15 Internacional Workshop on Operation Research IWOR 2023

Numerical strategy for the solution of the nonlinear system of a Discrete Shapelet Transform II for pattern detection

No programado

20m

Facultad de Matemática y Computación

Ponente

Damian Valdés Santiago (Universidad de La Habana)

Descripción

This research presents a comprehensive numerical study to show the impact of the numerical method for solving the non--linear equations system to find the high--pass filter of a Discrete Shapelet Transform (DST-II). For that, we compared $12$ iterative algorithms to obtain the filter from the null vector, and then establishing a combination of numerical methods to improved the solution precision. The continuation method converged for $37,86\mathrm{\%}$ of the patterns ($103$, in total) starting from null vector, while its combination with Newton's method decrease very significantly the number of function evaluations ($t(61)=12.84,p<0.001,r=0.85$). The convergence was reached for pattern lengths up to $26$ samples. Compared to other $13$ wavelet filters, shapelets achieved sensitivity $=0.98$, specificity $=0.85$, positive predictive value $=0.86$, negative predictive value $=0.98$ and $AUC=75.83\mathrm{\%}$. Thus, pattern detection was significantly disturbed by the numerical method for finding the high--pass filter of a DST-II, and we propose the use of the Newton method using the pre-iteration continuation algorithm in order to solve the non-lineal equation system.