F transforms; Fuzzy partition; Keypoints; Multi-scales; Multiscale representations; Non-traditional; Scale theory; Simplified algorithms; Time-series analysis; Times series

We are focused on a new method of time series analysis that is based on the extraction of representative keypoints. We use the multi-scale theory based on the use of non-traditional kernels derived from the theory of F-transforms. The sequence of kernels corresponds to what is called as 2-adic fuzzy partitions. This leads to simplified algorithms and comparable efficiency in the selection of keypoints. We reduce the number of representative keypoints and enhance robustness of their selection. We also propose a new keypoint descriptor and test it on matching financial time series with high volatility.