A.M. Nosovskiy - Dr. Sc. (Biol.), Leading Scientific. Employee, Institute of Medical-Biological Problems, Russian Academy of Sciences, Moscow E-mail: nam@imbp.ru Yu.Yu. Osipov - Ph. D. (Med.) (1943-2015) S.V. Pozdnyakov - Ph. D. (Med.), Head of laboratory, Institute of Medical-Biological Problems, Russian Academy of Sciences, Moscow E-mail: pozdnyakov-sv@yandex.ru E.V. Kaminskaya - Senior Research Scientist, Institute of Medical-Biological Problems, Russian Academy of Sciences, Moscow E-mail: evk@imbp.ru

SSA (Singular spectrum analysis or singular spectrum analysis) is a method of time series analysis, based on the transformation of one-dimensional time series into a multidimensional series with the subsequent application to the resulting multivariate time series of principal component. A method of converting a one-dimensional row in the MDX is a «convolution» in the time series matrix containing fragments of the time series, obtained with some shift. General view of the shear procedure is like a \"caterpillar\", so the method is often called «the Caterpillar»: the length of the fragment is called the length of «caterpillar», and the shift of one fragment relative to another step «tracks». Generally used step 1. Singular spectrum analysis (SSA) combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. The origins of SSA include principal component method and the classical theorem of karunen-Loev for spectral decomposition next time and digital images. In practical applications, various modifications of the SSA. Can be divided into two main areas, it is SSA as a universal method [2] for solving problems of General purpose, such as the selection of a trend detection of periodicities, adjustment for seasonality, smoothing, noise reduction, and spectral SSA for analysis of stationary time series [3,4], which has a great number of applications in those areas where they are observed, in particular, outside of the ship activities. SSA can be used without first setting the model for the analysis of arbitrary, including non-stationary series. The main purpose of SSA is to decompose the series into sum of interpretable components such as trend, periodic components and noise. Thus knowledge of the parametric form of these components is not required. For the first time revealed the phenomenon of periodic change of the sign of the correlation between heart rate and level of energy expenditure of astronauts during EVA. This phenomenon requires further study and explanation. It is possible that these data indicate a more complex non-linear dependencies between these physiological parameters in extreme conditions, in particular when performing HCC than previously thought.

 

1. Eisner J.V., Tsonis A.A. Singular Spectrum Analysis. A New Tool in Time Series Analysis. New York and London: Plenum Press. 1996. 164 p.
2. Golyandina N., Nekrutkin V., Zhigljavsky A. Analysis of Time Series Structure: SSA and Related Techniques. London: Chapman & Hall/CRC. 2001. 305 p.
3. A. s. № 15985. Primenenie metoda singuljarnogo spektralnogo analiza v biologii i medicine // N.V. Savina, L.KH. Bragin, A.M. Goncharova, A.M. Nosovskijj.
4. Nosovskijj A.M., Savina N.V., Osipov JU.JU, Filipenkov S.N. Primenenie metoda singuljarnogo spektralnogo analiza vremennykh rjadov s propuskami dlja ocenki adaptacionnykh vozmozhnostejj organizma pri vnekorabelnojj dejatelnosti kosmonavtov // Biomedicinskaja radioehlektronika. 2009. № 3. S. 9-13.