Éditeur(s) : HAL CCSD Springer Verlag
Résumé : A preliminary version appeared in the 18th ACM-SIAM Symposium on Discrete Algorithms, pp. 746- 755, 2007
International audience
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define various variants of Voronoi diagrams depending on the class of objects, the distance function and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow one to define information-theoretic Voronoi diagrams in sta- tistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connection with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation.
ISSN: 0179-5376

hal-00488441
https://hal.archives-ouvertes.fr/hal-00488441
https://hal.archives-ouvertes.fr/hal-00488441/document
https://hal.archives-ouvertes.fr/hal-00488441/file/BVD-DCG.pdf

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : under revision for IJCV
International audience
The k-nearest neighbors (k-NN) classification rule has proven extremely successful in countless many computer vision applications. For example, image categorization often relies on uniform voting among the nearest prototypes in the space of descriptors. In spite of its good properties, the classic k-NN rule suffers from high variance when dealing with sparse prototype datasets in high dimensions. A few techniques have been proposed to improve k-NN classification, which rely on either deforming the nearest neighborhood relationship or modifying the input space. In this paper, we propose a novel boosting algorithm, called UNN (Universal Nearest Neighbors), which induces leveraged k-NN, thus generalizing the classic k-NN rule. We redefine the voting rule as a strong classifier that linearly combines predictions from the k closest prototypes. Weak classifiers are learned by UNN so as to minimize a surrogate risk. A major feature of UNN is the ability to learn which prototypes are the most relevant for a given class, thus allowing one for effective data reduction. Experimental results on the synthetic two-class dataset of Ripley show that such a filtering strategy is able to reject "noisy" prototypes. We carried out image categorization experiments on a database containing eight classes of natural scenes. We show that our method outperforms significantly the classic k-NN classification, while enabling significant reduction of the computational cost by means of data filtering.
ISSN: 0920-5691

hal-00481712
https://hal.archives-ouvertes.fr/hal-00481712
DOI : 10.1007/s11263-012-0539-2
ARXIV : 1001.1221

Éditeur(s) : HAL CCSD IEEE
Résumé : Object classification is a challenging task in computer vision. Many approaches have been proposed to extract meaningful descriptors from images and classifying them in a supervised learning framework. In this paper, we revisit the classic k-nearest neighbors (k-NN) classification rule, which has shown to be very effective when dealing with local image descriptors. However, k-NN still features some major drawbacks, mainly due to the uniform voting among the nearest prototypes in the feature space. In this paper, we propose a generalization of the classic k-NN rule in a supervised learning (boosting) framework. Namely, we redefine the voting rule as a strong classifier that linearly combines predictions from the k closest prototypes. To induce this classifier, we propose a novel learning algorithm, MLNN (Multiclass Leveraged Nearest Neighbors), which gives a simple procedure for performing prototype selection very efficiently. We tested our method on 12 categories of objects, and observed significant improvement over classic k-NN in terms of classification performances.
International Workshop on Image Analysis for Multimedia Interactive Services
Desenzano del Garda, Italy

hal-00481725
https://hal.archives-ouvertes.fr/hal-00481725
https://hal.archives-ouvertes.fr/hal-00481725/document
https://hal.archives-ouvertes.fr/hal-00481725/file/pbnn_wiamis_10.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Recently, a large amount of work has been devoted to the study of spectral clustering — a powerful unsupervised classification method. This paper brings contributions to both its foundations, and its applications to text classification. Departing from the mainstream, concerned with hard membership, we study the extension of spectral clustering to soft membership (probabilistic, EM style) assignments. One of its key features is to avoid the complexity gap of hard membership. We apply this theory to a challenging problem, text clustering for languages having permeable borders, via a novel construction of Markov chains from corpora. Experiments with a readily available code clearly display the potential of the method, which brings a visually appealing soft distinction of languages that may define altogether a whole corpus.
ISSN: 0031-3203

hal-00329991
https://hal.archives-ouvertes.fr/hal-00329991
DOI : 10.1016/j.patcog.2008.06.024