Image classification becomes a big challenge since it concerns on the one hand millions or billions of images that are available on the web and on the other hand images used for critical real-time applications. This classification involves in general learning methods and classifiers that must require both precision as well as speed performance. These learning problems concern a large number of application areas: namely, web applications (profiling, targeting, social networks, search engines), "Big Data" and of course computer vision such as the object recognition and image classification. This thesis concerns the last category of applications and is about supervised learning algorithms based on the minimization of loss functions (error) called "calibrated" for two kinds of classifiers: k-Nearest Neighbours (kNN) and linear classifiers. Those learning methods have been tested on large databases of images and then applied to biomedical images. In a first step, this thesis revisited a Boosting kNN algorithm for large scale classification. Then, we introduced a new method of learning these NN classifiers using a Newton descent approach for a faster convergence. In a second part, this thesis introduces a new learning algorithm based on stochastic Newton descent for linear classifiers known for their simplicity and their speed of convergence. Finally, these three methods have been used in a medical application regarding the classification of cells in biology and pathology.
