@InProceedings{FilisbinoGiraThom:2016:TeFiMu,
               author = "Filisbino, Tiene Andr{\'e} and Giraldi, Gilson Antonio and 
                         Thomaz, Carlos Eduardo",
          affiliation = "{National Laboratory for Scientific Computing} and {National 
                         Laboratory for Scientific Computing} and Department of Electrical 
                         Engineering, FEI",
                title = "Tensor Fields for Multilinear Image Representation and Statistical 
                         Learning Models Applications",
            booktitle = "Proceedings...",
                 year = "2016",
               editor = "Aliaga, Daniel G. and Davis, Larry S. and Farias, Ricardo C. and 
                         Fernandes, Leandro A. F. and Gibson, Stuart J. and Giraldi, Gilson 
                         A. and Gois, Jo{\~a}o Paulo and Maciel, Anderson and Menotti, 
                         David and Miranda, Paulo A. V. and Musse, Soraia and Namikawa, 
                         Laercio and Pamplona, Mauricio and Papa, Jo{\~a}o Paulo and 
                         Santos, Jefersson dos and Schwartz, William Robson and Thomaz, 
                         Carlos E.",
         organization = "Conference on Graphics, Patterns and Images, 29. (SIBGRAPI)",
            publisher = "Sociedade Brasileira de Computa{\c{c}}{\~a}o",
              address = "Porto Alegre",
             keywords = "Tensor Fields, Dimensionality Reduction, Tensor Subspace Learning, 
                         Ranking Tensor Components, Reconstruction, MPCA, Face Image 
                         Analysis.",
             abstract = "Nowadays, higher order tensors have been applied to model 
                         multidimensional image data for subsequent tensor decomposition, 
                         dimensionality reduction and classification tasks. In this paper, 
                         we survey recent results with the goal of highlighting the power 
                         of tensor methods as a general technique for data representation, 
                         their advantage if compared with vector counterparts and some 
                         research challenges. Hence, we firstly review the geometric theory 
                         behind tensor fields and their algebraic representation. 
                         Afterwards, subspace learning, dimensionality reduction, 
                         discriminant analysis and reconstruction problems are considered 
                         following the traditional viewpoint for tensor fields in image 
                         processing, based on generalized matrices. We show several 
                         experimental results to point out the effectiveness of multilinear 
                         algorithms for dimensionality reduction combined with discriminant 
                         techniques for selecting tensor components for face image 
                         analysis, considering gender classification as well as 
                         reconstruction problems. Then, we return to the geometric approach 
                         for tensors and discuss opened issues in this area related to 
                         manifold learning and tensor fields, incorporation of prior 
                         information and high performance computational requirements. 
                         Finally, we offer conclusions and final remarks.",
  conference-location = "S{\~a}o Jos{\'e} dos Campos, SP, Brazil",
      conference-year = "4-7 Oct. 2016",
             language = "en",
                  ibi = "8JMKD3MGPAW/3M9LKLL",
                  url = "http://urlib.net/ibi/8JMKD3MGPAW/3M9LKLL",
           targetfile = "Survey-Paper-Tutorial-Sib-19-07-2016.pdf",
        urlaccessdate = "2024, May 03"
}