On a method of ordering and clustering of objects
On a Statistical measure of Discrimination
On metric divergences of probability measures
Standard properties of -divergences of probability measures are widely applied in various areas of information processing. Among the desirable supplementary properties facilitating employment of mathematical methods is the metricity of -divergences, or the metricity of their powers. This paper extends the previously known family of -divergences with these properties. The extension consists of a continuum of -divergences which are squared metric distances and which are mostly new but include...
On selecting the best features in a noisy environment
This paper introduces a novel method for selecting a feature subset yielding an optimal trade-off between class separability and feature space dimensionality. We assume the following feature properties: (a) the features are ordered into a sequence, (b) robustness of the features decreases with an increasing order and (c) higher-order features supply more detailed information about the objects. We present a general algorithm how to find under those assumptions the optimal feature subset. Its performance...
On the construction of points estimates for the Mahalanobis distance in discriminant analysis
On the optimality of the max-depth and max-rank classifiers for spherical data
The main goal of supervised learning is to construct a function from labeled training data which assigns arbitrary new data points to one of the labels. Classification tasks may be solved by using some measures of data point centrality with respect to the labeled groups considered. Such a measure of centrality is called data depth. In this paper, we investigate conditions under which depth-based classifiers for directional data are optimal. We show that such classifiers are equivalent to the Bayes...
On the order equivalence relation of binary association measures
Over a century of research has resulted in a set of more than a hundred binary association measures. Many of them share similar properties. An overview of binary association measures is presented, focused on their order equivalences. Association measures are grouped according to their relations. Transformations between these measures are shown, both formally and visually. A generalization coefficient is proposed, based on joint probability and marginal probabilities. Combining association measures...
On the Wilks Λ statistic as a tool for model selection in mixed variable discriminant analysis
Optimal quantization for the one–dimensional uniform distribution with Rényi--entropy constraints
We establish the optimal quantization problem for probabilities under constrained Rényi--entropy of the quantizers. We determine the optimal quantizers and the optimal quantization error of one-dimensional uniform distributions including the known special cases (restricted codebook size) and (restricted Shannon entropy).
PC-PARIS - An Interactive Software System for Statistical Pattern Recognition
Pirámides indexadas y disimilaridades piramidales.
En este trabajo se pretende una formalización de las bases matemáticas sobre las que se amparan los modelos de clasificación y representación piramidal, estableciéndose para ello una relación entre los conceptos de pirámide indexada y disimilaridad piramidal. Asimismo se precisa el concepto de información redundante, contenida en una estructura piramidal, y se dan criterios objetivos para poder prescindir de ella sin que ello suponga una modificación de la estructura piramidal.
Pondération des variables pour la classification de données binaires
Programme de classification hiérarchique par l'algorithme de la recherche en chaîne des voisins réciproques
Programme pour la discrimination barycentrique entre deux populations et l'étude par permutation aléatoire de la discriminabilité entre celles-ci
Propriétés asymptotiques en classification (consistance des solutions de problèmes approches)
Propriétés et caractérisations topologiques d'une représentation pyramidale
Ce texte présente quelques caractéristiques géométriques des dissimilarités robinsoniennes. Ces dissimilarités constituent un modèle très général de représentation des mesures de proximité entre objets (ou groupes d'objets) lorsque ces entités sont rangées suivant un ordre total. Les propriétés géométriques des dissimilarités robinsoniennes sont exposées en utilisant les notions de segment et de frontière introduites pour une dissimilarité quelconque. Nous considérons ensuite l'ensemble des dissimilarités...
Propriétés théoriques et pratiques et applications d'une nouvelle règle de classement
Quantifying the impact of different copulas in a generalized CreditRisk + framework An empirical study
Without any doubt, credit risk is one of the most important risk types in the classical banking industry. Consequently, banks are required by supervisory audits to allocate economic capital to cover unexpected future credit losses. Typically, the amount of economical capital is determined with a credit portfolio model, e.g. using the popular CreditRisk+ framework (1997) or one of its recent generalizations (e.g. [8] or [15]). Relying on specific distributional assumptions, the credit loss distribution...
Quelques méthodes de segmentation
Rang moyen et agrégation de classements