Sequential algorithms for data analysis with kernel-based methods

In recent years, many methods of analysis and classification of data based on reproducing kernel Hilbert spaces have been developed. Most of these methods incorporate the fundamental principle dictated by Vapnik et al. in Support Vector Machines, which consists in extending linear algorithms to the non-linear case by using kernels. Kernel Fisher Discriminant (KFD) is one of these nonlinear methods which provides interesting results in many practical cases. However, the use of KFD requires storage and processing of matrices whose size equals the number of available data. This may be critical when the training set is large. This paper presents a sequential KFD algorithm which does not require the manipulation of large matrices. Sequential algorithms that fulfil the same requirements as KFD are also presented to perform Kernel Principal Component Analysis (KPCA) and Kernel Generalized Discriminant Analysis (KGDA).Au cours de la dernière décennie, de multiples méthodes pour l'analyse et la classification de données fondées sur la théorie des espaces de Hilbert à noyau reproduisant ont été développées. Elles reposent sur le principe fondamental du kernel trick, initialement exploité par Vapnik et col. dans le cadre des Support Vector Machines. Celui-ci permet d'étendre au cas non-linéaire des traitements initialement linéaires en utilisant la notion de noyau. La méthode KFD, pour Kernel Fisher Discriminant, constitue ainsi une généralisation non-linéaire de l'analyse discriminante de Fisher. Bien que son efficacité soit indiscutable, on déplore le fait que sa mise en oeuvre nécessite le stockage et la manipulation de matrices de dimension égale au nombre de données traitées, point critique lorsque l'ensemble d'apprentissage est de grande taille. Cet article présente un algorithme séquentiel palliant cette difficulté puisqu'il ne nécessite, ni la manipulation, ni même le stockage de telles matrices. Un parallèle est également proposé entre KFD et KPCA, acronyme de Kernel Principal Component Analysis, cette dernière méthode constituant une extension au cas non-linéaire de l'analyse en composantes principales. Cet article s'achève par la présentation d'un algorithme séquentiel à noyau pour la méthode GDA, Generalized Discriminant Analysis, qui étend l'analyse discriminante de Fisher au cas multi-classe

A new method for generic three dimensional human face modelling for emotional bio-robots

Existing 3D human face modelling methods are confronted with difficulties in applying flexible control over all facial features and generating a great number of different face models. The gap between the existing methods and the requirements of emotional bio-robots applications urges the creation of a generic 3D human face model. This thesis focuses on proposing and developing two new methods involved in the research of emotional bio-robots: face detection in complex background images based on skin colour model and establishment of a generic 3D human face model based on NURBS. The contributions of this thesis are: A new skin colour based face detection method has been proposed and developed. The new method consists of skin colour model for skin regions detection and geometric rules for distinguishing faces from detected regions. By comparing to other previous methods, the new method achieved better results of detection rate of 86.15% and detection speed of 0.4-1.2 seconds without any training datasets. A generic 3D human face modelling method is proposed and developed. This generic parametric face model has the abilities of flexible control over all facial features and generating various face models for different applications. It includes: The segmentation of a human face of 21 surface features. These surfaces have 34 boundary curves. This feature-based segmentation enables the independent manipulation of different geometrical regions of human face. The NURBS curve face model and NURBS surface face model. These two models are built up based on cubic NURBS reverse computation. The elements of the curve model and surface model can be manipulated to change the appearances of the models by their parameters which are obtained by NURBS reverse computation. A new 3D human face modelling method has been proposed and implemented based on bi-cubic NURBS through analysing the characteristic features and boundary conditions of NURBS techniques. This model can be manipulated through control points on the NURBS facial features to build any specific face models for any kind of appearances and to simulate dynamic facial expressions for various applications such as emotional bio-robots, aesthetic surgery, films and games, and crime investigation and prevention, etc