Agrupamento espectral para dados de formas

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.NenhumaA coleta de informações geométricas, a partir do avanço da tecnologia, e o estudo das formas de objetos tem se tornado cada vez mais comum e importante. A análise estatística de formas (AEF) utiliza métodos estatísticos para a análise de estruturas geométricas e suas aplicações podem ser encontradas em diferentes áreas da ciência. No entanto, um dos problemas de interesse na AEF é estender os métodos clássicos de análise estatística para dados de formas de objetos, ou propor novos métodos para esse tipo de dado. Na AEF é comum existir a necessidade de agrupamento em um conjunto de dados de modo a obter grupos com características mais homogêneas. Os métodos de agrupamento são ferramentas úteis para explorar estruturas em conjuntos de dados sendo utilizados, por exemplo, em para reconhecimento não-supervisionado de padrões. O método k-médias figura entre os métodos de agrupamento mais antigos e mais comumente utilizados na prática. Mas, apesar de sua simplicidade e eficiência, o algoritmo k-médias apresenta algumas deficiências. Por causa disso, há a necessidade da proposição de métodos alternativos que possam apresentar bons resultados em situações onde o algoritmo k-médias falha. Os métodos de agrupamento espectral surgem a partir de conceitos da teoria espectral dos grafos onde o problema de agrupamento é configurado como um problema de corte no grafo em que uma função objetivo apropriada deve ser otimizada. Neste trabalho apresentamos uma adaptação do algoritmo de agrupamento espectral de Ng, Jordan & Weiss para dados de formas planas de objetos e comparamos a uma adaptação do algoritmo k-médias para dados de formas planas. Foram realizadas aplicações om 14 conjuntos de dados reais e verificou-se que o algoritmo espectral adaptado de Ng, Jordan & Weiss, considerando as distâncias de procrustes completa e euclidiana no espaço tangente obteve desempenho superior ao método de agrupamento k-médias, fornecendo evidências de que a adaptação proposta é eficiente para dados dessa natureza

Cluster Analysis of Myelin Nerve Fibers of the Periferal Nerve

One of the unsolved issues in neuromorphology is the classification of myelin nerve fibers (MNF). Objective: to use cluster analysis to classify the sciatic nerve MNF. Material and methods. The work was performed using 5 one-year-old male Wistar rats. Semi-thin sections were stained with methylene blue. MNF morphometry was performed using ImageJ, and statistical processing – using the software environment R. Results of the study. Ward’s and k-means methods were used to cluster the MNF. Three clusters of MNFs are defined and their parameters are determined. The presented algorithm for adapting the literature data to the format of the obtained results includes determining the total average for the combined set of each indicator and the total variance, which is the sum of intragroup and intergroup variances. Conclusions: 1) for the classification of MNF it is advisable to use cluster analysis; 2) clustering should be performed according to the transsection areas of the axial cylinder and myelin sheath; 3) the number of clusters is determined by the agglomerative method of Ward, and their metrics – by the iterative method of k-means; 4) three clusters of MNF of the rat sciatic nerve differ in the transsection areas of the fibers, the axial cylinder and the myelin sheath and the percentage of nerve fibers; 5) when comparing identical indicators according to the obtained and literature data, the results were equivalent in the areas of the axial cylinder and myelin sheath and their shape coefficients, despite the fact that the classification of myelin fibers and their morphometry was performed using different methods

Seasonal Wind Energy Characterization in the Gulf of Mexico

In line with Mexico’s interest in determining its wind resources, in this paper, 141 locations along the states of the Gulf of Mexico have been analyzed by calculating the main wind characteristics, such as the Weibull shape (c) and scale (k) parameters, and wind power density (WPD), by using re-analysis MERRA-2 (Modern-Era Retrospective Analysis for Research and Applications version 2) data with hourly records from 1980–2017 at a 50-m height. The analysis has been carried out using the R free software, whose its principal function is for statistical computing and graphics, to characterize the wind speed and determine its annual and seasonal (spring, summer, autumn, and winter) behavior for each state. As a result, the analysis determined two different wind seasons along the Gulf of Mexico;, it was found that in the states of Tamaulipas, Veracruz, and Tabasco wind season took place during autumn, winter, and spring, while for the states of Campeche and Yucatan, the only two states that shared its coast with the Caribbean Sea and the Gulf of Mexico, the wind season occurred only in winter and spring. In addition, it was found that by considering a seasonal analysis, more accurate information on wind characteristics could be generated; thus, by applying the Weibull distribution function, optimal zones for determining wind as a resource of energy can be established. Furthermore, a k-means algorithm was applied to the wind data, obtaining three clusters that can be seen by month; these results and using the Weibull parameter c allow for selecting the optimum wind turbine based on its power coefficient or efficiency

Hierarchical Graphical Models for Multigroup Shape Analysis using Expectation Maximization with Sampling in Kendall's Shape Space

This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation, and scale, following the notion in Kendall shape space.While individual shapes are derived from their group shape model, each group shape model is derived from a single population shape model. The hierarchical model follows the natural organization of population data and the top level in the hierarchy provides a common frame of reference for multigroup shape analysis, e.g. classification and hypothesis testing. Unlike typical shape-modeling approaches, the proposed model is a generative model that defines a joint distribution of object-boundary data and the shape-model variables. Furthermore, it naturally enforces optimal correspondences during the process of model fitting and thereby subsumes the so-called correspondence problem. The proposed inference scheme employs an expectation maximization (EM) algorithm that treats the individual and group shape variables as hidden random variables and integrates them out before estimating the parameters (population mean and variance and the group variances). The underpinning of the EM algorithm is the sampling of pointsets, in Kendall shape space, from their posterior distribution, for which we exploit a highly-efficient scheme based on Hamiltonian Monte Carlo simulation. Experiments in this paper use the fitted hierarchical model to perform (1) hypothesis testing for comparison between pairs of groups using permutation testing and (2) classification for image retrieval. The paper validates the proposed framework on simulated data and demonstrates results on real data.Comment: 9 pages, 7 figures, International Conference on Machine Learning 201