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2011

A Signal Processing Approach to Fourier Analysis of Ranking Data: The Importance of Phase

11 years 4 months ago
A Signal Processing Approach to Fourier Analysis of Ranking Data: The Importance of Phase
—Ranking data is a type of data obtained in some elections, in customer surveys, as well as from web search results. Such data may be considered as a type of signal defined on the group of permutations of n objects, denoted Sn. There exists a Fourier transform for Sn obtained from group representation theory, which is well known in the mathematics literature. However, previous work has not approached the transform from a signal processing perspective: in particular, there is no discussion of what constitutes “magnitude” and “phase”, nor any analysis of what phase information might tell us beyond a wellknown connection to group translation. This paper explores the properties of the phase spectrum of ranking data; in particular, a novel contribution is the formulation of the bispectrum for ranking data, which may be used for studying phase linearity. Analysis of two well-known ranking data sets shows that they are surprisingly well fit by linear phase approximations.
Ramakrishna Kakarala
Added 29 May 2011
Updated 29 May 2011
Type Journal
Year 2011
Where TSP
Authors Ramakrishna Kakarala
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