EXPLORATORY STUDY ON ESTIMATION, DETECTION AND ROBUSTNESS OF A DISCRETE SHAPELET TRANSFORM II

Abstract

The Discrete Shapelet Transform II is designed to detect patterns, locating them in time and frequency. This transform solves a system of nonlinear equations to obtain the high–pass filter of the pattern–adapted wavelet (shapelet). This paper presents an exploratory study case to inquire about the impact of the numerical method for estimating shapelets, considering numerical indicators and the detection of two artificial patterns. Powell’s method with Anderson pre–iteration get orthogonal, perfect reconstruction, finite impulse response, near–linear phase and compact support filters. For pattern detection, we take the detail coefficient with the highest value of the normalized measure S, instead of S = 1 used in the original publications. Compared to other wavelet filters, higher values of S were obtained where the pattern was inserted. Accurate detection of repeated patterns and robust detection when modifying the amplitudes were obtained. Modest noise robustness of detection was verified. The results showed the need for further study to evaluate the impact of the numerical method and the choice of the initial guess to estimate the shapelet using a larger number of numerical methods, patterns and signals. As a consequence of the analysis and discussion, we suggest new research questions about this transform to be answer in further research.