Multi-scale representation; Keypoint; Fuzzy partition; Fuzzy transform

Our first contribution to this topic is as follows: we show that in the case of large datasets, dimensionality reduction should be divided into several subtasks, determined by the choice of keypoints as centers corresponding to clusters. For specific time series datasets, we connect keypoints to centers that maximize the values of the non-local Laplacians. Moreover, we propose to use the scale space approach and consider a scale-dependent sequence of non-local Laplacians. As a second contribution, we use non-traditional kernels obtained from the theory of F-transforms [11]. This allows to simplify the scaling and selection of keypoints, reduce their number and increase reliability. We also propose a new keypoint descriptor and test it against high volatility financial time series.