Abstract
We will show that the hierarchical linear subspace method is a tree that divides the distances between the subspaces. By doing so, the data is divided into disjoint entities. The asymptotic upper bound estimation of the maximum applicable number of subspaces is logarithmically constrained by the number of represented elements and their dimension. The search in such a tree starts at the subspace with the lowest dimension. In this subspace, the set of all possible similar images is determined. In the next subspace, additional metric information corresponding to a higher dimension is used to reduce this set. The distances between the subspaces correspond to the values represented by the difference between the mean distance of all the points in one space and a corresponding mean distance of the objects in a subspace. The theoretical estimation of temporal complexity of the algorithmic is logarithmic. The costs are equivalent to the search costs in an tree plus the additional costs of the dimension of the data space.
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Acknowledgements
The author would like to thank for the permission to use the data-set for experimental tests purposes to TM Deserno, Dept. of Medical Informatics, RWTH Aachen, Germany. The author would like to gratefully acknowledge two anonymous reviewers for their valuable suggestions. The author would also like to thank Patricia Lima, for the help during the manuscript preparation.
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Wichert, A., Teixeira, P., Santos, P. et al. Subspace tree: high dimensional multimedia indexing with logarithmic temporal complexity. J Intell Inf Syst 35, 495–516 (2010). https://doi.org/10.1007/s10844-009-0104-9
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DOI: https://doi.org/10.1007/s10844-009-0104-9