Research And Design Of Generalized Correlation Coefficient Calculation Method Based On Systolic Array

Correlation analysis originated in the statistical period,and it is still a hot research direction until now.It usually uses correlation coefficient as an indicator to measure the relationship between two random variables or two signals.Among the many correlation coefficients,the Pearson product distance correlation coefficient,Spearman correlation coefficient,and Kendall correlation coefficient are the most well-researched and widely used,and the scenarios used are also different.Theoretical research shows that the Pearson product distance correlation coefficient is abnormally sensitive to data with nonlinear transformation or impulsive noise,so data with nonlinear transformation or impulsive noise is not suitable for using the Pearson product distance correlation coefficient.The Del coefficient is very insensitive to nonlinear transformation or impulse noise data and has good robustness,so when the data has nonlinear transformation or impulse noise,the latter two correlation coefficients can be considered.The researchers found that these types of correlation coefficients are intrinsically related.A generalized correlation coefficient was proposed to summarize the three correlation coefficients.Different correlation coefficients can be derived by entering different data.With the advent of the era of big data,more and more data needs to be processed,which brings great challenges to the calculation of correlation coefficients.The systolic array architecture is widely used in various special computing processors for parallel computing of big data.Affected by the above aspects,this paper proposes a circuit that realizes the unified calculation of the generalized correlation coefficient based on the pulsating array.And did the following work.First,by comparing the calculation of the systolic array architecture with the calculation of the CPU and GPU,the FPGA was finally selected as the implementation tool of the systolic array circuit,and the example of matrix multiplication was analyzed in detail to illustrate the use of the systolic array with parallelism and pipeline linear Framework to implement the importance of the framework.Second,according to the generalized correlation coefficient expression,the definition expressions of the three correlation coefficients are equivalently transformed into the same structure.It is found that the numerator and denominator are very similar in the process of operation realization and the operation is independent,and can be implemented in parallel.Therefore,a unified realization circuit for partial calculation of generalized correlation coefficients is proposed,which can flexibly switch to solve different correlation coefficients.Third,the hardware programming language is used to build a circuit based on the generalized correlation coefficient operation of the pulsating array on the FPGA-related software platform,and the simulation experiments are conducted in three correlation coefficient modes.In the experiment,two main conclusions are drawn: First,the special calculation circuit for correlation coefficient based on pulsating array proposed in this paper has the characteristics of flexibility,parallelism and pipeline linearity.Second,it can quickly calculate the correlation of local data in two sets of random data.