Uncovering and Displaying the Coherent Groups of Rank Data by Exploratory Riffle Shuffling

Let n respondents rank order d items, and suppose that . Our main task is to uncover and display the structure of the observed rank data by an exploratory riffle shuffling procedure which sequentially decomposes the n voters into a finite number of coherent groups plus a noisy group: where the noisy group represents the outlier voters and each coherent group is composed of a finite number of coherent clusters. We consider exploratory riffle shuffling of a set of items to be equivalent to optimal two blocks seriation of the items with crossing of some scores between the two blocks. A riffle shuffled coherent cluster of voters within its coherent group is essentially characterized by the following facts: 1) Voters have identical first TCA factor score, where TCA designates taxicab correspondence analysis, an L1 variant of correspondence analysis;2) Any preference is easily interpreted as riffle shuffling of its items;3) The nature of different riffle shuffling of items can be seen in the structure of the contingency table of the first-order marginals constructed from the Borda scorings of the voters;4) The first TCA factor scores of the items of a coherent cluster are interpreted as Borda scale of the items. We also introduce a crossing index, which measures the extent of crossing of scores of voters between the two blocks seriation of the items. The novel approach is explained on the benchmarking SUSHI data set, where we show that this data set has a very simple structure, which can also be communicated in a tabular form.

Improved modulation format identification based on Stokes parameters using combination of fuzzy c-means and hierarchical clustering in coherent optical communication system

In this Letter, we develop the Stokes space-based method for modulation format identification by combing power spectral density and a cluster analysis to identify quadrature amplitude modulation（QAM） and phase-shift keying（PSK） signals. Fuzzy c-means and hierarchical clustering algorithms are used for the cluster analysis.Simulations are conducted for binary PSK, quadrature PSK, 8PSK, 16-QAM, and 32-QAM signals. The results demonstrate that the proposed technique can effectively classify all these modulation formats, and that the method is superior in lowering the threshold of the optical signal-to-noise ratio. Meanwhile, the proposed method is insensitive to phase offset and laser phase noise.