Invariant Clustering Using Scattering Matrices.
NAVAL RESEARCH LAB WASHINGTON DC
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One of the most difficult problems in clustering analysis is the choice of an appropriate distance metric. This problem arises because in many instances an object is described by n measurements involving different units for example, a radar signal may be described by its frequency in gigahertz, its interpulse period in milliseconds, and its pulsewidth in microseconds. In this report I circumvent the problems by considering clustering algorithms which are invariant to scaling of the axes and hence to the choice of units. I compare quality of the clustering produced by the various algorithms by examining several test cases. No single algorithm yield the correct solution in all of the cases, but a possible hybrid approach is to cluster the points using the product of the determinants of the scattering matrices and switch to the sum of the determinants if the product algorithm yields only degenerate solutions. Author
- Theoretical Mathematics