Generalized Nets Model of Dimensionality Reduction in Time Series

The paper considers the generalized nets as an extension of Petri nets applied for modeling of the methodology called Symbolic Essential Attributes Approximation (Krawczak and Szkatula, 2014). SEAA was developed to reduce the dimensionality of multidimensional time series by generating a new nominal representation of the original data series. In general the approach is based on the concept of data series envelopes and essential attributes obtained by a multilayer neural network. The symbolic data series representation - which just describes the compressed representation of the original data series - is obtained via discretization of the real-valued essential attributes. In this paper the generalized nets were used to model the logistic of processes involved in SEAA methodology. First the basic of the theory of generalized nets is introduced, next SEAA methodology processes are modeled via the generalized nets the new model of SEAA.

[1]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[2]  Jessica Lin,et al.  Finding Motifs in Time Series , 2002, KDD 2002.

[3]  Maciej Krawczak,et al.  Nominal time series representation for the clustering problem , 2012, 2012 6th IEEE International Conference Intelligent Systems.

[4]  Cyrus Shahabi,et al.  TSA-tree: a wavelet-based approach to improve the efficiency of multi-level surprise and trend queries on time-series data , 2000, Proceedings. 12th International Conference on Scientific and Statistica Database Management.

[5]  Eamonn J. Keogh,et al.  Derivative Dynamic Time Warping , 2001, SDM.

[6]  Maciej Krawczak,et al.  On Perturbation Measure of Clusters: Application , 2013, ICAISC.

[7]  Diego Vidaurre,et al.  Dimensionality reduction for time series data , 2014 .

[8]  Maciej Krawczak,et al.  An approach to dimensionality reduction in time series , 2014, Inf. Sci..

[9]  Xindong Wu,et al.  10 Challenging Problems in Data Mining Research , 2006, Int. J. Inf. Technol. Decis. Mak..

[10]  Tak-Chung Fu,et al.  A review on time series data mining , 2011, Eng. Appl. Artif. Intell..

[11]  Krassimir T. Atanassov,et al.  Generalized nets , 1991 .

[12]  Bin Wang.  A New Clustering Algorithm On Nominal Data Sets , 2010 .

[13]  Jonathan Goldstein,et al.  When Is ''Nearest Neighbor'' Meaningful? , 1999, ICDT.

[14]  Erkki Oja,et al.  Principal components, minor components, and linear neural networks , 1992, Neural Networks.

[15]  Edward Y. Chang,et al.  Distance-function design and fusion for sequence data , 2004, CIKM '04.

[16]  Maciej Krawczak,et al.  A Clustering Algorithm Based on Distinguishability for Nominal Attributes , 2012, ICAISC.

[17]  A. Meystel,et al.  Intelligent Systems , 2001 .

[18]  M. Krawczak,et al.  A hybrid approach to dimension reduction in classification , 2011 .

[19]  Eamonn J. Keogh,et al.  Locally adaptive dimensionality reduction for indexing large time series databases , 2001, SIGMOD '01.

[20]  Yannis Manolopoulos,et al.  Feature-based classification of time-series data , 2001 .

[21]  Maciej Krawczak,et al.  Time series envelopes for classification , 2010, 2010 5th IEEE International Conference Intelligent Systems.

[22]  Radeva,et al.  Review and bibliography on generalized nets theory and applications , 2002 .

[23]  Maciej Krawczak.  Multilayer Neural Networks: A Generalized Net Perspective , 2013 .

[24]  Maciej Krawczak,et al.  Multilayer Neural Networks: A Generalized Net Perspective , 2013 .

[25]  Maciej Krawczak,et al.  A new measure of groups perturbation , 2013, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS).