Agrupamento espectral para dados de formas

Abstract

With the advance of tecnology, the collection of geometrical information from images became usual. Statistical shape analysis uses statistical methods to analysis geometrical structures and can be applied in several areas. One particular problem of interest in statistical shape analysis is the adaptation of classical statistical methods for shape data or the proposition of new methods. In statistical shape analysis it is common the need for lustering shape data to obtain lusters with similar characteristics. Clustering methods are useful tools to explore structures in data and have been used for unsupervised pattern recognition. The k-means algorithm is among the oldest and most widely used lustering methods. Despite its simplicity and efficiency, the k-means algorithm has some problems. Because of this, it is important to propose alternate methods that and be useful where the k-means fails. Spectral lustering methods arise from spectral theory of graphs and the lustering problem and be formulated as a graph cut where an appropriate objective function should be optimized. In this work we propose an adaptation of the Ng, Jordan & Weiss spectral lustering algorithm for plannar shape data. We performed applications on 14 plannar shape data sets and verified that the adapted version of the Ng, Jordan & Weiss algorithm considering the full procrustes distance and the euclidean distance on the shapes tangent spa e outperforms the version of thek-means algorithm for plannar shapes, corroborating that the proposed adaptation is efficient for shape data.