After this short introduction to clustering, I can talk about the different issues of my thesis.

The main goal is of course to find the best possible clustering ! If we do something then let's do it as well as possible... But how ?

Among the different clustering models, the partionned based ones are the most used. The study of my thesis is about the K-Means method and its variants (fuzzy partition and credal) with the Mahalanobis distance. Finding the best clustering means finding the best possible partition.

To achieve this, we can use mathematical optimization methods. We will also need criteria to evaluate the obtained partitions and deduce the quality of the methods.What is really innovative in this study is not only the application of more sophisticated optimization methods but all new problems appear with the Mahalanobis distance.