Prática de ensino supervisionado no 1.º e 2.º ciclo do ensino básico: esquemas organizadores facilitadores da aprendizagem em História e Geografia

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino de 1.º e 2.º Ciclos do Ensino Básico

Probabilistic consensus clustering using evidence accumulation

Clustering ensemble methods produce a consensus partition of a set of data points by combining the results of a collection of base clustering algorithms. In the evidence accumulation clustering (EAC) paradigm, the clustering ensemble is transformed into a pairwise co-association matrix, thus avoiding the label correspondence problem, which is intrinsic to other clustering ensemble schemes. In this paper, we propose a consensus clustering approach based on the EAC paradigm, which is not limited to crisp partitions and fully exploits the nature of the co-association matrix. Our solution determines probabilistic assignments of data points to clusters by minimizing a Bregman divergence between the observed co-association frequencies and the corresponding co-occurrence probabilities expressed as functions of the unknown assignments. We additionally propose an optimization algorithm to find a solution under any double-convex Bregman divergence. Experiments on both synthetic and real benchmark data show the effectiveness of the proposed approach.