Informatics and Applications
2020, Volume 14, Issue 1, pp 31-39
ALIGNMENT OF ORDERED SET CARTESIAN PRODUCT
- A. V. Goncharov
- V. V. Strijov
Abstract
The work is devoted to the study of metric methods for analyzing objects with complex structure. It proposes to generalize the dynamic time warping method of two time series for the case of objects defined on two or more time axes. Such objects are matrices in the discrete representation. The DTW (Dynamic Time Warping) method of time series is generalized as a method of matrices dynamic alignment. The paper proposes a distance function resistant to monotonic nonlinear deformations of the Cartesian product of two time scales. The alignment path between objects is defined. An object is called a matrix in which the rows and columns correspond to the axes of time. The properties of the proposed distance function are investigated. To illustrate the method, the problems of metric classification of objects are solved on model data and data from the MNIST dataset.
[+] References (15)
- Hill, N.J., T. N. Lal, M. Schroder, T. Hinterberger, B. Wil-helm, F. Nijboer, U. Mochty, G. Widman, C. Elger,
B. Scholkopf, A. Kubler, and N. Birbaumer. 2006. Classifying EEG and ECoG signals without subject training for fast BCI implementation: Comparison of nonparalyzed and completely paralyzed subjects. IEEE T. New. Sys. Reh. 14(2):183-186.
- Sakoe, H., and S. Chiba. 1971. Adynamic programming approach to continuous speech recognition. 7th Congress (International) on Acoustics Proceedings. 3:65-69.
- Aghabozorgi, S., S. S.Ali, and T. Y. Wah. 2015. Time-series clustering - a decade review. Inform. Syst. 53:16-38.
- Warrenliao, T. 2005. Clustering of time series data - a survey. Pattern Recogn. 38(11):1857-1874.
- Hautamaki, V., P. Nykanen, and P. Franti. 2008. Time- series clustering by approximate prototypes. 19th Conference (International) on Pattern Recognition Proceedings. D:1-4.
- Faloutsos, C., M. Ranganathan, and Y. Manolopoulos. 1994. Fast subsequence matching in time-series databases. SIGMODRec. 23(2):419-429.
- Basalto, N., R. Bellotti, F D. Carlo, P. Facchi, and S. Pascazio. 2007. Hausdorff clustering of financial time series. PhysicaA 379(2):635-644.
- Gorelick, L., M. Blank, E. Shechtman, M. Irani, and R. Basri. 2007. Actions as space-time shapes. IEEE T. Pattern Anal. 29(12):2247-2253.
- Smyth, P. 1997. Clustering sequences with hidden Markov models. Adv. Neural In. 9:648-654.
- Banerjee, A., and J. Ghosh. 2001. Clickstream clustering using weighted longest common subsequences. Workshop on Web Mining, SIAM Conference on Data Mining Proceedings. 33-40.
- Aach, J., and G. M. Church. 2001. Aligning gene expression time series with time warping algorithms. Bioinformatics 17(6):495-508.
- Yi, B.K., and C. Faloutsos. 2000. Fast time sequence indexing for arbitrary Lp norms. 26th Conference (International) on Very Large Data Bases Proceedings. 385-394.
- Goncharov, A.V., and V. V. Strijov. 2018. Analysis of dis-similarity set between time series. Computational Mathe-matics Modeling 29(3):359-366.
- Alon, J., V. Athitsos, and S. Sclaroff. 2005. Online and of-fline character recognition using alignment to prototypes. 8th Conference (International) on Document Analysis and Recognition. 2:839-843.
- Goncharov, A. V. Alignment of Ordered Set Cartesian Product mDTW. Software implementation of the algorithm. Available at: https://github.com/Intelligent- Systems-Phystech/PhDThesis/tree/master/Goncharov 2019/MatrixDTW/code (accessed December 27, 2019).
[+] About this article
Title
ALIGNMENT OF ORDERED SET CARTESIAN PRODUCT
Journal
Informatics and Applications
2020, Volume 14, Issue 1, pp 31-39
Cover Date
2020-03-30
DOI
10.14357/19922264200105
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
distance function; dynamic alignment; distance between matrices; nonlinear time warping; space-time series
Authors
A. V. Goncharov  and V. V. Strijov , 
Author Affiliations
Moscow Institute of Physics and Technology, 9 Institutskiy Per., Dolgoprudny, Moscow Region 141700, Russian Federation
A. A. Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 40 Vavilov Str., Moscow 119333, Russian Federation
|