In classification problems one wants to find simple rules to attribute objects to known (discriminant analysis) or still unknown groups (cluster analysis). Markov-models consist of states and transition probabilities between them; in aggregated analysis the states correspond to groups of individuals or profiles, and a crucial question for the validity of the model is the choice of the groups.
In all these situations the concept of group is central, and group membership must be determined by way of a number of properties of the objects, individuals, profiles etc. These variables may be observed ones or be latent. Groups must be homogeneous, whereas different groups must be heterogeneous. Homogeneity and heterogeneity may, however, be defined in many different ways depending on the context, the type of variables (value scale), the objective, the methodology, and the availability of algorithms.
A first objective of the project is to obtain an overview of the available concepts of homogeneity and heterogeneity, with special emphasis on the two basic situations of interest to the promotors: classification and aggregated Markov analysis. This should allow to put their above-mentioned recent own results in frame. The second objective is to further refine and combine the concepts and methodologies of Principal Component Analysis, Profile-Based models and Hidden Markov models.