Graphs are commonly used to model objects with pairwise relationships. Hypergraphs, which are generalization of graphs where edges connect any number of vertices, are needed for modeling when the objects under study have multi-way relationships. Standard application areas include the study of protein interaction, gene expression networks, fraud detection, program optimization and the spread of epidemics, and so on. Applications in many other areas are are plentiful, as almost all systems containing interacting or coexisting entities can be modeled as a (hyper)graph. Clustering in graphs and hypergraphs is the problem of detecting tightly connected, highly related sets of vertices. Depending on the task, knowledge about the structure of the (hyper)graph can reveal information such as voter behavior, the formation of new trends, existing terrorist groups and recruitment or a natural partitioning of data records onto pages.
Homeland project's goal is to combine graph/hypergraph clustering with machine learning and obtain clustering algorithms with general objective functions to be used in varying applications.
Homeland project is funded by PHC Procope programme. PHC Procope is the French-German Hubert Curien Partnership. It is implemented in Germany by the Deutscher Akademischer Austausch dienst (DAAD) and in France by Ministry of Europe and Foreign Affairs (Ministère de l'Europe et des Affaires étrangères) and by the Ministry Higher Education, Research and Innovation (Ministère de l'Enseignement supérieur, de la Recherche et de l'Innovation).
Homeland project is carried out by Marcelo Fonseca Faraj from the Algorithm engineering group at the Heidelberg University, Felix Hausberger from the Heidelberg University, Christian Schulz (head of the Algorithm engineering group at the Heidelberg University), and Bora Uçar, from CNRS and LIP, ENS de Lyon. Other short term particpants include Felix Hausberger, Daniel Hammer, and Loris Wilwert from Heidelberg University.