost makes most of the previous algorithms unacceptable for clustering very large databases. The -means algorithm is well known for its efficiency in this respect. At the same time, working only on...
An automatic hybrid method for retinal blood vessel extraction
The extraction of blood vessels from retinal images is an important and challenging task in medical analysis and diagnosis. This paper presents a novel hybrid automatic approach for the extraction of retinal image vessels. The method consists in the application of mathematical morphology and a fuzzy clustering algorithm followed by a purification procedure. In mathematical morphology, the retinal image is smoothed and strengthened so that the blood vessels are enhanced and the background information...
An ℓ1-oracle inequality for the Lasso in finite mixture gaussian regression models
We consider a finite mixture of Gaussian regression models for high-dimensional heterogeneous data where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by an ℓ1-penalized maximum likelihood estimator. We shall provide an ℓ1-oracle inequality satisfied by this Lasso estimator with the Kullback–Leibler loss. In particular, we give a condition on the regularization parameter of the Lasso to obtain such an oracle inequality....
Analyse des interactions entre partitions prises 2 à 2. Théorie et application en biologie