Granular Representation of Temporal Signals Using Differential Quadratures
This article presents the general idea of granular representation of temporal data, particularly signal sampled with constant frequency. The core of presented method is based on using fuzzy numbers as information granules. Three types of fuzzy numbers are considered, as interval numbers, triangular numbers and Gaussian numbers. The input space contains values of first few derivatives of underlying signal, which are computed using certain numerical differentiation algorithms, including polynomial interpolation as well as polynomial approximation. Data granules are constructed using the optimization method according to objective function based on two criteria: high description ability and compactness of fuzzy numbers.
The data granules are subject to the clustering process, namely fuzzy c-means. The centroids of created clusters form a granular vocabulary. Quality of description is quantitatively assessed by reconstruction criterion. Results of numerical experiments are presented, which incorporate exemplary biomedical signal, namely electrocardiographic signal.
KeywordsFuzzy Number Reconstruction Error Temporal Signal Triangular Fuzzy Number Information Granule
Unable to display preview. Download preview PDF.
- 2.Braci, M., Diop, S.: On numerical differentiation algorithms for nonlinear estimation. In: Proc. 42nd IEEE Conf. on Decision and Control, Maui, Hawaii, USA, pp. 2896–2901 (2003)Google Scholar
- 7.Mark, R., Moody, G.: MIT-BIH Arrhythmia Database Directory. MIT, Cambridge (1988)Google Scholar
- 8.Moody, G.B., Mark, R.G.: The MIT-BIH arrhythmia database on CD-ROM and software for use with it. In: Proc. Conf. Computers in Cardiology, San Diego, CA, pp. 185–188 (1990)Google Scholar
- 9.Ortolani, M., Hofer, H., et al.: Fuzzy Information Granules in Time Series Data. In: Proc. IEEE Int. Conf. on Fuzzy Systems, pp. 695–699 (2002)Google Scholar