title: Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
abstract: In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures.
authors.affiliation: Department of Human Intelligence Systems, Kyushu Institute of Technology, Japan.
authors.forename: Tohru
authors.initials: T
authors.lastname: Iwasaki
authors.affiliation: Department of Human Intelligence Systems, Kyushu Institute of Technology, Japan. Electronic address: furukawa@brain.kyutech.ac.jp.
authors.forename: Tetsuo
authors.initials: T
authors.lastname: Furukawa
mesh_terms: D000465:Algorithms; D021621:Imaging, Three-Dimensional / Q000379:methods; D016571:Neural Networks, Computer
keywords: Generative topographic map; Relational data; Self-organizing map; Tensor decomposition