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A Signal Processing Approach to Fourier Analysis of Ranking Data: The Importance of Phase.
- Source :
-
IEEE Transactions on Signal Processing . 04/01/2011, Vol. 59 Issue 4, p1518-1527. 10p. - Publication Year :
- 2011
-
Abstract
- 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 S_n. There exists a Fourier transform for S_n 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 well-known 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1053587X
- Volume :
- 59
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Signal Processing
- Publication Type :
- Academic Journal
- Accession number :
- 59196120
- Full Text :
- https://doi.org/10.1109/TSP.2010.2104145