Agrupamento em análise estatística de formas

Abstract

In this work, the k-means algorithm proposed by Hartigan and Wong is adapted to the case of random element observations in general metric space. Simulation results show that the performance of the algorithm in the case when the metric space is the shape space of the plane configurations, is independent on the choice of the usual shape metrics, more precisely the regular, complete and partial Procrustes distance. Besides, this modified version of the algorithm, applied to the shape space with any of the three metrics, exhibits the same performance as the original algorithm applied to the partial tangent Procrustes coordinates. The current study was motivated by the problem of identification of species of half-beak fish Hemiramphus balao and Hemiramphus brasiliensis.Currently, the parameters used for identification of these species are subject to certain operational difficulties, which often result in erroneous classification of the specimens. The algorithm was used to perform clustering of shape configuration samples, and two groups with statistically distinct shapes have been identified. These groups exhibit a pronounced difference regarding position of the head in relation to the body: for one group the head is slightly inclined upwards, while for the other group the head is slightly inclined downwards. Observation of these characteristics on the photos of fish specimens on which the two species were correctly classified, leads to identification of group 1 as Hemirapmphus balao and group 2 as species Hemiramphus brasiliensis. Therefore, head position with relation to body (which represents information entirely on the specimen shape) represents a rather robust parameter for identification of species.