Полярные геомагнитные возмущения и связанные с ними явления : материалы международного симпозиума «Полярные геомагнитные явления», 25-31 мая 1986 г., Суздаль / Междунар. геодез. и геофиз. союз, междунар. ассоциация геомагнетизма и аэрономии, АН СССР, КНЦ, ПГИ. – Апатиты : [б. и.], 1989.

I.V.Kovalevsky, Yu.I.Morozov, M.K.Fedoseeva CLUSTER CLASSIFICA T ION M ETHODS AS ADEQUATE INSTRUMENT O F INVESTIGATION OF SYSTEM PHYSICAL P H E NOME NA CONNECTED W I T H G EOMAGNETOSPHERIC STORMS AND SUBSTORMS 1. I n t r o d u c t i o n . Geomagnetospherlo atorma (GMS) la a complicated phyai- cal p h enomenon requ iring corresponding adequate Investigation methods for ita atudy. A store of such methods is a method of pattern recognition (PR) - a n e w interdisciplinary direction, r e v elation of existing law in the vaet amount of various information obtained during complicated processes and ph e n omena investigations as one of its m a i n go a l s /1/. One of the powerful PR means is the "cluster analysis". The m a i n no t i o n of this me t h o d is fu z z y no t i o n of "similarity", operationalized on the base of introduction of any standard of distance b etween the Investigated symptoms in the multidimensional spaoe. Here the similarity of the symptoms is m a n i f es t e d by the fact that some of t h e m compose groups-olusters. 2. Sequentlonal cluster analysis uti l i z a t i o n i n geomagnetoapherlc atorma i nv e s t i g a t i o n . To increase the reliability of the c luster analysis c o nclusi ons we propose to use sequential analysis /2/ as a powerful methodical i n s t r ument based on the full and orthogonal systems of basis funotions of fragmen- tarlly-constant character - W a l s h function (see Fig.1), H a a r fu n c t i o n etc. Th e n together w i t h n a t u r a l l y a risi ng definition of the distance b e t we e n the processes <!„„ =-i-(1 - (where f (t) , e(t) are expensed into t Б 2 n n n Fourier series by W a l s h function f E F v (t) , g-( t ).- E G ч> (t) one can iv i t П introduce "rough" distance d . ^ = -g-( 1 - where only a portion of the highest to the modulus F o u r i er-Walsh coefficients ( Fn , & n ) is taken into account i n the sum. The ma i n peculiarity of this a p proach is that rough r epresentation of ?(t) , q ( t ) processes (sea F i g , 2) preserves the most i m portant features of the process - the character and the value of the d iscont inuities, etc. B y me a n s of this c l u s t e rization data us i n g ro u g h distance ma y ba obtained the most stable essential connections controlling the data obtai n e d on the base of precise distance. The most convenient form of r esults p r e sentation i n the clusterization is a den d r o g r a m (Fig. 3, 4), i.e. graphical repreaentation of a dendritei co m p l e x n o n - o riented graphs without closed cycles whose ribs are the m i n i m u m distance b e t w e e n the investigated processes composing its apices. N o t i o n "minimum" is u n d erstood fr o m the point of view of "nearest neighbour" finding. All the ribs have be e n put in order by their gradual decrease (S1 - m a x i m u m distance of all taken into account in the den drite, S2 is the next I n value distance a n d so on). Using this approach there is also inf o r m a t i o n about clusteri s a t i o n process iteelf - dendrite decay into a series of rel a t i v e l y independent groups, wi t h i n them subgroups denoted b y brackets a n d underlinings demonstrate the property of stability (in "rough" picture). The above a na lysis me t h o d ha s been us e d b y us in GMS i nvestigation as a complicated time inhomogeneoua complex of plasma processes takijng place in the systemi p e rturbed solar w i n d (interplanetary mediumj-geomagnetosphere- i onо cipherо (conducting geomagnetoaphere base). To illustrate the m a i n 83