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The natural pseudo-distance of spaces endowed with filtering
functions is precious for shape classification and retrieval; its optimal estimate
coming from persistence diagrams is the bottleneck distance, which
unfortunately suffers from combinatorial explosion. A possible algebraic
representation of persistence diagrams is offered by complex polynomials;
since far polynomials represent far persistence diagrams, a fast comparison
of the coefficient vectors can reduce the size of the database to be
classified by the bottleneck distance. This article explores experimentally
three transformations from diagrams to polynomials and three distances
between the complex vectors of coefficients
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