A new framework intended for representing and segmenting multidimensional datasets resulting in low spatial complexity\nrequirements and with appropriate access to their contained information is described. Two steps are going to be taken in account.\nThe first step is to specify (n ? 1)D hypervoxelizations, n ? 2, as Orthogonal Polytopes whose nth dimension corresponds to color\nintensity. Then, the nD representation is concisely expressed via the Extreme Vertices Model in the n-Dimensional Space (nDEVM).\nSome examples are presented, which, under our methodology, have storing requirements minor than those demanded by\ntheir original hypervoxelizations. In the second step, 1-Dimensional Kohonen Networks (1D-KNs) are applied in order to segment\ndatasets taking in account their geometrical and topological properties providing a non-supervised way to compact even more the\nproposed n-Dimensional representations.The application of our framework shares compression ratios, for our set of study cases,\nin the range 5.6496 to 32.4311. Summarizing, the contribution combines the power of the nD-EVM and 1D-KNs by producing very\nconcise datasets� representations. We argue that the new representations also provide appropriate segmentations by introducing\nsome error functions such that our 1D-KNs classifications are compared against classifications based only in color intensities.\nAlong the work, main properties and algorithms behind the nD-EVM are introduced for the purpose of interrogating the final\nrepresentations in such a way that it efficiently obtains useful geometrical and topological information.
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