Ponente
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 $37,86\%$ 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 $AUC = 75.83\%$. 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.
