|A self-organizing framework for object recognition is described. We describe a hierarchical database structure for image retrieval. The SHOSLIF (Self-Organizing Hierarchical Optimal Subspace Learning and Inference Framework) system uses the theories of optimal linear projection for automatic optimal feature selection and a hierarchical structure to achieve a logarithmic retrieval complexity. A...

The proposed approach leads to analyzing the associations between a set of quantitative variables and several qualitative variables measured on a same set of individuals. In a decision-making context, the proposed method can be considered as a generalization of discriminant analysis to the multiple groups’ variables case. It’s described as a principal component analysis of the centres of gravit...

This chapter details similarity discriminant analysis (SDA), a new framework for similaritybased classification. The two defining characteristics of the SDA classification framework are similarity-based and generative. The classifiers in this framework are similarity-based, because they classify based on the pairwise similarities of data samples, and they are generative, because they build clas...

Introduction Discriminant function analysis is used to determine which continuous variables discriminate between two or more naturally occurring groups. For example, a researcher may want to investigate which variables discriminate between fruits eaten by (1) primates, (2) birds, or (3) squirrels. For that purpose, the researcher could collect data on numerous fruit characteristics of those spe...

Linear discriminant analysis (LDA) has been an active topic of research during the last century. However, the existing algorithms have several limitations when applied to visual data. LDA is only optimal for gaussian distributed classes with equal covariance matrices and just classes-1 features can be extracted. On the other hand, LDA does not scale well to high dimensional data (over-fitting) ...

We propose new algorithms for computing linear discriminants to perform data dimensionality reduction from R to R, with p < n. We propose alternatives to the classical Fisher’s Distance criterion, namely, we investigate new criterions based on the: Chernoff-Distance, J-Divergence and Kullback-Leibler Divergence. The optimization problems that emerge of using these alternative criteria are non-c...

Fisher linear discriminant analysis (LDA) can be sensitive to the problem data. Robust Fisher LDA can systematically alleviate the sensitivity problem by explicitly incorporating a model of data uncertainty in a classification problem and optimizing for the worst-case scenario under this model. The main contribution of this paper is show that with general convex uncertainty models on the proble...

Quadratic discriminant analysis is a common tool for classification, but estimation of the Gaussian parameters can be ill-posed. This paper contains theoretical and algorithmic contributions to Bayesian estimation for quadratic discriminant analysis. A distribution-based Bayesian classifier is derived using information geometry. Using a calculus of variations approach to define a functional Bre...

Linear Discriminant Analysis (LDA) is a popular feature extraction technique in statistical pattern recognition. However, it often suffers from the small sample size problem when dealing with high dimensional data. Moreover, while LDA is guaranteed to find the best directions when each class has a Gaussian density with a common covariance matrix, it can fail if the class densities are more gene...

Daar de proefschriften in de reeks van de Faculteit Economische en Toegepaste Economische Wetenschappen het persoonlijk werk zijn van hun auteurs, zijn alleen deze laatsten daarvoor verantwoordelijk. i Acknowledgements " De laatste loodjes wegen het zwaarst " is surely an appropriate Dutch expression, regarding the work of the last few months. My years of research were great as well as very tou...