Systematic synthesis of parallel architectures for the computation of higher order cumulants

Selected Methods for non-Gaussian Data Analysis

“…As discussed further in Chapter 4 and Section 5.1 such Pearson's correlation carry a whole information about the auto-correlation given a Gaussian distribution of ∆X. Otherwise, complementary to the multi-fractal approach, we may use higher order cumulant's approach, as discussed in [95,40], see also Section 5.4. Exemplary tri-variate auto-correlation would be…”

“…In this chapter, we will concentrate on multivariate higher order cumulants, applicable to analyse non-Gaussian distributed multivariate data. For their practical application in multivariate non-Gaussian data analysis refer to signals analysis, for example in signal filtering [207,208], finding the direction of received signals [17,18,19,20] and signal autocorrelation analysis [95]. Furthermore, those cumulants are used in hyper-spectral image analysis [47], financial data analysis [209,210] and neuroimage analysis [211,212].…”

“…If our series is represented by Z (k) that is not distributed according to multivariate Gaussian, we may want to consider higher order cumulants approach in place of standard auto-correlation function, see [40,95].…”

“…To show a significance of higher order cumulants in auto-correlation analysis in the computer science refer to [95], where the parallel computer architecture for the calculation of 4'th order cumulant that measures auto-correlation is discussed. Further in [218] the novel algorithm for the FPGA (Field Programmable Gate Array) based architecture was used to calculate the third order auto-correlation cumulant.…”

Efficient Computation of Higher-Order Cumulant Tensors

“…Some potential applications of higher-order cumulants include signal filtering problems where the normality assumption is not required (see [25,32] and references therein). Another application is finding the direction of received signals [45,41,10,33] and signal auto-correlation analysis [37]. Higher-order cumulants are used in hyper-spectral image analysis [26], financial data analysis [2,29] and neuroimage analysis [9,5].…”