An Eigenspace Approach to Isotypic Projections for Data on Binary Trees
Department of Mathematics
Harvey Mudd College
Advisor: Michael Orrison, Department of Mathematics, Harvey Mudd College
Second Reader: Shahriar Shahriari, Department of Mathematics, Pomona College
The classical Fourier transform is, in essence, a way to take data and
extract components (in the form of complex exponentials) which are
invariant under cyclic shifts. We consider a case in which the
components must instead be invariant under automorphisms of a binary
tree. We present a technique by which a slightly relaxed form of the
generalized Fourier transform in this case can eventually be computed
using only simple tools from linear algebra, which has possible
advantages in computational efficiency.
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