Novel Representation of Multidimensional Datasets: The Framework nD-EVM/Kohonen

In this paper we are going to describe the steps that conform a novel approach for representation of multidimensional datasets through the proposed Framework nD-EVM/Kohonen. In this sense two phases are going to be taken in account: 1) the application of 1-Dimensional Kohonen Self-Organizing Maps (1D-KSOMs) in order to achieve (n-1)D hypervoxelizations' segmentations, n ≥ 2, taking in account their geometrical and topological properties to characterize the information contained in the datasets. 2) The segmented multidimensional datasets are specified as Orthogonal Polytopes whose n-th Dimension is associated to a 1D-KSOM classification. Subsequently, the nD representation is concisely expressed via the Extreme Vertices Model in the n-Dimensional Space (nD-EVM). There is presented a comparative analysis based on the use of False Color Maps in order to understand they way our considered 1D-KSOMs distribute appropriately their weights vectors along the classification space, even better than classifications based exclusively on color intensity. Additionally, we present some arguments to sustain that a 1D-KSOM is an adequate option in terms of temporal complexity and, on the other hand, that our representation is concise in terms of spatial complexity because of the nD-EVM properties. Index Terms Representation and Manipulation of Hypervoxelizations, Polytopes Representation Schemes, Geometrical and Topological Interrogations, 1-Dimensional Kohonen Self-Organizing Maps, False Color Maps