VII SBAI/ II IEEE LARS. São Luís, setembro de 2005 CASCADED NONLINEAR PRINCIPAL COMPONENTS ANALYSIS: NA APPLICATION IN EXTRACTION OF HUMAN MOVEMENTS FROM VIDEO SEQUENCES Matheus Figueiredo † Silvia Botelho * matheus@cpgei.cefetpr.br silviacb@ee.furg.br Rodrigo de Bem * Tânia Mezzadri Centeno † rodrigo@ee.furg.br mezzadri@cpgei.cefetpr.br William Lautenschlager * pink@ee.furg.br *FURG Av. Itália km 8 CEP, Rio Grande, RS, Brazil † CEFETPR 7 de setembro 3165 CEP, Curitiba, PR, Brazil ABSTRACT This article presents a methodology to extract principal components of large set of data, called C-NLPCA (Cascaded nonlinear principal component analysis), and evaluates its use in the extraction of main human movements in image series, aiming for the development of methodologies and techniques for skill transfer from humans to robotic/virtual agents. The C-NLPCA is an original data multivariate analysis method based on the NLPCA (Nonlinear Principal Component Analysis). This method has as main features the capability of taking principal variability components from a large set of data, considering the existence of possible nonlinear relations among them. The proposed method is used to extract principal movements of video sequence of human activities, which can be reconstructed in cybernetic and robotic contexts. Aiming for the validation of the method a human moving hand test is presented, where C-NLPCA is applied and the patterns of the movements obtained from it are confronted with linear traditional techniques. KEYWORDS: neural networks, PCA, image processing, skill, transfer, robotic. RESUMO Este artigo tem como principal objetivo apresentar a metodologia empregada para o processamento do C- NLPCA (Cascaded Nonlinear Principal Component Analysis), e avaliar seu uso na extração de componentes principais de movimentos de series de imagens digitais 2D, visando ao desenvolvimento e metodologias e técnicas que permitam a execução de tal tarefa com eficiência e robustez. O método C-NLPCA é um método de análise multivariada de dados, baseado no NLPCA (Nonlinear Principal Component Analysis), que tem como principais características a capacidade de extrair componentes principais de variação de grande conjuntos de variáveis. PALAVRAS-CHAVE: redes neurais, PCA, processamento de imagens, transferência de habilidades. 1 INTRODUÇÃO The principal components analysis (PCA) is a statistic method used for data multivariate analysis (J. F. Hair et al., 1995). Such a method provides linear relations among the elements in a set of variables, giving as output the principal components (PC) which describe the variability patterns in such a set. However, when the variables have nonlinear relationships among then, classical PCA can not be applied. In this case, we have a set of alternatives methods (Lee, 2000; Diamantaras and Kung, 1996; Scholz and Vigrio, 2002). An efficient method is NLPCA (Nonlinear Principal Component Analysis) (Kramer, 1991). This approach takes advantage of the capacity to treat nonlinearities from the artificial neural networks (ANN). Nevertheless, due to internal saturation problems of the ANN (Malthouse, 1998; Hsieh, 2001), the application of the NLPCA method is restricted to the data analysis with limited number of variables involved (limited dimensional size). The authors have been working for the extension of the NLPCA technique to allow treatment of higher dimension